Effective and Generalizable Graph-Based Clustering for

Research ArticleEffective and Generalizable Graph-Based Clustering forFaces in the Wild

Leonardo Chang 1 Airel Perez-Suarez2 and Miguel Gonzalez-Mendoza1

1Tecnologico de Monterrey School of Engineering and Science Monterrey Mexico2Advanced Technologies Application Center CENATAV Havana Cuba

Correspondence should be addressed to Leonardo Chang lchangtecmx

Received 6 October 2019 Accepted 14 November 2019 Published 14 December 2019

Guest Editor Horacio Rostro-Gonzalez

Copyright copy 2019 Leonardo Chang et al+is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Face clustering is the task of grouping unlabeled face images according to individual identities Several applications require thistype of clustering for instance social media law enforcement and surveillance applications In this paper we propose an effectivegraph-based method for clustering faces in the wild +e proposed algorithm does not require prior knowledge of the data +isfact increases the pertinence of the proposed method near to market solutions +e experiments conducted on four well-knowndatasets showed that our proposal achieves state-of-the-art results regarding the clustering performance also showing stability fordifferent values of the input parameter Moreover in these experiments it is shown that our proposal discovers a number ofidentities closer to the real number existing in the data

1 Introduction

With the broad establishment in recent years of videosurveillance systems and the billions of cameras embeddedin smartphones face analysis from images is an increasinglyprevalent task for government agencies and industry alikeWhile face analysis has been an active research area forseveral decades most of the prior work was focused on faceverificationidentification in relatively constrained envi-ronments (eg near-frontal poses and under controlledlighting conditions) [1 2]

Less studied is the problem of clustering faces in un-constrained environments Face clustering is the task ofgrouping unlabeled face images according to the individualidentities present in the data Figure 1 shows an overview ofthe face clustering workflow followed in this paper Severalchallenges must be confronted for clustering faces capturedin unconstrained scenarios In surveillance applications thequality of available face images is typically quite low pre-senting arbitrary poses illumination changes occlusionsand low resolution

In this paper we propose an effective graph-basedmethod for clustering faces in the wild For obtaining face

representations we use a deep convolutional network spe-cifically a 29-layer ResNet (from Residual Neural Network)which produces a 128-dimensional face descriptor Forclustering face descriptors we propose to use a graph-basedclustering algorithmwhose result is later processed in order tojoin homogeneous clusters that could have been divided in theclustering step caused by the sparseness of the input graph

+e main contribution of our proposal is that no as-sumption about the data is used Only a threshold parameteris required to build the initial face graph Regarding thisthreshold our experiments on four well-known face datasetsshowed that it is possible to recommend a single thresholdvalue that will provide clustering results closer to the bestpossible results+is is a significant advantage of the proposedmethod since in real applications usually there are no labeleddata where parameters can be trained Also the number ofidentities discovered by our proposal was closer to the groundtruth number of identities compared to those discovered bythe other evaluated algorithms achieving state-of-the-artclustering results under several evaluation measures

+e rest of the paper is organized as follows Section 2describes some relevant and previous work on face clusteringand graph-based clustering Later in Section 3 our method

HindawiComputational Intelligence and NeuroscienceVolume 2019 Article ID 6065056 12 pageshttpsdoiorg10115520196065056

for clustering faces is detailed Experimental evaluation andcomparison of our method with state-of-the-art algorithmsare reported in Section 4 Section 5 concludes the paper

2 Related Work

21 Face Clustering Face clustering is the task of groupingfaces by their underlying identity It is closely related to theface recognition problem but has several fundamental dif-ferences In face recognition the goal is to verify (1 1comparison against an enrollment face image) or find (1 Ncomparisons against a face gallery) the identity of a givensubject assuming that the identity of subjects in the galleryenrollment is known beforehand +erefore face recogni-tion could be considered a supervised classification task Incontrast face clustering is considered an unsupervisedclassification problem since no labeled data are provided+ere are some works in face clustering considered assemisupervised clustering where several constraints mainlyfrom videos can be converted into must-link and cannot-link constraints and later used to improve face clustering[3 4 5] While a large body of work has been conducted onboth face recognition and data clustering in general thechallenging problem of face clustering is a less studied topicespecially when dealing with a large number of images andsubjects and also for unconstrained scenarios

Cao et al [6] developed a tensor clustering algorithm forface images which can handle the faces with different ex-pressions illuminations block occlusions random pixelcorruptions and various disguises+eir method firstly findsa lower-rank approximation of the original tensor data usingan L1-norm optimization function +en they compute thehigh-order singular value decomposition of the approximatetensor to obtain the final clustering results +e authorsformulate the process of approximation into a framework oftensor principal component analysis with L1-norm

Otto et al [7] developed a version of the rank-orderclustering algorithm of Zhu et al [8] leveraging an ap-proximate nearest neighbor method for improved scalabilityand simplifying the actual clustering procedure to achieveimproved scalability and clustering performance +e au-thors evaluated large-scale clustering performance by

combining the Labeled Faces in theWild (LFW) dataset withup to 123 million of unlabeled images (downloaded from theweb) and clustering the augmented dataset Also clusteringresults on video frames leveraging the YouTube Faces (YTF)database are presented

Shi et al [4] proposed a face clustering method calledConditional Pairwise Clustering (ConPaC) to group a facecollection according to the subject identity ConPaC uses adirect estimation of an adjacencymatrix derived from pairwisesimilarities between faces which are computed over a learneddeep residual network representation +e method is alsoextended to the semisupervised clustering by accepting a set ofpairwise constraints (either must-link or cannot-link assign-ments) on the similarity matrix+e evaluation was performedon two unconstrained face datasets ie LFW and IJB-B

Shi et al [9] proposed a self-learning framework for faceclustering which consists of two major stages imagedecorrelation and self-paced learning +e authors extendedthe two-dimensional whitening reconstruction [10] tohandle local image patches in order to reduce image re-dundancy while preserving significant local features +enthe authors group the semantically similar faces by using aself-paced learning model which is inspired by the followingobservations the learning process of humans goes from easyto complex tasks the prior knowledge of human mightchange with the increase in learned experience and moreprior knowledge usually leads to better prediction accuracy+e method proposed in [9] was evaluated in controlledenvironments in a subset of the Extended Yale-B [11] andAR [12] databases and in unconstrained environments in asubset of the LFW [13]

