An Efficient Normalized Rank Based SVM for Room Level ...downloads.hindawi.com/journals/misy/2017/6268797.pdf · ResearchArticle An Efficient Normalized Rank Based SVM for Room Level

Research ArticleAn Efficient Normalized Rank Based SVM for Room LevelIndoor WiFi Localization with Diverse Devices

Yasmine Rezgui Ling Pei Xin Chen Fei Wen and Chen Han

Shanghai Key Laboratory of Navigation and Location-Based Services School of Electronic Information and Electrical EngineeringShanghai Jiao Tong University Shanghai 200240 China

Correspondence should be addressed to Ling Pei lingpeisjtueducn

Received 23 February 2017 Revised 3 May 2017 Accepted 11 May 2017 Published 9 July 2017

Academic Editor Elena-Simona Lohan

Copyright copy 2017 Yasmine Rezgui et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposes an efficient and effective WiFi fingerprinting-based indoor localization algorithm which uses the ReceivedSignal Strength Indicator (RSSI) ofWiFi signals In practical harsh indoor environments RSSI variation and hardware variance cansignificantly degrade the performance of fingerprinting-based localization methods To address the problem of hardware varianceand signal fluctuation inWiFi fingerprinting-based localizationwe propose a novel normalized rank based SupportVectorMachineclassifier (NR-SVM) Moving from RSSI value based analysis to the normalized rank transformation based analysis the principalfeatures are prioritized and the dimensionalities of signature vectors are taken into account The proposed method has been testedusing sixteen different devices in a shopping mall with 88 shops The experimental results demonstrate its robustness with no lessthan 9875 correct estimation in 9375 of the tested cases and 100 correct rate in 5625 of cases In the experiments the newmethod shows better performance over the KNN Naıve Bayes Random Forest and Neural Network algorithms Furthermorewe have compared the proposed approach with three popular calibration-free transformation based methods including differencemethod (DIFF) Signal Strength Difference (SSD) and theHyperbolic Location Fingerprinting (HLF) based SVMThe results showthat the NR-SVM outperforms these popular methods

1 Introduction

With the fast growing of ubiquitous computing the rapidadvances in mobile devices and the availability of wirelesscommunication wireless indoor positioning systems havebecome very popular in recent years Moreover leveragingpublic infrastructure has many advantages such as cost effi-ciency operational practicability and pervasive availability

Various short-range radio frequency technologies arebroadly researched to address positioning task in GNSSdenied area for instance Radio Frequency Identification(RFID) [1] Wireless Local Area Network (WLAN akaWiFi) [2 3] Bluetooth [4 5] ZigBee [6] Ultra Wide Band(UWB) [7] and cellular networks [8] All these means arehigh potential alternatives to indoor positioning Meanwhileindoor localization based on signals of opportunity (SoOP) isstill a challenging task since it requires stable interior wirelesssignals and adequate adaptation of the signals which are notoriginally designed for positioning purpose

Fingerprinting method [9] is one of the most popu-lar and promising indoor positioning mechanisms It isa technique based upon existing WiFi infrastructure andthus requires no dedicated infrastructure to be installed Itallows positioning by making use of signal characteristicsusing the signature matching technique Fingerprinting tech-nique is accomplished by two steps Firstly it stores WiFisignatures from different radio wave transmitters for eachreference position Then it compares the current signatureof a device with prerecorded signatures to find the closestmatch

Different techniques and solutions have been proposedproviding a varying mix of resolution accuracy stabilityand challenges Early examples of a positioning system thatuses fingerprinting are RADAR [2] and Horus [10] systemsHorus system is based on the probabilistic approach whichconsiders the statistical characteristics of the RSSIs andtheir distribution The Lognormal distribution [10] Weibullfunction [5] Gaussian distribution [11] and the double peak

HindawiMobile Information SystemsVolume 2017 Article ID 6268797 19 pageshttpsdoiorg10115520176268797

2 Mobile Information Systems

Gaussian distribution [12] were used to model the RSSIdistributionHowever RADAR systemwas the first introduc-ing the fingerprinting technique based on the deterministicapproach [13] using 119870-Nearest Neighbor method (KNN)[14] Nowadays the use of machine learning algorithms(ML) as in [15] has increasingly gained more popularityin indoor navigation domain because of their witnessedrobustness among them are Naıve Bayes classifier [16 17]Support Vector Machine (SVM) [17 18] Random Forest[18 19] and Neural Network [20 21] However their modelgeneralization to different userrsquos terminals has seldom beenconsidered

RSSI fluctuation and diversiform smartphones can signif-icantly degrade the positioning accuracy of WiFi localizationsystems as well as the patterns between training and testingsignature vectors The WiFi device used to train the radiomap during the calibration phase may especially differ fromthe ones used during the positioning phase WiFi modulesfrom different providers have varying receive signal gainswhich make the RSSI vary using different devices at the samelocation [22] This hardware variance problem is not onlylimited to differences in the WiFi chipsets used by trainingand tracking devices Besides it arises when the same WiFichipsets are connected to different antenna types andorpackaged in different encapsulation materials

To address this issue several studies have proposedmethods to improve the robustness of positioning systemsagainst mobile devices heterogeneity For example the useof an unsupervised learning [23] the Hyperbolic LocationFingerprinting (HLF) [24] the DIFF method [25] andthe Signal Strength Difference method (SSD) [26] are therepresentative ones In this paper a new method applying anintermediate step of absolute RSSI value transformation bymaking use of ML algorithms is proposed

The indoor navigation market addresses various appli-cations like Location Based Services (LBS) the guidance offirefighters and peoplemanagementMoreover it can benefitfrom the room level accuracy [27ndash29] to extract statisticalinformation which can be deployed to better market tocustomers find hangouts in airports and even most popularshop in shopping malls and so forth In this work we focuson a room localization which is the prediction of an occupiedroom in which the mobile device is currently in This taskis more practical to attain since it does not require the floormap of the desired indoor environment which is not alwaysavailable in practice

To achieve a high room level accuracy based WiFi fin-gerprinting technique we have investigated various databasedefinitions and the impact of signature clustering in ourprevious work [30] with respect to relevant requirementparameters In this paper we propose a normalized ranktransformation based SVM approach to solve the issue ofmobile terminal diversity during the positioning phase Weconsider and compare between the performances of theaforementioned ML algorithms and calibration-free trans-formations to validate our solution This approach aimsat generalizing the use of the preconstructed radio mapderived from one device to manifold devices and guaranteelocalization accuracy in the meantime

2 Normalized Rank Transformation

Aiming to mitigate the effect of signal fluctuation andhardware variance issue we introduce the intermediate nor-malized rank transformation step to freeze the variation ofthe RSSI This solution has been defined principally to dealwith SVM classifier Moving from RSSI value based analysisto the normalized rank transformation based analysis theprincipal features are prioritized and the dimensionalities ofsignature vectors are considered

21 Rank Transformation In the conventional classificationbased on SVMor any otherML algorithms for fingerprinting-based indoor localization the features are defined as thesignal strength received from all the visible access points(APs) to build the model However the received signalstrength is inherently time varying at a specific locationMoreover device diversity will impact both learning andpositioning phases

In order to find the perfect match between the userlocation and the predefined locations in the radio mapusing SVM classifier as well as attenuate the susceptibilityof decision boundaries to RSSI variation the enhancementof data learning to build a robust model is a key Theimprovement of the accuracy is related to the strong decisionboundaries between the different classes The input variablesare redefined and the absolute RSSI values are replaced first bytheir corresponding rank values Let 1198751119872 be the RSSI vectorof the119872 visible APs and 119878119894 the corresponding absolute RSSIvalue of the AP(119894) such that

1198751119872 = 1198781 1198782 119878119872 (1)

11987510158401119872 = 11987810158401 11987810158402 1198781015840119872 (2)

11987810158401 le 11987810158402 le sdot sdot sdot le 1198781015840119872 (3)

Ψ119894 = Ψ119894minus1 + 1 for 1198781015840119894minus1 = 1198781015840119894Ψ119894minus1 otherwise (4)

11987510158401119872 is the new defined RSSI vector by rearranging the APsThe rearrangement is based on (3) in which the throughputsof received signals are in ascending order Equation (4)explains how to decide the rank vector If RSSIs values aredistinct (1198781015840119894minus1 = 1198781015840119894 119894 indicates the position of the AP in the119872dimensional vector) successive numbers denoted by Ψ119894 willbe assigned Otherwise the same rank will be allocated Theinitial value is equal to one andΨ119872 does not have to be equalto the dimension of the initial RSSI vector By adopting thisprocedure the most reliable APs with high RSSI are taggedwith the high rank values

22 Normalized Rank Transformation The observed set ofAPs is not fixed over time at every calibration point andconsequently the dimension of the transformed rank vectors

Mobile Information Systems 3

Oine stage

Online stage

Collecting RSSI Radio map building Normalized ranktransformation

New deneddatabase

Classier trainingParameters adjustment

Trained model

CollectingRSSI

Dimensionalitycheck

Normalized ranktransformation

Classication using

machine learning

algorithms

Returnposition

Figure 1 Proposed system architecture

Hence the new formulated rank vector has to be adapted tothe varying assigned tags and needs to be normalized

NR = 120582Ψ1 120582Ψ2 120582Ψ119872 such that 120582 = 1Ψ119872 (5)

NR119894 isin [0 1] such that NR119894 = 120582Ψ119894 (6)

Equation (5) defines the normalized rank vector which isdenoted as NR and satisfies (6) where 120582 is the normalizationfactor corresponding to the inverse of the highest assignedrank Ψ119872 in the transformed rank vector This normalizationstep will result in keeping the prioritization of the mostreliable APs Furthermore it helps attenuating the effect ofthe noisy points as the hyperplanes are always dominated bythe high values

