Human Mobility Model Establishment with Hidden Markov Model · Human Mobility Model Establishment with Hidden Markov Model SEUNG HO RYU Hongik University Department of Computer Engineering

Human Mobility Model Establishment with Hidden Markov Model

SEUNG HO RYUHongik University

Department of Computer Engineering72-1, Sangsu, Mapo, Seoul

[email protected]

HA YOON SONGHongik University

Department of Computer Engineering72-1, Sangsu, Mapo, Seoul

[email protected]

Abstract: Mobility Models of humans is one of the essential knowledge for mobile computing, location basedservice, and any other related fields. The human mobility models increasingly being complicated according to theexpansion of cities and development of life style. Nowadays, portable devices can embed GPS or other positioningfunctionality and thus the mobility pattern can easily be collected. In this paper we will show the process toconstruct human mobility models from positioning data set collected by authors. As a preprocessing, notablepositions of human mobility was identified from the positioning data sets. Hidden Markov Model was introducedin order to establish human mobility models. Baum-Welch algorithm successfully derives human mobility modelswith UMDHMM tools. We believe that we partially automated the process for human mobility model construction.

Key–Words: Human Mobility Model, Positioning Data, Hidden Markov Model, Human Location Clustering

1 IntroductionA lot of research has been conducted in order to un-derstand human mobility patterns. In addition, a lot ofresearch area requires sophisticated human mobilitymodel. For example, Mobile ad-hoc network requiresrealistic mobility model. As well, virus dissemina-tion on mobile devices, spreading of contagious dis-ease, air pollution and human mobility pattern, juve-nile movement pattern and harmful environment, arenotable ones which require human mobility models.Many parameters required to explain human mobilitypattern. The human mobility pattern is clearly intoindividual ones and aggregated ones. Individual mo-bility clearly depends on personality. For example,people prefer highways instead of local roads.Sociallevel is another parameter, and students usually asideby home or its neighboring area with radius of 1Km.An example of group mobility is clearly found in mil-itary. One of the notable result of recent research ex-plains that human mobility pattern can be predictedwith probability up to 93% [1].

In this paper, a human mobility model describinghuman mobility pattern will be presented. Our aim isto understand human mobility by presenting a processof human mobility model generation. From the set ofpositioning data of authors, we will demonstrate theprocess to extract human mobility model with Hid-den Markov Model. The positioning data has essen-tial elements of < latitude, longitude, time > andthe set of the elements composes the positioning dataset. We will describe the basics of Hidden MarkovModel (HMM) in section 2. Section 3 shows the pro-cess of human mobility generation from the position-

ing data set. Section 4 will present human mobilitymodel and 5 will conclude this paper with possiblefuture researches.

2 Theoretical Background: HiddenMarkov Model

Positioning data set contains positions as well astimestamps of positions thus requires multidimen-sional processing. Thus Markov model is one of thecandidate for human mobility model while the multi-dimensionality of positioning data set is a well fit forHidden Markov Model which is capable to representcomplex models. Thus human mobility model basedon Hidden Markov Model [2] is developed in order todescribe complex patterns and predictions of patterns.

We can produce two different model using HMM,location oriented model and time oriented model. Aswell, tools for HMM can be applied for automatedproduction of models.

HMM has three parameters, and the process forseeking optimal values for parameters, so called ma-chine learning, is the major problem to be solved. Thethree parameters of HMM are:

Θ = (A,B, π)

• State Transition Probability A

aij = P (qt + 1 = sj |qt = si), 1 ≤ i, j ≤ nn∑

j=1

aij = 1

Recent Researches in Information Science and Applications

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Figure 1: Result of clustering of KHU’s data

Figure 2: Result of clustering SHY’s positioning data

where aij stands for the transition probabilityfrom state si at time t to sj at time t+1, and nstands for the number of states.

• Observation Probability B

bj(vt) = P (ot = vt|qt = sj), i ≤ j ≤ n, i ≤ k ≤ mm∑i=1

bj(vt) = 1

where bj(vk) stands for the probability, at statesj , a symbol vk is observed, and m stands for thenumber of symbol.