22 Graph-Based Clustering Clustering is a fundamentaltechnique in pattern recognition and data mining whichaims to organize a set of objects into a set of classes calledclusters+e idea is that objects belonging to the same clusterare similar enough to infer they are of the same type whileobjects belonging to different clusters are different enough toassume they are of different types [14]

Many clustering algorithms have been proposed so fark-means single link CURE (meaning Clustering UsingRepresentatives) DBSCAN (meaning Density-Based Spatial

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Unlabeled image gallery Face clusters

Figure 1 Given an unlabeled face image gallery face clustering is performed by (1) aligning faces (2) computing a face representation foreach face and (3) performing feature clustering in this representation space

2 Computational Intelligence and Neuroscience

Clustering of Applications with Noise) and ExpectationMaximization are well-known examples see [15] Severalclustering algorithms have been successfully applied incontexts like information retrieval [16] bioinformatics [17]medicine [18] image segmentation [19] and cybersecurity[20] among others

An important class of clustering algorithms is graph-based clustering algorithms +ese algorithms represent thecollection of objects as a graph G langV Erang whereV is the setof vertices ie objects of the problem at hand and E is theset of edges and each edge represents the (dis)similarityrelationship existing between a pair of objects G could bedirected or undirected depending on the function used forcomputing the (dis)similarity between the vertices G alsocan be weighted or unweighted in the first case the weightof an edge e isin E is denoted as we

Graph-based algorithms provide a simple way to rep-resent both the objects and the relations among them Alsothey do not impose any restriction to the representationspace of the objects or the (dis)similarity measure betweenobjects these characteristics increase their practical use-fulness Usually graph-based algorithms build the clusteringthrough a covering of the graph G using a special kind ofsubgraph [21] In this context each subgraph or a modi-fication of it is assumed to be a cluster Nevertheless thereare also graph-based algorithms which use other approacheslike optimization [22] or game theory [23] among others

Since in this work we are addressing the clustering offace images and taking into account that we do not wantimages from different subjects to share a cluster we focus onproducing a disjoint clustering Nevertheless other types ofclustering are reported in the literature such as overlappingand fuzzy clustering

23 Clustering Evaluation +e notion of Clustering Eval-uation Measure or Clustering Validity Index emerged as ananswer to the necessity of selecting from a set of clusteringalgorithms and a given dataset the one having the bestperformance It is expected that these validation measurescan be impartial and do not have any preferences on anyparticular clustering algorithm +e evaluation measuresreported so far can be classified as external or internal [14]

External measures evaluate a clustering solution basedon how much this solution resembles a given set of classescommonly known as ground truth which has been manuallylabeled by human experts On the contrary internal mea-sures rely only on the information in the clusters and theyvalidate the solutions taking into account the accomplish-ment of one or more properties which are implicitly orexplicitly measured by the index From these two kinds ofmeasures the most widely used are the external measures

Several external measures have been reported in theliterature entropy [24] Jaccard coefficient [25] andV-measure [26] among others these measures are differentaccording to their mathematical foundations biases andlimitations Also several works have analyzed whichproperties or mathematical constraints should be fulfilled byan evaluation measure [26ndash29] In fact the work of Amigo

et al [27] proposes four formal constraints which cover mostof the previously reported ones

For evaluating the face clustering algorithm proposed inthis work we employ the same measures used in [4] that iswe use the Pairwise Fmeasure [4] and the BCubed Fmeasure[27] +e Pairwise Fmeasure denoted as F-measure is anindex commonly used in the literature for evaluatingclustering results which in turn fulfills two of the fourconstraints introduced in [27] cluster homogeneity andcluster completeness +is measure is defined as follows

F-measure 2 middot PW Precision middot PW RecallPW Precision + PW Recall

(1)

where PW Precision and PW Recall denote the pairwiseprecision and pairwise recall respectively and they aredefined as follows

PW Precision T11

T11 + T10

PW Recall T11

T11 + T01

(2)

where T11 are the number of pairs of objects (images in ourcase) which belong to the same cluster and to the same classT10 is the number of pairs of objects belonging to the samecluster but in different classes and T01 is the number of pairs ofobjects which belong to the same class but to different clusters

On the contrary given that F-measure has a bias to largeclusters we decided to use also the BCubed Fmeasuredenoted as FBcubed which in turn meets the four con-straints proposed in [27] and weights clusters linearly basedon their size +is measure is defined as follows

FBcubed 2 middot Bcubed Precision middot Bcubed RecallBcubed Precision + Bcubed Recall

(3)

where Bcubed Precision and Bcubed Recall denote theBcubed precision and Bcubed recall respectively and theyare defined as follows

Bcubed Precision 1N

middot 1113944N

i11113944jisinCi

Correctness(i j)

Ci

11138681113868111386811138681113868111386811138681113868

Bcubed Recall 1N

middot 1113944N

i11113944jisinLi

Correctness(i j)

Li

11138681113868111386811138681113868111386811138681113868

(4)

where N is the number of objects Ci and Li refer to the ith

cluster and class respectively | middot | refers to the size of the setand Correctness(i j) is 1 if the ith and jth objects belong bothto the same cluster and to the same class otherwise its valueis 0

3 Proposed Face Clustering

31 Face Descriptor In recent years deep convolutionalneural networks have led to a series of breakthroughs forunconstrained face recognition allowing us to deal with faceimages containing extreme poses illumination and reso-lution variations Since we are interested in clustering facesin unconstrained scenarios we use a face representation

Computational Intelligence and Neuroscience 3

based on a deep convolutional neural network +e model isa ResNet network with 29 convolutional layers obtained byDavis [30] It is a version of the ResNet-34 network proposedin [31] where five layers were removed and the number offilters per layer was reduced by half in order to improve theefficiency Figure 2 shows the network architecture of theResNet network used

For a given input face image five landmark points aredetected (ie the corners of the eyes and the bottom of the nose)using the implementation provided in [30] Using the detectedpoints as reference 2D face alignment is performed by usingaffine transformations to obtain a face of 150times150 pixels and025 padding+e aligned image is used as input of the ResNet-29 network and a 128-dimensional face descriptor is obtainedFigure 3 shows an overview of the face representation process

32 Clustering Method Based on the advantages offered bygraph-based algorithms and taking into account that we wantto process a large number of images we decided to adopt theChinese Whispers approach [32] (CW for short) CW is anefficient and effective algorithm for obtaining a partition ofnodes from a weighted and undirected graph In our case theinput graph G is built using the images represented using thedescriptor proposed in Section 31 as vertices and using theEuclidean distance for measuring the distance between twoimages It is important to highlight that in the computation ofthe input graph we only consider those edges whose weightsare less than a predefined threshold Details and discussionabout the impact of this threshold in the clustering results areprovided in Section 43