3 Proposed Method

In this section we give more details about the proposedapproach which is composed of two main stages the offlinestage and the online stage as illustrated in Figure 1

31 The Offline Stage This stage consists of 3 major stepsStep 1 data collection and association Step 2 normalizedrank transformation Step 3model building and parametersadjustment

Step 1 (data collection and association) Selection of thesampling Reference Point within the region of interest isrequired to further collect the RSSI by a mobile node fromall the available APs Since the propagation of the radiosignal in indoor environments is very complicated severalobservations in the same location are needful A singlesignature for each location is assigned by combining (suchas through averaging) 119909 sampling times Let 119877 be the totalnumber of studied rooms and 119872 the total number of APs(119877+1)times(119872+1) is the radiomapmatrixwhere each row vectoris along with its corresponding position except the first 119872

dimensional vector space which contains theMACaddressesof the119872 visible access points denoted by (AP)119877119872Step 2 (normalized rank transformation) This intermediatestep is achieved by separately considering each row vector ofthe radio mapThis consideration follows the described stepsin Section 2 proceeding from (1) to (6)

Step 3 (model building and parameters adjustment) Themodel is built based on the new defined database and thetransformed normalized rank values The parameters of thelearning method are tuned upon the obtained performanceusing the same device that is utilized to construct the radiomap The scrutinized criteria are the accuracy precision andthe recall such that

Accuracy = TP + FNTP + FP + TN + FN

Precision = TPTP + FP

Recall = TPTP + FN

(7)

where TP FP TN and FN are True Positive False PositiveTrue Negative and False Negative respectively Classificationaccuracy alone may hide details about the performance ofclassification model It can also be misleading in the case ofhavingmore than two classes in the dataset It gives the overallperformance of the model considering all correct predictionsdivided by the total number of the datasets However it doesnot point out if all classes are predicted equally or whethersome classes are neglected by the model The formulationsof the precision and the recall are used in our study toextract more information from the generated model Theprecision gives the percentage of the correctly predictedinstances among the total number of positive predictionswhile the recall is the percentage of correctly predictedinstances among the total number of positives


(I) Dimensionality check(1) for 119895 = 1 2 119872 do(2) for 119894 = 1 2 119873 do(3) if [(AP)119877119872](119895) = [(AP)Ob](119894)(4) Keep (RSSI)(119894) of Ob vector at the position (119895)(5) elseif 119894 = 119873 amp [(AP)119877119872](119895) = [(AP)Ob](119894)(6) Pad position (119895) with zero value(7) Loop(II) Normalized rank transformation

(i) Keep only non-zero positions and get the new Ob1015840 vector(ii) Rearrange RSSI value in ascending order(iii) Assign transformed Normalized Rank value(1) Initialize the Normalized Rank (NR-Ob) vector(2) for 119896 = 2 3 iterator do(3) if (Ob1015840)119896 = (Ob1015840)119896minus1(4) (NR-Ob)119896 = Ψ119896minus1(5) else(6) (NR-Ob)119896 = Ψ119896minus1 + 1(7) Loop(8) 120582 = max(NR-Ob)(1iterator)(9) Normalize NR-Ob vector by 120582 and remapping to119872 dimensional space(10)Consider the transformed normalized rank vector for positioning

(III) ML Classification(IV) Return the final position

Algorithm 1 Proposed normalized rank transformation method during runtime phase

32 The Online Stage This part is fully detailed in Algo-rithm 1 Like the offline phase this stage consists of threemain steps Step 1 dimensionality check Step 2 normalizedrank transformation Step 3 ML classification and positionestimation

Step 1 (dimensionality check) During our database con-struction considering 119872 visible APs leads to the need ofdimensionality check This step checks each given observedvector at the location which is denoted (Ob) and is to beidentified Let 119873 be the total number of visible APs of (Ob)vector Dimensionality transformation from 119873 dimensionspace to 119872 dimension space is established such that theRSSI value at 119894 location in (Ob) vector corresponding to aspecific AP at 119895 location in (AP)119877119872 vector should be storedat the same 119895 location However for the unseen APs theircorresponding RSSI values are padded with zero to achievethe same dimension in both vectors Furthermore it allowspatternmatching to take the same features into considerationduring the location estimation process

Step 2 (normalized rank transformation) TheRSSI values aretransformed to the normalized rank values by keeping the119872dimensional space of the observed vector

Step 3 (ML classification and position estimation) Thetransformed normalized rank vector (NR-Ob) is comparedwith the trained model to find the best match The physicalposition of the model which has the best match in the newradio map will be labeled as the estimated position

The same RSSI transformation has been applied in bothoffline and online stages Several classifiers will be trainedusing the new radio map generating the training model tovalidate our approach

4 Classification Methods

In this section we introduce the differentmethods adopted inour work All the studied algorithms fall under the categoryof the supervised techniques

41 Support Vector Machine Support Vector Machine isone of the best off-the-shelf supervised learning algorithmswhich is used for both classification and regression tasksIt has been originally developed for binary classificationproblems and further expanded to perform even multiclassclassification tasks It uses hyperplanes to define decisionboundaries separating data points of different classes inthe case of linearly separable data In addition SVMs canefficiently perform a nonlinear classification by using kerneltrick In this case original data are mapped into a high-dimensional or even infinite-dimensional feature space [3132]

SVM aims to construct a hyperplane with the maximalmargin between different classes In most cases data arenot perfectly linearly separable which makes the separatinghyperplane susceptible to outliers Therefore a restrictednumber of misclassifications should be tolerated aroundthe margins The resulting optimization problem for SVMs


where a violation of the constraints is penalized depends onthe regularization norm considered

411 L1 Regularization Norm for SVM The L1 norm definesa Support Vector Machine with a linear sum of the slackvariable to make the hyperplanes less sensitive to outliers itis written as

min119908120585119887

119869 (119908 120585) = 12 1199082 + 119862 119873sum119894=1

120585119894 (8)

Subject to 119910119894 (119908119879120601 (119909119894) + 119887) ge 1 minus 120585119894119894 = 1 119873 120585119894 ge 0 119894 = 1 119873 (9)

119910119894 = sign (119908119879120601 (119909119894) + 119887) (10)

where 119869 is the cost function 119908 is the weight vector and 119862 isthe positive regularization constantwhich defines the tradeoffbetween complexity and proportion of nonseparable samplesThe problem formulation in (8) and (9) refers to the primaloptimization problem Introducing the Lagrange multipliers120572119894 ge 0 we obtain the following dual problem

max120572

119882(120572)= 119873sum119894=1

120572119894 minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895120601 (119909119894)119879 120601 (119909119895)Subject to

119873sum119894=1

119910119894120572119894 = 0 0 le 120572119894 le 119862(11)

The optimal hyperplane is the one which maximizes themargin and the optimal values of 119908 and 119887 are found bysolving a constrained minimization problem using Lagrangemultipliers The function that solves the quadratic program-ming problem and with the use of the positive definitemapping function that satisfies Mercerrsquos condition is suchthat

119896 (119909 119909119894) = 120601 (119909)119879 120601 (119909119894) (12)

It also satisfies the Karush-Kuhn-Tucker (KKT) conditionsThe decision function can be expressed as

119910119894 = sign( 119873sum119894=1

120572119894119910119894119896 (119909 119909119894) + 119887) (13)

The classification accuracy produced by SVMs may showvariations depending on the choice of the kernel function andits parameters Various types of kernels can be chosen

(i) Linear

119870(119909 119909119894) = 119909119879119909119894 (14)

(ii) Polynomial of degree 119889119870(119909 119909119894) = (120574 + 119909119879119909119894)119889 120574 ge 0 (15)

(iii) Radial basis function (RBF)

119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205752 ) (16)

(iv) Sigmoid

119870(119909 119909119894) = tanh (1198961 sdot 119909119879119909119894 + 1198962)119889 (17)

The KKT condition is given by

120572119894 (119910119894 (119908119879119909119894 + 119887) minus 1 + 120585119894) = 0119887119894120585119894 = (119862 minus 120572119894) 120585119894 = 0 (18)

120572119894 are Lagrange multipliers and the value 120585119894 indicates thedistance of119909119894 with respect to the decision boundary since that

(i) if 120572119894 = 0 then 120585119894 = 0 therefore 119909119894 is correctly classifiedand lies outside the margin

(ii) 0 lt 120572119894 lt 119862 then (119910119894(119908119879119909119894 +119887)minus1+120585119894) = 0 and 120585119894 = 0thus 119910119894(119908119879119909119894 + 119887) = 1 and 119909119894 is the support vector

(iii) 120572119894 = 119862 then (119910119894(119908119879119909119894 + 119887) minus 1 + 120585119894) = 0 and 120585119894 ge 0therefore 119909119894 is a bounded support vector in the case0 le 120585119894 lt 1 119909119894 is correctly classified however for 120585119894 ge1 119909119894 is misclassified

412 L2 Regularization Norm for SVM The L2 norm definesa Support Vector Machine which uses the square sum ofthe slack variable in the objective function The consideredoptimization problem is as follows

min119908120585119887

119869 (119908 120585) = 12 1199082 + 1198622119873sum119894=1

1205851198942Subject to 119910119894 (119908119879119909119894 + 119887) ge 1 minus 120585119894

119894 = 1 119873 120585119894 ge 0 119894 = 1 119873(19)

The dual problem is expressed by introducing the Lagrangemultipliers 120572119894

max120572

119882(120572)= 119873sum119894=1

120572119894minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895 (119896 (119909 119909119894) + 120575119894119895119862 )Subject to

119873sum119894=1

119910119894120572119894 = 0 120572119894 ge 0 for 119894 = 1 119873

(20)

where 120575119894119895 is Kroneckerrsquos delta function in which 120575119894119895 = 1 for119894 = 119895 and 0 otherwiseThe KKT conditions in this case are given by

119910119894( 119873sum119895=1

120572119895119910119895 (119896 (119909 119909119894) + 120575119894119895119888 ) + 119887) minus 1 = 0 (21)


42 KNN 119870-NearestNeighbor algorithm is a nonparametricsupervised classifier in which the target label is predicted byfinding the nearest neighbor class considering the majorityvote of its 119870 neighbors In the case of 119870 = 1 the target issimply assigned to the class of its nearest neighborThe closestclass in this work is identified using the Euclidean distance

119863119894119895 = radic 119872sum119896=1

(119883119894119896 minus 119883119895119896)2 (22)

where 119863119894119895 is the distance between the observed point andeach signature vector in the radio map 119883119894 corresponds tothe runtime fingerprint 119883119895 is the offline fingerprint and 119872corresponds to the dimension of the RSSI Vector The bestchoice of the calibration points 119870 selected in this work hasbeen set equal to one since it generated better results

43 Naıve Bayes Naıve Bayes is a probabilistic classifierbased on applying Bayes theorem with strong naıve indepen-dence assumptions between the features Each data instancegenerates a tuple 119883 of attribute values ⟨1199091 1199092 119909119872⟩ Theidentification of the corresponding label from a finite set oflabels119877 consists onmaximumaposteriori (MAP) estimationThe theorem states the following relationship

119875 (119903 | 1199091 1199092 119909119872) = 119901 (119903) 119875 (1199091 1199092 119909119872 | 119903)119875 (1199091 1199092 119909119872) (23)

since 119875(1199091 1199092 119909119872) is constant given the input set

119903 = argmax119901 (119903) 119875 (1199091 1199092 119909119872 | 119903)119903 = argmax119901 (119903) 119872prod

119894=1

119875 (119909119894 | 119903) (24)

where 119903 is the estimated room which is predicted giventhe transformed rank values from 119872 APs 119901(119903) is the priorprobability of the class ldquo119903rdquo and 119875(119909119894 | 119903) corresponds to thelikelihood Both terms are estimated from the training dataWe adopt the implementation of Naıve Bayes considering thefact that continuous variable with each class is distributedaccording to a Gaussian distribution

119875 (119909119894 = V | 119903) = 1radic21205871205752119903 119890

minus(Vminus119906119903)221205752119888 (25)

44 Random Forest Random Forest (RF) is a classifier inwhich a multitude of decision trees are generated The RFchooses the tree which has the highest votes after theirclassification results The most occurring class number inthe output of the decision trees is the final output of the RFclassifier A recursive process in which the input dataset iscomposed of smaller subsets allows the training of each deci-sion treeThis process continues until all the tree nodes reachthe similar output targetsThe Random Forest classifier takesweights based on the input as a parameter that resembles thenumber of the decision trees [18]

45 Artificial Neural Network Artificial Neural Network(ANN) is one of the most effective models in ML It hasbeen inspired by the biological neural networks in the humanbrain It is made of several units or neurons of the followingform

119867119895 = 120590(119887 + 119873sum119894=1

119908119894119895119909119894) (26)

where 120590 is a nonlinear activation function 119887 is the bias termand 119908119894119895 are the associated weights to the column vector 119909(corresponding either to the input data or the precedinglayer)

In this paper our selected activation function is thesigmoid function as in the following [20]

120590 (119909) = 11 + 119890minus119909 (27)

The nodes in ANN are structured into successive layers inputlayer which corresponds to the input data hidden layers andoutput layer The required number of hidden layers dependson the nonlinearity of the relation between input and outputBackpropagation algorithm is used to adjust weights and biasvalues of the edges and to minimize the loss function

5 Experimental Results and Analysis

Our experiments were conducted in Metro City shoppingmall in Shanghai and we considered about 88 different shopsduring the calibration phase Figure 2 shows one floor plan ofthis shopping mall Only one device has been used to buildthe radio map based on the collected RSSI measurementsThe total visible 119872 APs considered herein are equal to 185Samsung Galaxy Note 2 mobile phone is considered as thereference device

During the testing phase sixteen different devices havebeen utilized to investigate hardware variance effect on local-ization accuracy These devices recorded the signal strengthfrom the available APs with their corresponding MACaddresses at the same locations in 8 shops In each shop sixtysamples have been recorded with a total of 480 samples basedon each single device Different database sizes denoted by 119878(corresponding to the number of assigned observations toeach position) have been utilized to investigate howmuch weneed to know ahead of time about what is being learnedThisanalysis aims to achieve an effective learning and correctlypredict the position for new observations unseen beforeMoreover the accuracy based on a single observation aswell as the needed fused data is studied The performance ofthe proposed method is evaluated through extensive experi-ments and the obtained results based on SVM are comparedwith other well-known and widely used ML algorithms inindoor localization In this section we assess the performanceof the built model based on a reference device to diversedevices In the first part we investigate database definitionbased on the collected RSSI value It is implemented byassigning a varied set of observations to each single locationand maintaining the absolute RSSI value during the runtime


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Aza Aza iYoo Paint BarNikon

Devil Park SubwayS24 Gong Cha

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S13 L16

S6 L9

VfreshJuice Bar

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Digtone Wacom Yamaha JBL

12 Bang

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Nice Claup

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Cloth Scenery

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Jucy Judy

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S11 L14

L10L11L17L18

3COINS

WCWC

WC

Food amp beverage

FashionCultural amp entertainment

Stairs

Escalator

Li

YIBOYO

Figure 2 3rd floor plan of Metro City shopping mall

phase The predicted location is calculated by matching thesample points on the radio map with the RSSI fingerprintclosest to the tracking device

The linear kernel of SVM based on risk minimizationprinciple is adopted to make the decision about the currentlocation Seeing that for themost part of analysis the numberof input variables exceeds the number of examples whichmakes the linear separation well suited based on Coverrsquostheorem [33] same kernel parameters are considered duringthe whole analysis to fairly compare the obtained resultsMoreover we checked the efficiency of the rank transforma-tion without any normalization In addition to evaluate theeffectiveness of the proposed method we considered abouttwo ways of normalization The first technique is the fullynormalized rank considering the total stored input in thedatabase However the second one is the vector normalizedrank method in which the normalization factor 120582 is takingthe value as described in Section 2

51 Experiments Based on RSSI Values Figure 3 shows thepositioning accuracy with different 119878 and the influence ofchanging the tracking device when using RSSI values inboth online and offline phase The vertical axis shows the

percentage of correctly predicted positions We look firstat the achieved accuracy in the case of using the sametraining device in the positioning phaseThe good and steadyperformance during this test can be seen with high precisionto estimate the location where only a few samples are enoughto attain the maximum accuracy Almost all locations areperfectly estimated in this case

However in the case of tracking device different from thetraining device during the runtime phase it works badly inhalf of the studied cases Besides this observation is muchmore remarkable if the number of fingerprint observationsin the same location is limited or very small Although theachieved correct rate for the remaining smartphones turnsaround 100 well-estimated location only some of them canbe distinguished in the figure Unsteady curves are noticeableand increasing the number of the encoded fingerprints basedon RSSI values at each location on the radio map does notalways improve the performance of the applied methodThisoutcome proves the degradation pattern caused by the changeof the utilized device to record the signal strength This isdue to the fact that RSSI stored in the database diverges fromthe RSSI captured using another piece of equipment Thislow estimation is coming from the different sensitivity of


3 4 5 6 7 8 92Number of samples to construct the database

Lenovo A788tHuawei GRA-CL00HTC One E8GioneeCoolpad 8730LBBKOppo A31c

MeizuBBK VivoSamsung trlteduosctcMeizu M2 noteSamsung klteduosznXiaomi CancroXiaomiOppo R7c

Samsung Galaxy Note 2

50

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(a)




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Accu

racy

20 30 40 50 6010Number of samples to construct the database

(b)

Figure 3 Localization accuracy using RSSI based on linear SVM (a) shows the accuracy based on a few samples (b) shows the accuracybased on large samples

manifold devices to the signal throughput which is relatedto both antennas and packaging materials

52 Experiments Based on the Rank Transformed ValuesIn this part we have redone the previous tests basedon the rank transformed values instead of exploiting thedirect RSSI value to predict the location The RSSI vector1198751119872 = 1198781 1198782 119878119872 is reformulated such that Ψ1119872 =Ψ1 Ψ2 Ψ119872 whereΨ119894 satisfies (4) and the normalizationfactor is initially ignored Figure 4 illustrates the locationaccuracy by changing the number of associated observationsto each Reference Point (RP) using multiple devices Aprominent improvement is noticeable using the rank trans-formed value and more stability is perceptible comparing tothe previous results The maximum correct rate estimationis much higher based on a few associated samples to thereference locationsThe reached perfect predictions based onthis test have not been attained based on RSSI analysis evenwhen we considered the integrality of captured observationsThe two exception cases ofXiaomi andOppoA31c devices willbe discussed in the next part

Ranking the signal throughput of an access point at aspecific location plays an essential role in delimiting therange of the interval in which the input variable is definedIt is additionally practical to broaden the application of abuilt model Moreover the prioritization of the most reliableinput variables when assigning rank values strengthens thegeneralization of the model and the performance of the usedmethod