Intuitively CW works as follows First it assigns adifferent class to each node in the graph After that thenodes are processed for a predefined number of iterations byassigning to each node the strongest class in their neigh-borhood Let v be a vertex +e strongest class in theneighborhood of v is the class whose sum of edges weights tov is maximal among the edges to which v belongs to In caseof ties among classes one of them is randomly selected

A drawback of the CW algorithm is that it can produce alarge number of clusters depending on the sparseness of theinput graph We were able to verify this fact from pre-liminary experiments using experimental datasets In factwhat is more concerning is that this drawback could makeCW divide a homogeneous cluster into two or more clusters

In order to overcome the aforementioned limitation ofCW we introduce a postprocessing phase composed of twosteps which works as follows

Let C C1 C2 CK1113864 1113865 be the set of clusters obtainedby the CW algorithm Let MinCi

and AvgCi with Ci isin C be

the lowest and the average weight of the edges inside clusterCi respectively Let W(CiCj) 1113936 we be the sum of the weightsof all edges e connecting clusters Ci and Cj such thatwe geMinCi

or we geMinCj

First we build from C a graph Gprime langVprime Eprimerang where eachvertex u isin Vprime is a cluster in C and there is an edge betweentwo clusters if they are neighbors Two clusters Ci and Cj areneighbors if W(CiCj)geAvgCi

or W(CiCj)geAvgCj +e in-

tuitive idea behind the construction of this graph is to

identify using a different level of abstraction those clustershighly related that could represent a single class divided intoseveral parts (ie subclusters) Once Gprime is built it is pro-cessed using the same strategy of CW in order to build thefinal set of disjoint clusters Figure 4 shows a graphicaloverview of the main steps of the proposed method

4 Experimental Evaluation

In this section we present the overall evaluation and com-parison of the proposed face clustering method First wedescribe the used datasets and evaluation protocols Secondlywe evaluate the clustering performance of our proposal andcompare it with related works in terms of clustering per-formance and computation time Finally we analyze the effectof threshold setting in the face clustering performance

41Datasets +e experiments were conducted on four well-known face datasets the Labeled Faces in the Wild [13] theYouTube Faces [33] the Extended Yale-B [11] and the AR[34] datasets +ese datasets feature both controlled andnoncontrolled environments with a wide range of varia-tions ie variations on expression illumination poseresolution background occlusions and resolution Figure 5shows some example images from the datasets used

(i) +e Labeled Faces in the Wild dataset (LFT) [13]was designed for studying the problem of un-constrained face recognition +e dataset contains13233 images of faces of celebrities and publicfigures collected from the web Each face is labeledwith the name of the person pictured +ere are1680 of the 5749 people in the dataset who havetwo or more distinct photos +e face imagespresent variations on expression illumination poseresolution and background

(ii) +e YouTube Faces (YTF) database [33] is a largevideo dataset designed for unconstrained face ver-ification in videos Similar to LFW the datasetconsists of videos of celebrities and public figures Itcontains 3425 videos of 1595 subjects with sig-nificant variations on expression illuminationpose resolution and background An average of215 videos is available for each subject +e averagelength of a video clip is 1813 frames For clusteringfaces in individual frames are used

(iii) +e Extended Yale-B face database (Extended YaleDatabase B) [11] was designed to conduct experimentsunder severe illumination variations It contains 38subjects where images were captured under 9 differentposes and 64 different illumination conditions A subsetcontaining the frontal face images under the 9 differentilluminations is also provided In this subset all theimages have been manually aligned and cropped to168times192 pixels In our experiments this subset is used

(iv) +e AR Face database (AR) [34] contains over 3200color images corresponding to 126 subjects (70 menand 56 women) Images in the AR feature frontal


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Figure 2 Network architecture of the ResNet-29 network used for face descriptor extraction+e dotted shortcuts increase dimensions+einput is a 150times150 image and the output is a 128 floating-point values vector

29-layer ResNet feature extractor

128-dimensional face representation

(a) (b) (c) (d) (e)

Figure 3 Face representation overview Given a face image (a) five keypoints are detected (b) which are used to normalize the faceimage +e normalized image (c) serves as input for a ResNet network (d) and its 128-dimensional output (e) is used as facerepresentation

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Figure 4 Proposed face clustering method overview (a) Faces graph Each vertex represents a face and an edge is drawn between faces withdistance less than a given threshold (b) Initial clustering result Each cluster is delimited by dotted lines (c) Graph obtained by consideringeach CW cluster as a vertex and drawing an edge between two clusters if they are neighbors (d) Clustering resulting from processing thegraph in Figure 4(c) using the CW algorithm (e) Final clustering obtained

(a)

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Figure 5 Continued


view faces with different facial expressions illu-mination conditions and occlusions (sunglassesand scarf) In this paper we use the face crops usedin [35] that include 2600 images of 50 subjects (25males and 25 females) manually aligned andcropped to 120times165 pixels

42 Clustering Evaluation In this section we evaluate theclustering performance of our proposal and compare it withother relevant approaches As a baseline we consider k-meansclustering with three different k values ie the true number ofsubjects the number of clusters obtained by our proposal andthe number of clusters obtained by the best-performingapproach different than ours Also as a baseline we considerthe Global Logical-Combinatorial Clustering algorithm

(GLC) [36] which have shown outstanding results in severalapplications and addressed the clustering problem from agraph theory point of view as in our proposal

We also compare the performance of our face clusteringmethod with that reported by two recent face clusteringapproaches ie Approximate Rank-order [7] and ConPaC[4] +e reported results for Approximate Rank-order andConPaC were obtained from their corresponding papers[4 7] where face representations different to that presentedin Section 31 were used In addition we include resultsusing the Approximate Rank-order algorithm with the facedescriptor described in Section 31 +is was not possible forthe case of ConPaC because neither code nor executable ofthe algorithm was publicly available +e rest of the

(c)

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Figure 5 Example face images from the (a) LFW (b) YTF (c) Extended Yale-B and (d) AR datasets Large intra- and interdataset variationsare present in the four datasets eg illumination pose resolution scale background and occlusion


algorithms compared in Tables 1ndash4 use the representationdescribed in Section 31