53 Experiments Based on the Normalized Rank Transforma-tion Method In order to evaluate the performance of thenormalized rank transformation we define two means ofnormalization Figure 5 represents the performance of thelearning method using the fully normalized rank transfor-mationThe normalization factor 120582 takes the inverse value of119872 where 119872 is the total visible APs considered in the radiomap while Figure 6 corresponds to the achieved results when120582 satisfies the condition of (5) It is noteworthy that bothwayscan provide more accurate results with some meaningfuldifferences

It appears that normalizing based on a fixed value needsmore samples to attain a good prediction if compared to thesecond normalization side by side It can be seen that forthe greatest part at least 6 samples are required to reach anapproximate 100 accurate prediction The recorded RSSIvalues using Xiaomi device have been compared with thoseobtained with the remaining devices where an unpredictedvariability has been registered We notice that some samplesare very similar for the same environment Meanwhile itcould exhibit a remarkable inconsistency in the recordedthroughput at the same position It seems that this mobilephone is very sensitive to changes and to the stability ofthe studied area which explains the registered uncertaintyThe maximum percentage of 875 achieved by Oppo A31cis further interpreted based on the confusion matrix

Nonetheless the second followed normalization basedon the highest assigned transformed rank value is rapidlyconverging to the maximum accuracy except for the special



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110

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(b)

Figure 4 Localization accuracy using the rank based on linear SVM (a) shows the accuracy based on a few samples (b) shows the accuracybased on large samples


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110

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racy




(a)

50

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(b)

Figure 5 Localization accuracy using the fully normalized rank based on linear SVM (a) shows the accuracy based on a few samples (b)shows the accuracy based on large samples



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110Ac

cura

cy




(a)

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(b)

Figure 6 Localization accuracy using the vector normalized rank based on linear SVM (a) shows the accuracy based on a few samples (b)shows the accuracy based on large samples

case of Xiaomi device that reached its maximum until theconsideration of the 10th sample This approach allowsconsidering the varying range of the allocated tags in thenew formulated vectors at one position and consequentlythe difference between vectors dimensionalities In contrastto the previous normalization in the case of 120582 = 1Ψ119872 itdoes not only perform as a scaling factor but also puts thetransformed values of both real location fingerprint vectorand the runtime vector as close as possible

54 Experiments Based on a Unique Set of ObservationsThe experiments in this scenario consider about one sampledesignating a special Reference Point In the test the storedfingerprints in the radio map are attained by averaging thewhole recorded dataset Figure 7 illustrates the percentageof the correct location determination based on a small sizedatabase using the linear SVM classification Figures 7(a)7(b) and 7(c) are respectively obtained by accounting forthe absolute RSSI value the inverse rank value and the rankvalue Finally Figure 7(d) shows the performance of thelearning method by applying the proposed method The aimof comparing between Figures 7(b) and 7(c) is to demonstratethe importance of considering the throughput signal of aninput variable in the right direction As notable in Figure 7(b)awrong direction leads to decreasing the accuracy comparingwith the reference Figure 7(a) based on RSSI value

On the one hand the allocation of tags in the rightorder results in providing the APs with a high received

signal strength by high ranks while the less reliable ones areassigned the low values On the other hand this will resultin the prioritization of the principal features by accordingminor consideration to theAPswith low signal strengthwhenbuilding the support vectors This is due to the fact that thedecision boundaries of the support vectors of SVMare alwaysdominated by the large quantities The built model in thiscase is much fitting the needs of this study than the inverserank transformation Moreover a significant improvement isapparent by implementing the proposed solution with no lessthan 9875 accurate estimation in 9375 of the tested casesand 100 accuracy in 5625 of cases

Now turning attention to Xiaomi device it turns outthat fusing data reduces the effect of the large variation inthe registered signal strength and enhances the predictionperformance We attempted to investigate the volume ofneeded data to be fused to consider one fingerprint for a givenReference Point (RP) From Figure 8 it appears that bothways of normalization herein work better than just applyingthe rank transformation with more stable prediction Quitesimilar performances are seen in Figures 8(b) and 8(c)increasing by the rise of combined information comparingwith Figure 8(a)

55 Algorithms Comparison This section is dedicated tothe comparison and the evaluation of the effectiveness ofSVM among multiple ML techniques within a single experi-mental environment To validate our proposed method we


0

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100

Accu

racy

2 4 6 8 10 12 14 16 180Device type

(7) Lenovo A788t(6) Huawei GRA-CL00(5) HTC One E8(4) Gionee(3) Coolpad 8730L(2) BBK(1) Oppo A31c

(8) Meizu(15) BBK Vivo(14) Samsung trlteduosctc(13) Meizu M2 note(12) Samsung klteduoszn(11) Xiaomi Cancro(10) Xiaomi(9) Oppo R7c

(16) Samsung Galaxy Note 2

(a)

2 4 6 8 10 12 14 16 180Device type

0

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racy




(b)

2 4 6 8 10 12 14 16 180Device type

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racy




(c)

2 4 6 8 10 12 14 16 180Device type

0

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100

Accu

racy




(d)

Figure 7 Localization accuracy comparison in the case of unique exemplification per location based on linear SVM (a) shows the attainedaccuracy based on RSSI value (b) shows the accuracy in the case of applying the inverse rank value (c) shows the accuracy in the case ofapplying the rank transformation value (d) Accuracy based on the normalized rank transformation () The inverse rank is the convertedabsolute RSSI vector by considering the opposite direction of (3)


20 30 40 50 6010Number of fused samples

50

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110

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racy

()




(a)


50

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110

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racy

()




(b)


50

60

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100

110

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racy

()




(c)

Figure 8 Localization accuracy in the case of unique exemplification per location based on linear SVM considering different data fusion size(a) shows the attained accuracy based on the rank value (b) shows the accuracy in the case of applying the proposed rank transformation(c) shows the accuracy in the case of applying the fully normalized rank transformation


Table 1 Percentage of accurately estimated locations based on linear SVM adopting multiple combinations of constraints violation alongwith comparison between RBF kernel and regularized Logistic Regression the radio map is defined upon RSSI values

DevicesClassification type

RBF kernelL2-Rlowast L2-N L2-R L2-N L2-R L1-N L2 LR L1-R L1(primal) (dual) (dual) (primal) L2-Nlowastlowast LRlowastlowastlowast

Oppo A31c 8708 8542 8542 8604 5229 5875 3729BBK 9417 9520 9520 9542 6145 7020 3500Coolpad 8730L 9062 8978 8978 9042 7042 7604 4145Gionee 9917 9937 9937 9937 5812 7312 3729HTC One E8 8208 8145 8145 8187 5458 5417 3604Huawei GRA-CL00 9792 9812 9812 9833 6375 6458 2875Lenovo A788t 9458 9478 9478 9500 5104 6625 2667Meizu 9958 9958 9958 9958 8854 8729 5270Oppo R7c 9812 9812 9812 9792 5562 7333 3645Xiaomi 7417 7417 7417 7417 4083 6395 3750Xiaomi Cancro 6958 6854 6854 6958 3750 4229 3291Samsung klteduoszn 9292 9250 9250 9312 6854 6333 4750Meizu M2 note 9771 9708 9708 9833 8375 7937 5812Samsung trlteduosctc 9395 9375 9375 9396 7250 6645 4167BBK Vivo 9687 9708 9708 9729 5791 6792 3020Standard device accuracy 9187 9187 9187 9229 7979 7895 5479Recall (ratio) 092 092 092 097 079 079 055Precision (ratio) 095 095 095 097 086 083 077(lowast) R stands for regularization (lowastlowast) N stands for norm (lowastlowastlowast) LR stands for logistic regression We put in bold the percentages lower than 90 for easinessof observation

Table 2 Algorithms comparison based on the percentage of the well-recognized positions the radio map defined upon RSSI values

Device typeClassification type

SVM Artificial Neural Network Naıve Bayes Random Forest KNN (119870 = 1)L2-R L2-NOppo A31c 8708 9750 7750 5958 4604BBK 9417 5625 3375 5938 4667Coolpad 8730L 9062 9771 6438 8000 8146Gionee 9917 7417 3771 6938 5896HTC One E8 8208 9188 5688 6271 8104Huawei GRA-CL00 9792 9333 4667 6604 7312Lenovo A788t 9458 7875 3583 6188 5333Meizu 9958 9979 9500 8400 9958Oppo R7c 9812 6292 3604 6375 5083Xiaomi 7417 8104 5500 5646 7812Xiaomi Cancro 6958 6375 3875 4417 5292Samsung klteduoszn 9292 9875 6729 7400 8708Meizu M2 note 9771 9771 8625 7438 9437Samsung trlteduosctc 9395 9729 6583 6896 8917BBK Vivo 9687 7500 3917 7500 5229Standard device accuracy 9187 9750 7750 8479 8708Recall (ratio) 092 097 077 085 087Precision (ratio) 095 097 085 093 093We put in bold the percentages lower than 90 for easiness of observation

compared the resulting estimation of the considered MLtechniques with their ground-truth locations Taking intoaccount the importance of using a common database and thesameway of data definition as considered in the offline phasethe conducted analysis is partitioned to two main tests Thefirst part is devoted to the tests based on RSSI value whilethe second one is devoted to the proposed normalized ranktransformation

551 Algorithms Comparison upon RSSI Value Both Tables 1and 2 have been obtained by considering the absolute RSSIvalue in the calibration and the positioning phase Table 1shows the influence on accuracy by changing the consideredregularization norm the selected kernel for SVM classifierand using the regularized logistic regressionHerein for SVMclassifier the linear kernel yielded better results than the RBFkernel which achieved only 5479 correct prediction by


Table 3 Percentage of accurately estimated locations based on linear SVM adopting multiple combinations of constraints violation alongwith comparison between RBF kernel and regularized Logistic Regression the radio map is defined upon the proposed normalized ranktransformation




fitting the parameters from our testbed which was expectedas stated in Coverrsquos theorem

It is noticeable that recognition rates and the general-ization ability of the test data by L2-SVM tend to be betterthan those by L1-SVM Moreover the differences in theperformance of L2-SVM applying either the dual or primaloptimization problem are imperceptible This means thatL2 regularization is estimating the violating variables moreconservatively than L1 regularization avoiding overfittingissue of the training samples L1 regularization SVM tendsto pick only a few variables in the case of the existence ofseveral highly correlated variables In addition the numberof selected variables is upper bounded by the size of thetraining data However L2 normkeeps the correlated variableby shrinking their corresponding coefficients

It is noteworthy that the L2 regularized logistic regressionbehaves quite similarly to L2 regularized support vector sinceboth of them tend to maximize the margin as reducing theloss although their considered loss is different It is perceptiblein a few cases that L2 regularized logistic regression producesslightly more accurate prediction compared to L2 regularizedSVM This is due to the fact that logistic regression is mod-eling probabilities and therefore some errors are calculatedeven for correctly classified training examples while L2-SVMdoes not SVMclassifier is purely discriminative anddesignedto give a binary classification while the regularized logisticregression estimates the a posteriori probability of classmembership In this work we desire a binary classificationand consequently identify the decision boundary directly

rather than estimate the probability of class membership Onthis basis we will look at the results of L2 regularized supportvector instead of the L2 regularized logistic regression on theupcoming comparison

Analysis using RSSI value based on linear SVM givesan acceptable result in most cases Nonetheless the modelgeneralization to manifold devices could facilely fail toachieve a very high precision for instance a low correctrate estimation has been registered with Oppo A31c HTCXiaomi and Xiaomi Cancro with respectively a rate of8708 8208 7417 and 6958 Table 2 illustrates theperformance of the optimized algorithms in which it canbe seen that the built model of Random Forest KNN andNaıve Bayes failed dramatically notably with heterogeneousdevices Good performances using Neural Network andSVM are noteworthy however SVM outperforms the wholeimplemented ML algorithms

552 Algorithms Comparison upon the Proposed NormalizedRank Transformation Tables 3 and 4 show the results of theproposednormalized rank transformation in both calibrationand positioning phase We investigated its usefulness consid-ering regularization across LR and SVM classifier for linearand RBF kernels as depicted in Table 3 as well as its suitabilityof operation based on several ML algorithms as presented inTable 4 In general we noticed the same previous observationbased on RSSI analysis regarding the regularization andkernel type However a significant improvement is perceivedmoving from the RSSI value consideration to the normalized


Table 4 Algorithms comparison based on the percentage of the well-recognized positions the radio map is defined upon the proposednormalized rank transformation


SVM Artificial Neural Network Naıve Bayes Random Forest KNN (119870 = 1)L2-ROppo A31c 8750 8667 5938 5729 5479BBK 9875 8958 6438 4708 6458Coolpad 8730L 100 100 9583 8208 8667Gionee 100 9354 6208 5250 6729HTC One E8 9875 9854 9625 8042 8312Huawei GRA-CL00 100 9854 7125 70 8104Lenovo A788t 9979 9667 6438 6083 7729Meizu 100 100 100 9354 9937Oppo R7c 9958 9354 6688 6167 6541Xiaomi 9917 8396 8604 7688 8083Xiaomi Cancro 100 9354 7875 6354 4812Samsung klteduoszn 100 9979 9958 8646 8750Meizu M2 note 100 9875 9958 8646 9250Samsung trlteduosctc 9958 9917 9979 8542 8375BBK Vivo 100 9646 6938 6396 7083Standard device accuracy 100 100 100 8938 9083Recall (ratio) 1 1 1 089 091Precision (ratio) 1 1 1 094 094We put in bold the percentages lower than 90 for easiness of observation

Table 5 Confusion matrix of OPPO A31c device

Shop 1 Shop 2 Shop 3 Shop 4 Shop 5 Shop 6 Shop 7 Shop 8Shop 1 60 0 0 0 0 0 0 0Shop 2 0 60 0 0 0 0 0 0Shop 3 0 0 60 0 0 0 0 0Shop 4 0 0 0 60 0 0 0 0Shop 5 0 0 0 0 60 0 0 0Shop 6 0 0 0 0 0 60 0 0Shop 7 0 0 0 0 0 0 60 0Shop 8 60 0 0 0 0 0 0 0

rank transformation The converted absolute RSSI valuesseem to be more stable and reliable rather than their initialvalues Analyzing the performance of the aforementionedML algorithms the accuracy based on the same deviceis ameliorated while the generalization of the model todiversiform devices has been outperformed based on NR-SVM This solution shows its significance improving theoptimized accuracy of SVM around the decision boundarieswhere 100 perfect prediction is achieved on the same devicebased linear L2-SVM Moreover no less than 9875 well-estimated locations are attained for the remaining devicesexcept the special case of Oppo A31c

It is interesting to further examine the positioning errorpercentile for the special case of Oppo A31c where only875 correct estimation has been recorded We have drawnits corresponding confusion matrix given in Table 5 tosummarize the performance of the classification algorithmfor this deviceThe vertical shop specification corresponds tothe actual locationwhile the horizontal ones are the predictedshopsThe diagonal part of thematrix delineates the correctly

classified instance where sixty samples are defined in eachshop for evaluation It is observed that both locations ldquoshop1rdquo and ldquoshop 8rdquo are highly confused where all vectors of shop8 were classified as location ldquoshop 1rdquo In the case of havinga high similarity between RSSI vectors in different locationstaking into account neither the initial RSSI values nor theirconverted NR values can significantly distinguish betweenthem and provide accurate estimation

56 RSSI Transformations Comparison Based on SVMSeveral studies have proposed methods to improve therobustness of positioning systems against device diversityCalibration-free approaches have introduced several ways ofRSSI reformulation This performance comparison is aimingto show the effectiveness of the proposedNR-SVM comparedwith the Hyperbolic Location Fingerprinting (HLF) theSignal Strength Differences (SSD) and the DIFF methodbased on SVM The difference of signal strength betweenpairs of APs namely DIFF was proposed in [25] to reducethe effect of diversity in devicesThemain difference between



50

60

70

80

90

100

110Ac

cura

cy




(a)

50

60

70

80

90

100

110

Accu

racy





(b)

Figure 9 Achieved accuracy based on SSD-SVM (a) shows the accuracy based on a few samples (b) shows the accuracy based on largesamples

the fundamental fingerprinting method and DIFF is thatthe latest uses the difference between pairs of APs insteadof the use of the absolute RSSI value SSD [26] takes alsothe advantages of Signal Strength Differences however itselects only independent sets ofDIFFMoreover theHLF [24]method uses the signal strength ratios between pairs of RSSIsas fingerprints

We implemented the aforestated RSSI value transforma-tions and estimated the location using SVM classifier Theresults show that both DIFF (Figure 10) and HLF (Figure 11)conversions perform better than the initial RSSI values(Figure 3) either when using a few samples or by consideringextrasite survey measurements to identify each location Itappears in our case of study that the SSD transformationachieves lower estimation in terms of accuracy comparingthe estimated positions with their ground-truth locationsFocusing on the obtained curve using the same device versusa few samples Figure 9(a) the performance is clearly belowthat of the absolute RSSI values The side effect of thisapproach is that the performance is not always better than theinitial RSSI value or even worse with homogeneous devicesnotwithstanding the enlargement of training samples Tofurther investigate this observation we carried out the testof HLF method based on independent sets only as shownin Figure 12 It turns out that this way of transformationbased on independent sets yields a significant loss of somediscriminative information which decreases the accuracyinstead of improving it

NR-SVM (Figure 6) performs the best and the experi-ments showa consistent result aswell as a high precision com-paring with three of the popular calibration-free techniquesDIFF SSD and HLF based on SVM The reached steadyperformance during the whole tests proves the feasibility ofconsidering few samples even in the case of manifold devicesConsequently it reduces the workload of the offline datatraining phase Furthermore it avoids the time-consumingsite survey in which a large number of observations arecollected to boost the reliability of the system

6 Conclusion

In this paper we have presented the normalized ranktransformation method for a room level determinationThe performance evaluation shows that is more efficient toredefine and reformulate the signal strength observed fromthe anchors adequately rather than to use the absolute RSSIvalues from an anchor node The importance of rankingdirection and the way of normalization have been comparedThe normalization factor based on the highest assigned rankresults in meaningful consideration of vector dimensionyielding higher accuracy and it is characterized by its fastconvergence to the maximum possible accuracy

We explore the efficiency of NR-SVM by formulatingthree of the most popular calibration-free transformationsproposed in the literature DIFF SSD and HLF are imple-mented based on SVM classifier It has been concluded that



50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)

Figure 10 Achieved accuracy based on DIFF-SVM (a) shows the accuracy based on a few samples (b) shows the accuracy based on largesamples


50

60

70

80

90

100

110

Accu

racy




(a)

15 20 25 30 35 40 45 50 55 6010Number of samples to construct the database

50

60

70

80

90

100

110

Accu

racy




(b)

Figure 11 Achieved accuracy based on HLF-SVM (a) shows the accuracy based on a few samples (b) shows the accuracy based on largesamples



50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)

Figure 12 Achieved accuracy based on independent HLF-SVM (a) shows the accuracy based on a few samples (b) shows the accuracy basedon large samples