For k-means we used the C++ OpenCV implementa-tion For GLC we used our own C++ implementation of themethod For the Approximate Rank-order algorithm weused the Python implementation publicly available online(httpsgithubcomvarun-sureshClustering) Since theclustering result of GLC Approximate Rank-order and ourproposal depends on a given distance threshold parameterand given that there is not a known effective method tocompute it we evaluate all the algorithms at several values ofthis parameter and report the best results Further analysis ofthe impact of this parameter in the face clustering result isprovided in Section 43

As it can be seen in Table 1 for the LFW dataset theproposed algorithm performs better than competing algo-rithms for both evaluation measures Our proposal alsoobtains a number of clusters that is closer to the true numberof identities of the LFW dataset On the contrary whenclustering the ResNet-29 face descriptors of the LFW theproposed method outperforms the Approximate Rank-or-der [7] algorithm what suggests that the obtained im-provement resides in the proposed clustering strategyConsequently it would be interesting to evaluate whetherusing the face descriptors utilized by Otto et al in [7] couldimprove the results of our proposed method with respect tothose of Approximate Rank-order

In addition as it can be seen in Table 1 the k-meansalgorithm obtains the lowest results for both F-measure andFBcubed in the LFW dataset Given that LFW dataset ishighly imbalanced [37] and most subjects have only a singleimage this result is expected since k-means is not able tohandle well-imbalanced data [4]

For the experiments conducted in the YTF dataset ourproposal also achieves the highest clustering performance asit can be observed in Table 2 In this case it is worth men-tioning that clustering the ResNet-29 face descriptors with theApproximate Rank-order [7] algorithm outperforms the re-sults reported in [7] when using Approximate Rank-orderwith their own face descriptors+is may suggest that the facedescriptor employed in our work ismore robust to the specificvariations present in the YTF which is a video datasetcaptured in uncontrolled environments On the contrarysince the data are better balanced in the YTF k-meansattained results closer to the rest of the algorithms whencompared to those obtained for the LFW (see Table 1) Similarbehavior is observed in Tables 3 and 4 for the Extended Yale-Band the AR datasets respectively

As it can be seen in Tables 3 and 4 the proposed al-gorithm also performs better than competing algorithms forboth evaluation measures discovering a number of clustersthat is closer to the true number of identities in both theExtended Yale-B and the AR datasets +ese datasets werecaptured in controlled environments with extreme illumi-nation variations and occlusions Since the face descriptordescribed in Section 31 was not trained to deal with suchextreme variations the clustering results are lower specif-ically for the AR dataset (see Table 4)

Table 1 Comparison of clustering results in the Labeled Faces inthe Wild (LFW) database

Method F-measure FBcubed ClustersResNet-29 + k-means (k 5749) 0158 0750 5749ResNet-29 + k-means (k 5761) 0153 0749 5761ResNet-29 + k-means (k 6352) 0143 0749 6352ResNet-29 +GLC 0920 0911 6809Approximate Rank-order [7] 0870 mdash 6508ConPaC [4] 0965 0922 6352ResNet-29 +Approximate Rank-order 0696 0859 6564

ResNet-29 + ours (proposed) 0973 0934 5761+e true number of identities is 5749 and the total number of face images is13233

Table 2 Comparison of clustering results in the YouTube Faces(YTF) database

Method F-measure FBcubed ClustersResNet-29 + k-means (k 1595) 0629 0657 1595ResNet-29 + k-means (k 1894) 0595 0656 1894ResNet-29 + k-means (k 3050) 0494 0610 3050ResNet-29 +GLC 0832 0787 21529Approximate Rank-order [7] 071 mdash mdashConPaC [4] mdash mdash mdashResNet-29 +Approximate Rank-order 0788 0800 5563


Table 3 Comparison of clustering results in the Extended Yale-Bdatabase

Method F-measure FBcubed ClustersResNet-29 + k-means (k 38) 0653 0703 38ResNet-29 + k-means (k 42) 0624 0661 42ResNet-29 + k-means (k 310) 0250 0271 310ResNet-29 +GLC 0737 0787 310Approximate Rank-order [7] mdash mdash mdashConPaC [4] mdash mdash mdashResNet-29 +Approximate Rank-order 0646 0788 125


Table 4 Comparison of clustering results in the AR Face database




It is important to highlight that as shown in Tables 1ndash4our proposed face clusteringmethod was able to discover thenumber of clusters (identities) with better clustering per-formance than the compared algorithms Also it achievedbetter clustering performance results for both evaluationmeasures specifically for the FBcubed which does not boostthe performance of the results as it might be the case of theF-measure since it is based on pairs

43 reshold Impact Evaluation As mentioned in Section32 our proposed face clustering algorithm depends on agiven distance threshold parameter to build the initial facegraph In the case of the Approximate Rank-order [7] al-gorithm a distance threshold is also specified it is thethreshold on similarity to balance between the precision andrecall rate for a particular dataset being clustered [7]

In this section we evaluate the impact of the distancethreshold parameter in the face clustering result of our

proposal across the four datasets Also we contrast theseresults with those obtained when varying the thresholdparameters for the Approximate Rank-order algorithm [7]Both algorithms were tested using several values of thethreshold and the results for the F-measure and FBcubedmetrics are reported in Figure 6

As it can be seen in Figure 6 the proposed face clusteringmethod achieved its best clustering results for very similarthreshold values ie 040 and 045+is behavior is observedfor the four datasets (ie LFW YTF EYaleB and AR) andthe two evaluation measures (ie F-measure and FBcubed)+e same behavior was not observed for the ApproximateRank-order algorithm [7] where the best results were ob-tained for very different threshold values It is worth notingthat the four datasets used in the experiments have differentconditions and characteristics eg large interdataset vari-ations of illumination pose resolution scale backgroundand occlusion see Section 41 +erefore it can be suggestedthat our proposed method is able to scale better for unseen

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Figure 6 Clustering performance for different threshold values on the LFW YTF Extended Yale-B and AR datasets obtained by (a) ourproposal and (b) the Approximate Rank-order algorithm [7] evaluated using F-measure and performance obtained by (c) our proposal and(d) the Approximate Rank-order algorithm [7] evaluated using FBcubed


data In other words when using our proposed algorithm onunseen data threshold values between 040 and 045 areexpected to obtain clustering results closer to its best possibleresults However for the Approximate Rank-order algo-rithm [7] it would be necessary to exhaustively test whichthreshold fits better for the new data +is is a significantadvantage of the proposed method since in real applicationsusually there are no labeled data where the threshold can betrained