SSD transformation may result in a significant loss of somediscriminative information and decreases the precision ofthe algorithm However both DIFF and HLF improved theperformance compared to the fundamental fingerprintingmethod based on RSSI values Moreover NR-SVM hasshown its distinguishability and reliability among the studiedtransformations

Another contribution presented in this paper is theexpansion of the application of the prebuild radiomap upon arecorded information via a single device to manifold devicestaking into account the quality and stability over time ofthe resulting outcomes Finally we investigate and compareour method based on different machine learning algorithmsand we showed that the linear L2 regularization norm of theSupportVectorMachine outperformedNaıve Bayes RandomForest Artificial Neural Network and KNN algorithms withmoderate dataset in terms of accuracy especially on handlingdevice heterogeneity

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the Shanghai Science andTechnology Committee under Grant 15511105100 and the

National Science and Technology Major Project under GrantGFZX0301010708

References

[1] J Hightower R Want and G Borriello ldquoSpoton an indoor3D location sensing technology based on Rf signal strengthrdquoUW-CSE 00-02-02 Department of Computer Science andEngineering University of Washington Seattle Wash USA2000

[2] P Bahl and V N Padmanabhan ldquoRadar an in-building RF-based user location and tracking systemrdquo in Proceedings ofthe 19th Annual Joint Conference of the IEEE Computer andCommunications Societies (IEEE INFOCOM rsquo00) pp 775ndash784Tel Aviv Israel March 2000

[3] R Chen L Pei J Liu and H Leppakoski ldquoWLAN and blue-tooth positioning in smart phonesrdquo in Ubiquitous PositioningandMobile Location-Based Services in Smart Phones pp 44ndash682012

[4] L Pei R Chen J Liu T Tenhunen H Kuusniemi and YChen ldquoInquiry-based bluetooth indoor positioning via RSSIprobability distributionsrdquo inProceedings of the 2nd InternationalConference on Advances in Satellite and Space Communications(SPACOMM rsquo10) pp 151ndash156 Athens Greece June 2010

[5] L Pei R Chen J Liu H Kuusniemi T Tenhunen and Y ChenldquoUsing inquiry-based Bluetooth RSSI probability distributionsfor indoor positioningrdquoGlobal Positioning Systems vol 9 no 2pp 122ndash130 2010


[6] G Gomes and S Helena ldquoIndoor location system using ZigBeetechnologyrdquo in Proceedings of the 3rd International Conferenceon Sensor Technologies and Applications (SENSORCOMM rsquo09)pp 152ndash157 Athens Greece June 2009

[7] K Pahlavan F O Akgul M Heidari A Hatami J M Elwelland R D Tingley ldquoIndoor geolocation in the absence of directpathrdquo IEEE Wireless Communications vol 13 no 6 pp 50ndash582006

[8] J MacHaj P Brida and J Benikovsky ldquoUsing GSM signals forfingerprint-based indoor positioning systemrdquo in Proceedings ofthe 10th International Conference (ELEKTRO rsquo14) pp 64ndash67Rajecke Teplice Slovakia May 2014

[9] Y Yuan L Pei C Xu Q Liu and T Gu ldquoEfficient WiFi finger-print training using semi-supervised learningrdquo in Proceedingsof the Ubiquitous Positioning Indoor Navigation and LocationBased Service (UPINLBS rsquo14) pp 148ndash155 Corpus Christ TexUSA November 2014

[10] M Youssef and A Agrawala ldquoThe Horus location determina-tion systemrdquoWireless Networks vol 14 no 3 pp 357ndash374 2008

[11] K Kaemarungsi and P Krishnamurthy ldquoProperties of indoorreceived signal strength for WLAN location fingerprintingrdquo inProceedings of the 1st Annual International Conference onMobileand Ubiquitous Systems Networking and Services (MOBIQUI-TOUS rsquo04) pp 14ndash23 Boston MA USA August 2004

[12] L N Chen B H Li K Zhao C Rizos and Z Q Zheng ldquoAnimproved algorithm to generate aWi-Fi fingerprint database forindoor positioningrdquo Sensors vol 13 no 8 pp 11085ndash11096 2013

[13] B Zhao L Pei C Xu and L Gu ldquoGraph-based efficientWiFi fingerprint training using un-supervised learningrdquo inProceedings of the 28th International Technical Meeting of theSatellite Division of the Institute of Navigation (ION GNSS rsquo15)pp 2301ndash2310 Tampa Convention Center Tampa Fla USASeptember 2015

[14] G Shakhnarovich P Indyk and T Darrell ldquoNearest-neighbormethods in learning and visionrdquo IEEE Transactions on NeuralNetworks vol 19 no 2 article 377 2008

[15] R M Faragher and R K Harle ldquoSmartSLAMmdashan efficientsmartphone indoor positioning system exploiting machinelearning and opportunistic sensingrdquo ION GNSS vol 13 pp1006ndash1019 2013

[16] Mitchell andM Tom ldquoMachine Learningrdquo inMcGraw-Hill Sci-enceEngineeringMath 2007 (Bayes Theorem) 156ndash163 (NaıveBayes classifier) 177-178 (KNN) 230ndash234

[17] L B Del Mundo R L D Ansay C A M Festin and R MOcampo ldquoA comparison of Wireless Fidelity (Wi-Fi) finger-printing techniquesrdquo in Proceedings of the 2011 InternationalConference on ICT Convergence (ICTC rsquo11) pp 20ndash25 SeoulSouth Korea September 2011

[18] A H Salamah M Tamazin M A Sharkas and M Khedr ldquoAnenhanced WiFi indoor localization System based on machinelearningrdquo in Proceedings of the 2016 International Conferenceon Indoor Positioning and Indoor Navigation (IPIN rsquo16) pp 1ndash8 Alcala de Henares Spain October 2016

[19] L Calderoni M Ferrara A Franco and D Maio ldquoIndoorlocalization in a hospital environment using random forestclassifiersrdquo Expert Systems with Applications vol 42 no 1 pp125ndash134 2015

[20] C Zhou and AWieser ldquoApplication of backpropagation neuralnetworks to both stages of fingerprinting based WIPSrdquo inProceedings of the 2016 4th International Conference on Ubiqui-tous Positioning Indoor Navigation and Location Based Services(UPINLBS rsquo16) pp 207ndash217 Shanghai China November 2016

[21] M S Ifthekhar N Saha and Y M Jang ldquoNeural network basedindoor positioning technique in optical camera communicationsystemrdquo in Proceedings of the 5th International Conference onIndoor Positioning and Indoor Navigation( IPIN rsquo14) pp 431ndash435 Busan South Korea October 2014

[22] L Pei M Zhang D Zou R Chen and Y Chen ldquoA surveyof crowd sensing opportunistic signals for indoor localizationrdquoMobile Information Systems vol 2016 Article ID 4041291 16pages 2016

[23] A W Tsui Y-H Chuang and H-H Chu ldquoUnsupervisedlearning for solving RSS hardware variance problem in WiFilocalizationrdquo Mobile Networks and Applications vol 14 no 5pp 677ndash691 2009

[24] M B Kjaeligrgaard and C V Munk ldquoHyperbolic location finger-printing a calibration-free solution for handling differences insignal strength (concise contribution)rdquo in Proceedings of the 6thAnnual IEEE International Conference on Pervasive Computingand Communications (PerCom rsquo08) Hong Kong China March2008

[25] F Dong Y Chen J Liu Q Ning and S Piao ldquoA calibration-free localization solution for handling signal strength variancerdquoinMobile Entity Localization and Tracking in GPS-Less Environ-nments pp 79ndash90 Springer Berlin Germany 2009

[26] A K M Mahtab Hossain Y Jin W Soh and H N Van ldquoSSDa robust RF location fingerprint addressing mobile devicesrsquoheterogeneityrdquo IEEE Transactions onMobile Computing vol 12no 1 pp 65ndash77 2013

[27] J Correa E Katz P Collins and M Griss ldquoRoom-LevelWiFi Location Trackingrdquo MRC-TR-2008-02 Carnegie MellonSilicon Valley CyLab Mobility Research Center 2008

[28] A Buchman andC Lung ldquoReceived signal strength based roomlevel accuracy indoor localisation methodrdquo in Proceedings ofthe 4th IEEE International Conference on Cognitive Infocom-munications (CogInfoCom rsquo13) pp 103ndash108 Budapest HungaryDecember 2013

[29] S N Patel K N Truong and G D Abowd ldquoPowerline posi-tioning a practical sub-room-level indoor location system fordomestic userdquo in Proceedings of the 8th International Conference(UbiComp rsquo06) pp 441ndash458 Orange County CA USA 2006

[30] R Yasmine and L Pei ldquoIndoor fingerprinting algorithm forroom level accuracy with dynamic databaserdquo in Proceedings ofthe 2016 4th International Conference on Ubiquitous PositioningIndoor Navigation and Location Based Services (UPINLBS rsquo16)pp 113ndash121 Shanghai China November 2016

[31] VN VapnikTheNature of Statistical LearningTheory Springer1995

[32] V N Vapnik Statistical Learning Theory Wiley New York NYUSA 1998 ISBN 978-0-471-03003-4 pp IndashXXIV 1ndash736

[33] T M Cover ldquoGeometrical and statistical properties of systemsof linear inequalities with applications in pattern recognitionrdquoIEEETransactions on Electronic Computers vol EC-14 no 3 pp326ndash334 1965