44 Computation Time Evaluation In this section wecompare the computation time required to process each ofthe experimental datasets used in Section 42 by the algo-rithms analyzed in the previous sections Since in [7] theApproximate Rank-order algorithm is evaluated using adifferent strategy for the extraction of face features and withthe aim of focusing the analysis only on the computationtime of clustering all the clustering algorithms were testedwith the same face feature descriptor ie the ResNet-29 facedescriptor introduced in Section 31 Using the same inputdata guarantees that the resulting time differences will begiven only by the differences concerning the clusteringalgorithm

Table 5 shows the computation time of each of theevaluated algorithms for clustering each of the experimentaldatasets the shortest time for each dataset is highlighted

As can be seen in Table 5 except for the YTF dataset theclustering time of the proposed algorithm is close to thefastest algorithm including k-means algorithm that has asimple clustering strategy+is fact shows that in addition toachieving the best clustering performance our proposal alsopresents computation times comparable to the rest of thestate-of-the-art algorithms Although the time for clusteringYTF is worse than the rest of the algorithms in that samedataset our algorithm achieves significantly better results

5 Conclusions

In this paper for the problem of clustering faces in the wildwe have proposed an effective graph-based method whichuses as face descriptor a ResNet-29 deep convolutionalnetwork +e proposed method outperforms several recentwell-known clustering algorithms in the LFW YTF EYaleBand AR datasets +e algorithm presented in this paper doesnot make any assumption about the face dataset to be

clustered Only a threshold parameter is required to buildthe initial face graph nevertheless in our experiments wewere able to find single threshold values in which clusteringresults are closer to the best possible results Given that thefour datasets used in our experiments were captured indifferent conditions and contexts it can be suggested that theproposed method is able to scale better than the othercompared methods +is is a significant advantage of theproposed face clustering method since in many real ap-plications there are no labeled data available where pa-rameters can be trained

Our future work will include the exploration of in-corporating pairwise constraints ie must-link and cannot-link relations in order to improve face clustering perfor-mance +is kind of constraint is very relevant for severalapplications for example faces tracked through a videosequence semilabeled datasets and others

Data Availability

+eLabeled Faces in theWild data used to support the findingsof this study are available at the authorsrsquo webpage at httpvis-wwwcsumassedulfw +ese prior studies (and datasets) arecited at relevant places within the text as reference [13] +eYouTube Faces data used to support the findings of this studyare available at the authorsrsquo web page at httpswwwcstauacilwolfytfaces +ese prior studies (and datasets) are cited atrelevant places within the text as reference [33] +e ExtendedYale-B data used to support the findings of this study areavailable at the authorsrsquo web page at httpvisionucsdeduiskwakExtYaleDatabaseExtYaleBhtml +ese prior studies(and datasets) are cited at relevant places within the text asreference [11]+e AR data used to support the findings of thisstudy are available at the authorsrsquo web page at (httpwww2eceohio-stateedu~aleixARdatabasehtml) +ese prior stud-ies (and datasets) are cited at relevant places within the text asreference [34]

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors wish to express their gratitude to the Tec-nologico de Monterrey and also to the Applied TechnologiesApplication Center

References

[1] B Lahasan S L Lutfi and R San-Segundo ldquoA survey ontechniques to handle face recognition challenges occlusionsingle sample per subject and expressionrdquo Artificial In-telligence Review vol 52 no 2 pp 949ndash979 2019

[2] Y Martindez-Diaz L S Luevano H Mendez-VazquezM Nicolas-Diaz L Chang and M Gonzalez-MendozaldquoShufflefacenet a lightweight face architecture for efficientand highly-accurate face recognitionrdquo in Proceedings of theIEEE International Conference on Computer Vision (ICCV)Workshops Seoul Korea October 2019

Table 5 Computation time comparison (HH MMSSms)

Method LFW YTF EYaleB ARNumber of images 13233 621126 2414 2600

ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289

ResNet-29 +ApproximateRank-order

00 04 06712

03 26 34220

00 00 29916

00 00 33099

ResNet-29 + ours(proposed)

00 00 16035

04 41 31604

00 00 00314

00 00 00267


[3] X Cao C Zhang C Zhou H Fu and H Foroosh ldquoCon-strained multi-view video face clusteringrdquo IEEE Transactionson Image Processing vol 24 no 11 pp 4381ndash4393 2015

[4] Y Shi C Otto and A K Jain ldquoFace clustering representationand pairwise constraintsrdquo IEEE Transactions on InformationForensics and Security vol 13 no 7 pp 1626ndash1640 2018

[5] C Zhou C Zhang X Li G Shi and X Cao ldquoVideo faceclustering via constrained sparse representationrdquo in Pro-ceedings of the 2014 IEEE International Conference on Mul-timedia and Expo (ICME) Chengdu China July 2014

[6] X Cao XWei Y Han and D Lin ldquoRobust face clustering viatensor decompositionrdquo IEEE Transactions on Cyberneticsvol 45 no 11 pp 2546ndash2557 2015

[7] C Otto D Wang and A K Jain ldquoClustering millions of facesby identityrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 40 no 2 pp 289ndash303 2018

[8] C Zhu F Wen and J Sun ldquoA rank-order distance basedclustering algorithm for face taggingrdquo in Proceedings of the2011 IEEE Conference on Computer Vision and Pattern Rec-ognition CVPRrsquo11 pp 481ndash488 IEEE Computer SocietyWashington DC USA 2011

[9] X Shi Z Guo F Xing J Cai and L Yang ldquoSelf-learning forface clusteringrdquo Pattern Recognition vol 79 pp 279ndash2892018

[10] X Shi Z Guo F Nie L Yang J You and D Tao ldquoTwo-dimensional whitening reconstruction for enhancing ro-bustness of principal component analysisrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 38 no 10pp 2130ndash2136 2016

[11] K-C Lee J Ho and J David ldquoKriegman Acquiring linearsubspaces for face recognition under variable lightingrdquo IEEETransactions on Pattern Analysis and Machine Intelligencevol 27 no 5 pp 684ndash698 2005

[12] A Martınez and R Benavente ldquo+e AR Face DatabaserdquoTechnical Report 24 Computer Vision Center BellateraBarcelona Spain 1998 httpscholargooglecomscholarhlenamplrampclientfirefox-aampcites1504264687621469812

[13] G B Huang and M Ramesh ldquoTamara berg and erik learned-miller Labeled faces in the wild a database for studying facerecognition in unconstrained environmentsrdquo Technical Re-port 07-49 University of Massachusetts Amherst MA USAOctober 2007

[14] D Pfitzner R Leibbrandt and D Powers ldquoCharacterizationand evaluation of similarity measures for pairs of clusteringsrdquoKnowledge and Information Systems vol 19 no 3 pp 361ndash394 2009

[15] A K Jain M N Murty and P J Flynn ldquoData clustering areviewrdquo ACM Computing Surveys vol 31 no 3 pp 264ndash3231999

[16] S Kumar and K K Bhatia ldquoClustering based approach fornovelty detection in text documentsrdquo Asian Journal ofComputer Science and Technology vol 8 no 2 pp 116ndash1212019

[17] A M Mabu R Prasad and R Yadav ldquoGene expressiondataset classification using artificial neural network andclustering-based feature selectionrdquo International Journal ofSwarm Intelligence Research (IJSIR) vol 11 no 1 pp 65ndash862020

[18] R Delshi Howsalya Devi A Bai and N Nagarajan ldquoA novelhybrid approach for diagnosing diabetes mellitus using far-thest first and support vector machine algorithmsrdquo ObesityMedicine vol 17 Article ID 100152 2019

[19] V S Kumar S A Sivaprakasam R Naganathan andS Kavitha ldquoFast K-Means technique for hyper-spectral image

segmentation by multiband reductionrdquo Pollack Periodicavol 14 no 3 pp 201ndash212 2019

[20] Z Felfli R George K Shujaee and M Kerwat ldquoCommunitydetection and unveiling of hierarchy in networks a density-based clustering approachrdquo Applied Network Science vol 4no 1 pp 1ndash8 2019

[21] A Perez-Suarez J F Martınez-Trinidad J A Carrasco-Ochoa and J E Medina-Pagola ldquoOClustR a new graph-based algorithm for overlapping clusteringrdquoNeurocomputingvol 121 pp 234ndash247 2013

[22] L Chaudhary and B Singh ldquoCommunity detection usingmaximizing modularity and similarity measures in socialnetworksrdquo in Smart Systems and IoT Innovations in Com-puting pp 197ndash206 Springer Berlin Germany 2020

[23] V Moscato A Picariello and G Sperlı ldquoCommunity de-tection based on game theoryrdquo Engineering Applications ofArtificial Intelligence vol 85 pp 773ndash782 2019

[24] M Steinbach G Karypis and V Kumar ldquoA comparison ofdocument clustering techniquesrdquo in Proceedings of the SixthACM SIGKDD International Conference on Knowledge Dis-covery and Data Mining Boston MA USA August 2000

[25] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent InformationSystems vol 17 no 2-3 pp 107ndash145 2001

[26] A Rosenberg J Hirschberg and V-measure ldquoA conditionalentropy-based external cluster evaluation measurerdquo in Pro-ceedings of the 2007 Joint Conference on Empirical Methods inNatural Language Processing and Computational NaturalLanguage Learning (EMNLP-CoNLL) pp 410ndash420 PragueCzech Republic June 2007

[27] E Amigo J Gonzalo J Artiles and F Verdejo ldquoA com-parison of extrinsic clustering evaluation metrics based onformal constraintsrdquo Information Retrieval vol 12 no 4pp 461ndash486 2009

[28] B E Dom ldquoAn information-theoretic external cluster-val-idity measurerdquo in Proceedings of the Eighteenth Conference onUncertainty in Artificial Intelligence UAIrsquo02 pp 137ndash145Morgan Kaufmann Publishers Inc San Francisco CA USA2002

[29] M Meilǎ ldquoComparing clusterings an axiomatic viewrdquo inProceedings of the 22Nd International Conference on MachineLearning ICMLrsquo05 pp 577ndash584 ACM New York NY USA2005

[30] E K Davis ldquoDlib-ml a machine learning toolkitrdquo Journal ofMachine Learning Research vol 10 pp 1755ndash1758 2009

[31] K He X Zhang S Ren and J Sun ldquoDeep residual learningfor image recognitionrdquo in Proceedings of the 2016 IEEEConference on Computer Vision and Pattern Recognition(CVPR) pp 770ndash778 Las Vegas NV USA June 2016

[32] C Biemann ldquoChinese Whispers an efficient graph clusteringalgorithm and its application to natural language processingproblemsrdquo in Proceedings of the First Workshop on GraphBased Methods for Natural Language Processing TextGraphs-1 pp 73ndash80 New York NY USA June 2006

[33] L Wolf T Hassner and I Maoz ldquoFace recognition in un-constrained videos with matched background similarityrdquo inProceedings of the IEEE Conference on Computer VisionPattern Recognition Colorado Springs CO USA June 2011

[34] A M Martinez and R Benavente ldquo+e AR Face DatabaserdquoTechnical report CVC New Delhi India 1998

[35] A M Martinez and A C Kak ldquoPCA versus LDArdquo IEEETransactions on Pattern Analysis and Machine Intelligencevol 23 no 2 pp 228ndash233 February 2001


[36] G Sanchez-Dıaz and J Ruiz-Shulcloper ldquoMID mining alogical combinatorial pattern recognition approach to clus-tering in large data setsrdquo in Proceedings of the 5th Iber-oamerican Symposium on Pattern Recognition pp 475ndash483Lisbon Portugal September 2000

[37] O Loyola-Gonzalez M A Medina-Perez J F Martınez-Trinidad et al ldquoPBC4cip a new contrast pattern-basedclassifier for class imbalance problemsrdquo Knowledge-BasedSystems vol 115 pp 100ndash109 2017


Computer Games Technology

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Advances in

FuzzySystems


Volume 2018


ReconfigurableComputing



Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

thinspArtificial Intelligence

Hindawiwwwhindawicom Volumethinsp2018


Civil EngineeringAdvances in


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia


Biomedical Imaging



Engineering Mathematics


RoboticsJournal of



Computational Intelligence and Neuroscience


Mathematical Problems in Engineering

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018


Human-ComputerInteraction

Advances in


Scientic Programming

Submit your manuscripts atwwwhindawicom

for clustering faces is detailed Experimental evaluation andcomparison of our method with state-of-the-art algorithmsare reported in Section 4 Section 5 concludes the paper