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Human-ComputerInteraction

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Gaussian distribution [12] were used to model the RSSIdistributionHowever RADAR systemwas the first introduc-ing the fingerprinting technique based on the deterministicapproach [13] using 119870-Nearest Neighbor method (KNN)[14] Nowadays the use of machine learning algorithms(ML) as in [15] has increasingly gained more popularityin indoor navigation domain because of their witnessedrobustness among them are Naıve Bayes classifier [16 17]Support Vector Machine (SVM) [17 18] Random Forest[18 19] and Neural Network [20 21] However their modelgeneralization to different userrsquos terminals has seldom beenconsidered

RSSI fluctuation and diversiform smartphones can signif-icantly degrade the positioning accuracy of WiFi localizationsystems as well as the patterns between training and testingsignature vectors The WiFi device used to train the radiomap during the calibration phase may especially differ fromthe ones used during the positioning phase WiFi modulesfrom different providers have varying receive signal gainswhich make the RSSI vary using different devices at the samelocation [22] This hardware variance problem is not onlylimited to differences in the WiFi chipsets used by trainingand tracking devices Besides it arises when the same WiFichipsets are connected to different antenna types andorpackaged in different encapsulation materials

To address this issue several studies have proposedmethods to improve the robustness of positioning systemsagainst mobile devices heterogeneity For example the useof an unsupervised learning [23] the Hyperbolic LocationFingerprinting (HLF) [24] the DIFF method [25] andthe Signal Strength Difference method (SSD) [26] are therepresentative ones In this paper a new method applying anintermediate step of absolute RSSI value transformation bymaking use of ML algorithms is proposed

The indoor navigation market addresses various appli-cations like Location Based Services (LBS) the guidance offirefighters and peoplemanagementMoreover it can benefitfrom the room level accuracy [27ndash29] to extract statisticalinformation which can be deployed to better market tocustomers find hangouts in airports and even most popularshop in shopping malls and so forth In this work we focuson a room localization which is the prediction of an occupiedroom in which the mobile device is currently in This taskis more practical to attain since it does not require the floormap of the desired indoor environment which is not alwaysavailable in practice

To achieve a high room level accuracy based WiFi fin-gerprinting technique we have investigated various databasedefinitions and the impact of signature clustering in ourprevious work [30] with respect to relevant requirementparameters In this paper we propose a normalized ranktransformation based SVM approach to solve the issue ofmobile terminal diversity during the positioning phase Weconsider and compare between the performances of theaforementioned ML algorithms and calibration-free trans-formations to validate our solution This approach aimsat generalizing the use of the preconstructed radio mapderived from one device to manifold devices and guaranteelocalization accuracy in the meantime

2 Normalized Rank Transformation

Aiming to mitigate the effect of signal fluctuation andhardware variance issue we introduce the intermediate nor-malized rank transformation step to freeze the variation ofthe RSSI This solution has been defined principally to dealwith SVM classifier Moving from RSSI value based analysisto the normalized rank transformation based analysis theprincipal features are prioritized and the dimensionalities ofsignature vectors are considered

21 Rank Transformation In the conventional classificationbased on SVMor any otherML algorithms for fingerprinting-based indoor localization the features are defined as thesignal strength received from all the visible access points(APs) to build the model However the received signalstrength is inherently time varying at a specific locationMoreover device diversity will impact both learning andpositioning phases

In order to find the perfect match between the userlocation and the predefined locations in the radio mapusing SVM classifier as well as attenuate the susceptibilityof decision boundaries to RSSI variation the enhancementof data learning to build a robust model is a key Theimprovement of the accuracy is related to the strong decisionboundaries between the different classes The input variablesare redefined and the absolute RSSI values are replaced first bytheir corresponding rank values Let 1198751119872 be the RSSI vectorof the119872 visible APs and 119878119894 the corresponding absolute RSSIvalue of the AP(119894) such that

1198751119872 = 1198781 1198782 119878119872 (1)

11987510158401119872 = 11987810158401 11987810158402 1198781015840119872 (2)

11987810158401 le 11987810158402 le sdot sdot sdot le 1198781015840119872 (3)

Ψ119894 = Ψ119894minus1 + 1 for 1198781015840119894minus1 = 1198781015840119894Ψ119894minus1 otherwise (4)

11987510158401119872 is the new defined RSSI vector by rearranging the APsThe rearrangement is based on (3) in which the throughputsof received signals are in ascending order Equation (4)explains how to decide the rank vector If RSSIs values aredistinct (1198781015840119894minus1 = 1198781015840119894 119894 indicates the position of the AP in the119872dimensional vector) successive numbers denoted by Ψ119894 willbe assigned Otherwise the same rank will be allocated Theinitial value is equal to one andΨ119872 does not have to be equalto the dimension of the initial RSSI vector By adopting thisprocedure the most reliable APs with high RSSI are taggedwith the high rank values

22 Normalized Rank Transformation The observed set ofAPs is not fixed over time at every calibration point andconsequently the dimension of the transformed rank vectors


Oine stage

Online stage


New deneddatabase


Trained model

CollectingRSSI

Dimensionalitycheck


Classication using

machine learning

algorithms

Returnposition



NR = 120582Ψ1 120582Ψ2 120582Ψ119872 such that 120582 = 1Ψ119872 (5)



3 Proposed Method








Recall = TPTP + FN

(7)



















min119908120585119887

119869 (119908 120585) = 12 1199082 + 119862 119873sum119894=1

120585119894 (8)


119910119894 = sign (119908119879120601 (119909119894) + 119887) (10)


max120572

119882(120572)= 119873sum119894=1

120572119894 minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895120601 (119909119894)119879 120601 (119909119895)Subject to

119873sum119894=1

119910119894120572119894 = 0 0 le 120572119894 le 119862(11)


119896 (119909 119909119894) = 120601 (119909)119879 120601 (119909119894) (12)


119910119894 = sign( 119873sum119894=1

120572119894119910119894119896 (119909 119909119894) + 119887) (13)


(i) Linear

119870(119909 119909119894) = 119909119879119909119894 (14)



119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205752 ) (16)

(iv) Sigmoid

119870(119909 119909119894) = tanh (1198961 sdot 119909119879119909119894 + 1198962)119889 (17)


120572119894 (119910119894 (119908119879119909119894 + 119887) minus 1 + 120585119894) = 0119887119894120585119894 = (119862 minus 120572119894) 120585119894 = 0 (18)






min119908120585119887

119869 (119908 120585) = 12 1199082 + 1198622119873sum119894=1


119894 = 1 119873 120585119894 ge 0 119894 = 1 119873(19)


max120572

119882(120572)= 119873sum119894=1

120572119894minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895 (119896 (119909 119909119894) + 120575119894119895119862 )Subject to

119873sum119894=1

119910119894120572119894 = 0 120572119894 ge 0 for 119894 = 1 119873

(20)


119910119894( 119873sum119895=1

120572119895119910119895 (119896 (119909 119909119894) + 120575119894119895119888 ) + 119887) minus 1 = 0 (21)



119863119894119895 = radic 119872sum119896=1

(119883119894119896 minus 119883119895119896)2 (22)



119875 (119903 | 1199091 1199092 119909119872) = 119901 (119903) 119875 (1199091 1199092 119909119872 | 119903)119875 (1199091 1199092 119909119872) (23)



119894=1

119875 (119909119894 | 119903) (24)


119875 (119909119894 = V | 119903) = 1radic21205871205752119903 119890

minus(Vminus119906119903)221205752119888 (25)



119867119895 = 120590(119887 + 119873sum119894=1

119908119894119895119909119894) (26)



120590 (119909) = 11 + 119890minus119909 (27)






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6 Conclusion





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Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in




Oine stage

Online stage


New deneddatabase


Trained model

CollectingRSSI

Dimensionalitycheck


Classication using

machine learning

algorithms

Returnposition



NR = 120582Ψ1 120582Ψ2 120582Ψ119872 such that 120582 = 1Ψ119872 (5)



3 Proposed Method








Recall = TPTP + FN

(7)



















min119908120585119887

119869 (119908 120585) = 12 1199082 + 119862 119873sum119894=1

120585119894 (8)


119910119894 = sign (119908119879120601 (119909119894) + 119887) (10)


max120572

119882(120572)= 119873sum119894=1

120572119894 minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895120601 (119909119894)119879 120601 (119909119895)Subject to

119873sum119894=1

119910119894120572119894 = 0 0 le 120572119894 le 119862(11)


119896 (119909 119909119894) = 120601 (119909)119879 120601 (119909119894) (12)


119910119894 = sign( 119873sum119894=1

120572119894119910119894119896 (119909 119909119894) + 119887) (13)


(i) Linear

119870(119909 119909119894) = 119909119879119909119894 (14)



119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205752 ) (16)

(iv) Sigmoid

119870(119909 119909119894) = tanh (1198961 sdot 119909119879119909119894 + 1198962)119889 (17)


120572119894 (119910119894 (119908119879119909119894 + 119887) minus 1 + 120585119894) = 0119887119894120585119894 = (119862 minus 120572119894) 120585119894 = 0 (18)






min119908120585119887

119869 (119908 120585) = 12 1199082 + 1198622119873sum119894=1


119894 = 1 119873 120585119894 ge 0 119894 = 1 119873(19)


max120572

119882(120572)= 119873sum119894=1

120572119894minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895 (119896 (119909 119909119894) + 120575119894119895119862 )Subject to

119873sum119894=1

119910119894120572119894 = 0 120572119894 ge 0 for 119894 = 1 119873

(20)


119910119894( 119873sum119895=1

120572119895119910119895 (119896 (119909 119909119894) + 120575119894119895119888 ) + 119887) minus 1 = 0 (21)



119863119894119895 = radic 119872sum119896=1

(119883119894119896 minus 119883119895119896)2 (22)



119875 (119903 | 1199091 1199092 119909119872) = 119901 (119903) 119875 (1199091 1199092 119909119872 | 119903)119875 (1199091 1199092 119909119872) (23)



119894=1

119875 (119909119894 | 119903) (24)


119875 (119909119894 = V | 119903) = 1radic21205871205752119903 119890

minus(Vminus119906119903)221205752119888 (25)



119867119895 = 120590(119887 + 119873sum119894=1

119908119894119895119909119894) (26)



120590 (119909) = 11 + 119890minus119909 (27)






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12 Bang

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Nice Claup

VIN-ETT

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Cloth Scenery

e Class

S9 Skinfood

Jucy Judy

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L10L11L17L18

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6 Conclusion





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Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in




















min119908120585119887

119869 (119908 120585) = 12 1199082 + 119862 119873sum119894=1

120585119894 (8)


119910119894 = sign (119908119879120601 (119909119894) + 119887) (10)


max120572

119882(120572)= 119873sum119894=1

120572119894 minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895120601 (119909119894)119879 120601 (119909119895)Subject to

119873sum119894=1

119910119894120572119894 = 0 0 le 120572119894 le 119862(11)


119896 (119909 119909119894) = 120601 (119909)119879 120601 (119909119894) (12)


119910119894 = sign( 119873sum119894=1

120572119894119910119894119896 (119909 119909119894) + 119887) (13)


(i) Linear

119870(119909 119909119894) = 119909119879119909119894 (14)



119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205752 ) (16)

(iv) Sigmoid

119870(119909 119909119894) = tanh (1198961 sdot 119909119879119909119894 + 1198962)119889 (17)


120572119894 (119910119894 (119908119879119909119894 + 119887) minus 1 + 120585119894) = 0119887119894120585119894 = (119862 minus 120572119894) 120585119894 = 0 (18)






min119908120585119887

119869 (119908 120585) = 12 1199082 + 1198622119873sum119894=1


119894 = 1 119873 120585119894 ge 0 119894 = 1 119873(19)


max120572

119882(120572)= 119873sum119894=1

120572119894minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895 (119896 (119909 119909119894) + 120575119894119895119862 )Subject to

119873sum119894=1

119910119894120572119894 = 0 120572119894 ge 0 for 119894 = 1 119873

(20)


119910119894( 119873sum119895=1

120572119895119910119895 (119896 (119909 119909119894) + 120575119894119895119888 ) + 119887) minus 1 = 0 (21)



119863119894119895 = radic 119872sum119896=1

(119883119894119896 minus 119883119895119896)2 (22)



119875 (119903 | 1199091 1199092 119909119872) = 119901 (119903) 119875 (1199091 1199092 119909119872 | 119903)119875 (1199091 1199092 119909119872) (23)



119894=1

119875 (119909119894 | 119903) (24)


119875 (119909119894 = V | 119903) = 1radic21205871205752119903 119890

minus(Vminus119906119903)221205752119888 (25)



119867119895 = 120590(119887 + 119873sum119894=1

119908119894119895119909119894) (26)



120590 (119909) = 11 + 119890minus119909 (27)






S5 L8


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12 Bang

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Nice Claup

VIN-ETT

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e Class

S9 Skinfood

Jucy Judy

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6 Conclusion





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Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

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Biomedical Imaging


Advances in


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min119908120585119887

119869 (119908 120585) = 12 1199082 + 119862 119873sum119894=1

120585119894 (8)


119910119894 = sign (119908119879120601 (119909119894) + 119887) (10)


max120572

119882(120572)= 119873sum119894=1

120572119894 minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895120601 (119909119894)119879 120601 (119909119895)Subject to

119873sum119894=1

119910119894120572119894 = 0 0 le 120572119894 le 119862(11)


119896 (119909 119909119894) = 120601 (119909)119879 120601 (119909119894) (12)


119910119894 = sign( 119873sum119894=1

120572119894119910119894119896 (119909 119909119894) + 119887) (13)


(i) Linear

119870(119909 119909119894) = 119909119879119909119894 (14)



119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205752 ) (16)

(iv) Sigmoid

119870(119909 119909119894) = tanh (1198961 sdot 119909119879119909119894 + 1198962)119889 (17)


120572119894 (119910119894 (119908119879119909119894 + 119887) minus 1 + 120585119894) = 0119887119894120585119894 = (119862 minus 120572119894) 120585119894 = 0 (18)






min119908120585119887

119869 (119908 120585) = 12 1199082 + 1198622119873sum119894=1


119894 = 1 119873 120585119894 ge 0 119894 = 1 119873(19)


max120572

119882(120572)= 119873sum119894=1

120572119894minus 12119873sum119894119895=1

119910119894119910119895120572119894120572119895 (119896 (119909 119909119894) + 120575119894119895119862 )Subject to

119873sum119894=1

119910119894120572119894 = 0 120572119894 ge 0 for 119894 = 1 119873

(20)


119910119894( 119873sum119895=1

120572119895119910119895 (119896 (119909 119909119894) + 120575119894119895119888 ) + 119887) minus 1 = 0 (21)



119863119894119895 = radic 119872sum119896=1

(119883119894119896 minus 119883119895119896)2 (22)



119875 (119903 | 1199091 1199092 119909119872) = 119901 (119903) 119875 (1199091 1199092 119909119872 | 119903)119875 (1199091 1199092 119909119872) (23)



119894=1

119875 (119909119894 | 119903) (24)


119875 (119909119894 = V | 119903) = 1radic21205871205752119903 119890

minus(Vminus119906119903)221205752119888 (25)



119867119895 = 120590(119887 + 119873sum119894=1

119908119894119895119909119894) (26)



120590 (119909) = 11 + 119890minus119909 (27)






S5 L8


S4

Kanpachi



S12

L15

S13 L16

S6 L9

VfreshJuice Bar

Physical


12 Bang

Dr Stretch

Nice Claup

VIN-ETT

JampM

Cloth Scenery

e Class

S9 Skinfood

Jucy Judy

L12

S10 L13

S11 L14

L10L11L17L18

3COINS

WCWC

WC

Food amp beverage


Stairs

Escalator

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YIBOYO












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(a)

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(b)

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(c)

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(d)




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6 Conclusion





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(a)


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(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in





119863119894119895 = radic 119872sum119896=1

(119883119894119896 minus 119883119895119896)2 (22)



119875 (119903 | 1199091 1199092 119909119872) = 119901 (119903) 119875 (1199091 1199092 119909119872 | 119903)119875 (1199091 1199092 119909119872) (23)



119894=1

119875 (119909119894 | 119903) (24)


119875 (119909119894 = V | 119903) = 1radic21205871205752119903 119890

minus(Vminus119906119903)221205752119888 (25)



119867119895 = 120590(119887 + 119873sum119894=1

119908119894119895119909119894) (26)



120590 (119909) = 11 + 119890minus119909 (27)






S5 L8


S4

Kanpachi



S12

L15

S13 L16

S6 L9

VfreshJuice Bar

Physical


12 Bang

Dr Stretch

Nice Claup

VIN-ETT

JampM

Cloth Scenery

e Class

S9 Skinfood

Jucy Judy

L12

S10 L13

S11 L14

L10L11L17L18

3COINS

WCWC

WC

Food amp beverage


Stairs

Escalator

Li

YIBOYO












50

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cy

(a)




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(a)

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(b)

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(c)

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(d)




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(a)


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(b)


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(b)





6 Conclusion





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(a)


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(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in




S5 L8


S4

Kanpachi



S12

L15

S13 L16

S6 L9

VfreshJuice Bar

Physical


12 Bang

Dr Stretch

Nice Claup

VIN-ETT

JampM

Cloth Scenery

e Class

S9 Skinfood

Jucy Judy

L12

S10 L13

S11 L14

L10L11L17L18

3COINS

WCWC

WC

Food amp beverage


Stairs

Escalator

Li

YIBOYO












50

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cura

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(a)




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(b)









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(a)

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(b)

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(c)

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(d)




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(a)


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(b)


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(b)





6 Conclusion





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(a)


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(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in








50

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(a)

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(b)

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(c)

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(d)




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6 Conclusion





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(a)


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(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in





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(a)

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(b)

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6 Conclusion





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(a)


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(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in





50

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(a)

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(b)

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(c)

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(b)





6 Conclusion





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(a)


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(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in




0

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(a)

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(b)

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(c)

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(d)




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(b)





6 Conclusion





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(a)


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(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in





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(a)


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(b)


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(b)





6 Conclusion





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(b)




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(a)


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Accu

racy




(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in




































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(b)





6 Conclusion





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(b)




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(a)


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Accu

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(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in


























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(b)





6 Conclusion





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(a)


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80

90

100

110

Accu

racy




(b)



50

60

70

80

90

100

110

Accu

racy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)




50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in















50

60

70

80

90

100

110Ac

cura

cy




(a)

50

60

70

80

90

100

110

Accu

racy





(b)





6 Conclusion





50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)



50

60

70

80

90

100

110

Accu

racy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)




50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in





50

60

70

80

90

100

110Ac

cura

cy




(a)

50

60

70

80

90

100

110

Accu

racy





(b)





6 Conclusion





50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)



50

60

70

80

90

100

110

Accu

racy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)




50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in





50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)



50

60

70

80

90

100

110

Accu

racy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)




50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in





50

60

70

80

90

100

110Ac

cura

cy




(a)


50

60

70

80

90

100

110

Accu

racy




(b)






Acknowledgments



References










































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in







































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in



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An Efficient Normalized Rank Based SVM for Room Level ...downloads.hindawi.com/journals/misy/2017/6268797.pdf · ResearchArticle An Efficient Normalized Rank Based SVM for Room Level