2 Related Work

21 Face Clustering Face clustering is the task of groupingfaces by their underlying identity It is closely related to theface recognition problem but has several fundamental dif-ferences In face recognition the goal is to verify (1 1comparison against an enrollment face image) or find (1 Ncomparisons against a face gallery) the identity of a givensubject assuming that the identity of subjects in the galleryenrollment is known beforehand +erefore face recogni-tion could be considered a supervised classification task Incontrast face clustering is considered an unsupervisedclassification problem since no labeled data are provided+ere are some works in face clustering considered assemisupervised clustering where several constraints mainlyfrom videos can be converted into must-link and cannot-link constraints and later used to improve face clustering[3 4 5] While a large body of work has been conducted onboth face recognition and data clustering in general thechallenging problem of face clustering is a less studied topicespecially when dealing with a large number of images andsubjects and also for unconstrained scenarios

Cao et al [6] developed a tensor clustering algorithm forface images which can handle the faces with different ex-pressions illuminations block occlusions random pixelcorruptions and various disguises+eir method firstly findsa lower-rank approximation of the original tensor data usingan L1-norm optimization function +en they compute thehigh-order singular value decomposition of the approximatetensor to obtain the final clustering results +e authorsformulate the process of approximation into a framework oftensor principal component analysis with L1-norm

Otto et al [7] developed a version of the rank-orderclustering algorithm of Zhu et al [8] leveraging an ap-proximate nearest neighbor method for improved scalabilityand simplifying the actual clustering procedure to achieveimproved scalability and clustering performance +e au-thors evaluated large-scale clustering performance by

combining the Labeled Faces in theWild (LFW) dataset withup to 123 million of unlabeled images (downloaded from theweb) and clustering the augmented dataset Also clusteringresults on video frames leveraging the YouTube Faces (YTF)database are presented

Shi et al [4] proposed a face clustering method calledConditional Pairwise Clustering (ConPaC) to group a facecollection according to the subject identity ConPaC uses adirect estimation of an adjacencymatrix derived from pairwisesimilarities between faces which are computed over a learneddeep residual network representation +e method is alsoextended to the semisupervised clustering by accepting a set ofpairwise constraints (either must-link or cannot-link assign-ments) on the similarity matrix+e evaluation was performedon two unconstrained face datasets ie LFW and IJB-B

Shi et al [9] proposed a self-learning framework for faceclustering which consists of two major stages imagedecorrelation and self-paced learning +e authors extendedthe two-dimensional whitening reconstruction [10] tohandle local image patches in order to reduce image re-dundancy while preserving significant local features +enthe authors group the semantically similar faces by using aself-paced learning model which is inspired by the followingobservations the learning process of humans goes from easyto complex tasks the prior knowledge of human mightchange with the increase in learned experience and moreprior knowledge usually leads to better prediction accuracy+e method proposed in [9] was evaluated in controlledenvironments in a subset of the Extended Yale-B [11] andAR [12] databases and in unconstrained environments in asubset of the LFW [13]

22 Graph-Based Clustering Clustering is a fundamentaltechnique in pattern recognition and data mining whichaims to organize a set of objects into a set of classes calledclusters+e idea is that objects belonging to the same clusterare similar enough to infer they are of the same type whileobjects belonging to different clusters are different enough toassume they are of different types [14]

Many clustering algorithms have been proposed so fark-means single link CURE (meaning Clustering UsingRepresentatives) DBSCAN (meaning Density-Based Spatial

1 F

ace a

lignm

ent

2 D

eep

face

des

crip

tor

3 G

raph

-bas

ed cl

uste

ring

Unlabeled image gallery Face clusters

Figure 1 Given an unlabeled face image gallery face clustering is performed by (1) aligning faces (2) computing a face representation foreach face and (3) performing feature clustering in this representation space












(1)


PW Precision T11

T11 + T10

PW Recall T11

T11 + T01

(2)




(3)


Bcubed Precision 1N

middot 1113944N

i11113944jisinCi

Correctness(i j)

Ci

11138681113868111386811138681113868111386811138681113868

Bcubed Recall 1N

middot 1113944N

i11113944jisinLi

Correctness(i j)

Li

11138681113868111386811138681113868111386811138681113868

(4)















or we geMinCj













7times

7 co

nv 3

22

3times

3 co

nv 2

56

2

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 1

28

2

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 6

4 2

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 6

4

3times

3 co

nv 6

4

Pool

2

Ave

rage

poo

l

fc 1

28

Inpu

t im

age

150

times15

0 px




(a) (b) (c) (d) (e)


06

06

2

0501

02

02

02

035

0601

01

06

02

02025

035

028

04

04

04

04

03

03

05

05

15

13

12

9

5

7

1

3

4

10

11

8

146

(a)

06

2

01

01

06

06

0202

02025

035

028

06

05

01

02

02

040

40

305

035

04

04

03

05

15

13

12

14

9

5

6

7

CB

CC

CA

CD

1

3

4

10

11

8

(b)

035

CB

CACD

CC

(c)

035CB

CACD

CC

(d)

Figure 4 Continued


01

06

06

05

01

02

02

02

035

060106

02

02

025

035

028

04

04

04

04

03

03

05

05

146

CB

CC

CA

2

15

13

12

9

5

7

1

3

4

10

11

8

(e)


(a)

(b)

Figure 5 Continued






(c)

(d)



























F-measure

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(a)

F-measure

0

025

05

075

1

Threshold005 01 015 02 025 03 05 07 09 11 13 15 17

YTFAR

LFWEYaleB

(b)

FBcubed

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(c)

FBcubed

0

025

05

075

1

Threshold005 01 015 02 04 06 08 10 12 14 16 18

YTFAR

LFWEYaleB

(d)







5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in














(1)


PW Precision T11

T11 + T10

PW Recall T11

T11 + T01

(2)




(3)


Bcubed Precision 1N

middot 1113944N

i11113944jisinCi

Correctness(i j)

Ci

11138681113868111386811138681113868111386811138681113868

Bcubed Recall 1N

middot 1113944N

i11113944jisinLi

Correctness(i j)

Li

11138681113868111386811138681113868111386811138681113868

(4)















or we geMinCj













7times

7 co

nv 3

22

3times

3 co

nv 2

56

2

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 1

28

2

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 6

4 2

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 6

4

3times

3 co

nv 6

4

Pool

2

Ave

rage

poo

l

fc 1

28

Inpu

t im

age

150

times15

0 px




(a) (b) (c) (d) (e)


06

06

2

0501

02

02

02

035

0601

01

06

02

02025

035

028

04

04

04

04

03

03

05

05

15

13

12

9

5

7

1

3

4

10

11

8

146

(a)

06

2

01

01

06

06

0202

02025

035

028

06

05

01

02

02

040

40

305

035

04

04

03

05

15

13

12

14

9

5

6

7

CB

CC

CA

CD

1

3

4

10

11

8

(b)

035

CB

CACD

CC

(c)

035CB

CACD

CC

(d)

Figure 4 Continued


01

06

06

05

01

02

02

02

035

060106

02

02

025

035

028

04

04

04

04

03

03

05

05

146

CB

CC

CA

2

15

13

12

9

5

7

1

3

4

10

11

8

(e)


(a)

(b)

Figure 5 Continued






(c)

(d)



























F-measure

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(a)

F-measure

0

025

05

075

1

Threshold005 01 015 02 025 03 05 07 09 11 13 15 17

YTFAR

LFWEYaleB

(b)

FBcubed

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(c)

FBcubed

0

025

05

075

1

Threshold005 01 015 02 04 06 08 10 12 14 16 18

YTFAR

LFWEYaleB

(d)







5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in













or we geMinCj













7times

7 co

nv 3

22

3times

3 co

nv 2

56

2

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 1

28

2

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 6

4 2

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 6

4

3times

3 co

nv 6

4

Pool

2

Ave

rage

poo

l

fc 1

28

Inpu

t im

age

150

times15

0 px




(a) (b) (c) (d) (e)


06

06

2

0501

02

02

02

035

0601

01

06

02

02025

035

028

04

04

04

04

03

03

05

05

15

13

12

9

5

7

1

3

4

10

11

8

146

(a)

06

2

01

01

06

06

0202

02025

035

028

06

05

01

02

02

040

40

305

035

04

04

03

05

15

13

12

14

9

5

6

7

CB

CC

CA

CD

1

3

4

10

11

8

(b)

035

CB

CACD

CC

(c)

035CB

CACD

CC

(d)

Figure 4 Continued


01

06

06

05

01

02

02

02

035

060106

02

02

025

035

028

04

04

04

04

03

03

05

05

146

CB

CC

CA

2

15

13

12

9

5

7

1

3

4

10

11

8

(e)


(a)

(b)

Figure 5 Continued






(c)

(d)



























F-measure

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(a)

F-measure

0

025

05

075

1

Threshold005 01 015 02 025 03 05 07 09 11 13 15 17

YTFAR

LFWEYaleB

(b)

FBcubed

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(c)

FBcubed

0

025

05

075

1

Threshold005 01 015 02 04 06 08 10 12 14 16 18

YTFAR

LFWEYaleB

(d)







5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




7times

7 co

nv 3

22

3times

3 co

nv 2

56

2

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 1

28

2

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 1

28

3times

3 co

nv 2

56

3times

3 co

nv 2

56

3times

3 co

nv 6

4 2

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 6

4

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 3

2

3times

3 co

nv 6

4

3times

3 co

nv 6

4

Pool

2

Ave

rage

poo

l

fc 1

28

Inpu

t im

age

150

times15

0 px




(a) (b) (c) (d) (e)


06

06

2

0501

02

02

02

035

0601

01

06

02

02025

035

028

04

04

04

04

03

03

05

05

15

13

12

9

5

7

1

3

4

10

11

8

146

(a)

06

2

01

01

06

06

0202

02025

035

028

06

05

01

02

02

040

40

305

035

04

04

03

05

15

13

12

14

9

5

6

7

CB

CC

CA

CD

1

3

4

10

11

8

(b)

035

CB

CACD

CC

(c)

035CB

CACD

CC

(d)

Figure 4 Continued


01

06

06

05

01

02

02

02

035

060106

02

02

025

035

028

04

04

04

04

03

03

05

05

146

CB

CC

CA

2

15

13

12

9

5

7

1

3

4

10

11

8

(e)


(a)

(b)

Figure 5 Continued






(c)

(d)



























F-measure

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(a)

F-measure

0

025

05

075

1

Threshold005 01 015 02 025 03 05 07 09 11 13 15 17

YTFAR

LFWEYaleB

(b)

FBcubed

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(c)

FBcubed

0

025

05

075

1

Threshold005 01 015 02 04 06 08 10 12 14 16 18

YTFAR

LFWEYaleB

(d)







5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




01

06

06

05

01

02

02

02

035

060106

02

02

025

035

028

04

04

04

04

03

03

05

05

146

CB

CC

CA

2

15

13

12

9

5

7

1

3

4

10

11

8

(e)


(a)

(b)

Figure 5 Continued






(c)

(d)



























F-measure

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(a)

F-measure

0

025

05

075

1

Threshold005 01 015 02 025 03 05 07 09 11 13 15 17

YTFAR

LFWEYaleB

(b)

FBcubed

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(c)

FBcubed

0

025

05

075

1

Threshold005 01 015 02 04 06 08 10 12 14 16 18

YTFAR

LFWEYaleB

(d)







5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








(c)

(d)



























F-measure

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(a)

F-measure

0

025

05

075

1

Threshold005 01 015 02 025 03 05 07 09 11 13 15 17

YTFAR

LFWEYaleB

(b)

FBcubed

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(c)

FBcubed

0

025

05

075

1

Threshold005 01 015 02 04 06 08 10 12 14 16 18

YTFAR

LFWEYaleB

(d)







5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




























F-measure

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(a)

F-measure

0

025

05

075

1

Threshold005 01 015 02 025 03 05 07 09 11 13 15 17

YTFAR

LFWEYaleB

(b)

FBcubed

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(c)

FBcubed

0

025

05

075

1

Threshold005 01 015 02 04 06 08 10 12 14 16 18

YTFAR

LFWEYaleB

(d)







5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









F-measure

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(a)

F-measure

0

025

05

075

1

Threshold005 01 015 02 025 03 05 07 09 11 13 15 17

YTFAR

LFWEYaleB

(b)

FBcubed

0

025

05

075

1

Threshold025 030 035 040 045 050 055

YTFAR

LFWEYaleB

(c)

FBcubed

0

025

05

075

1

Threshold005 01 015 02 04 06 08 10 12 14 16 18

YTFAR

LFWEYaleB

(d)







5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








5 Conclusions




Data Availability




Acknowledgments


References





ResNet-29 + k-means 00 01 07663

00 14 01229

00 00 00110

00 00 00223

ResNet-29 +GLC 00 00 15638

04 36 39981

00 00 00276

00 00 00289


00 04 06712

03 26 34220

00 00 29916

00 00 33099


00 00 16035

04 41 31604

00 00 00314

00 00 00267













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in












Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




Documents

Effective and Generalizable Graph-Based Clustering for