• Initial State Probability Vector π

πi = P (q1 = si), i ≤ i ≤ n

n∑i=1

πt = 1

where πi stands for initial probability of HMMat state si.

Θ must be found optimally in order to describe thereal phenomena accurately.

In order to construct HMM, we need to solve thefollowing three problems.• Calculating observation probability from obser-

vation sequence• Deriving state sequence from observation se-

quence• Construction HMM from observation sequence

The problem solving process requires huge amount ofcomputation. The following generation algorithms areused for HMM construction, while the last has beenregarded as the best.


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• Probability Evaluation with Forward-backwardalgorithms

• Decoding with Viterbi algorithm• Hidden-Learning with Baum-Welch

In this paper, positioning data set is used as observa-tion sequence of HMM representing human mobilitymodel.

3 Model Generation Process3.1 Positioning Data Set

We collected positioning data for person with variousmobile devices such as iPhone, Android based smart-phones, GARMIN 62s [3] and Garmin EDGE 800 [4].Each device has different policy for positioning datacollection and of course has environmental errors ofpositioning. Some special cases, we cannot collectany positioning data at specific locations, due to therestrictions of positioning system, such as at under-ground area or near iron wired bridges.

3.2 Mobility Model Generation

Figure 1 shows the trail of positioning data setfor a specific person, named KHU, with GoogleEarth [5]. We used UMDHMM for HMM construc-tion. UMDHMM [6] supports Forward-backward,Viterbi and Baum-Welch algorithms for HMM con-struction. We need to preprocess positioning dataset in order to use UMDHMM, since UMDHMM re-quires observation sequence as its inputs. We need tofigure out the frequent places of human mobility andnamed the places as clusters. The preprocessing hasfollowing substages:

• Scan the positioning points and limit the area ofthem

• Initialize clusters with points inside a cluster.• Calculate the number of points in clusters.• Determine the center of clusters with probability

distributions.• Calibrate the probability of a point belonging to

a cluster with velocity of the point.• Iterate EM clustering algorithm.• Generate the observed sequence of the clusters• Generate an estimated Hidden Markov Model by

UMDHMM

First, we need to figure out the total mobility re-gion with maximum and minimum positions. Usinglatitude and longitude, Figure 1 also shows the identi-fied region which has area of 28 km by 15 km, and thecombination of total region and mobile pattern. Thedetails of cluster identification can be found in [7].The final cluster results for KHU are also in Figure 1

and details of cluster information can be found in Ta-ble 1.

Each cluster of KHU can be mapped on realplaces as follows:

- Cluster 1 : University- Cluster 2 : Home- Cluster 3 : Bucheon city- Cluster 4 : Myong-dong, Central Seoul- Cluster 5 : Kimpo Airport- Cluster 6 : Gangman, Southern Seoul

From Table 1, six clusters were identified by theduration of stable points. Clusters 1 and 2 have moredata than other clusters as well as longer durationand frequent visits for these clusters. Other clustershave smaller area with smaller number of positioningpoints. For sure, table 1 shows related statistics ofmax and mean distance of cluster area, mean velocityin clusters, the number of positioning data in clustersas well as the center location of clusters.

For another person’s human mobility, namedSHY, Figure 2 shows clusters. Details of each clus-ters can be found in Table 2. Figure 2 shows 17 clus-ters, which categorized into Seoul and Kangwon area.Since SHY lives in Seoul, 14 clusters were found inSeoul city area. Table 2 shows detailed informationfor SHY’s clusters. Cluster 6 has only 4 positions butit is a meaningful cluster since all four positions are instable state rather than mobile state.

4 ResultIn this section, we present the result. Hidden MarkovModels for two set of mobility trails, respectively forKHU and SHY will be provided as ΘKHU and ΘSHY .ΘKHU is as follows:

• KHU’s Hidden Markov Model ΘKHU

ΘKHU = (A,B, π)

• KHU’s State Transition Matrix A

A=

0.175 0.003 0.191 0.631 0.0000.001 0.996 0.001 0.001 0.0010.642 0.003 0.114 0.241 0.0000.325 0.003 0.434 0.238 0.0000.000 0.005 0.000 0.000 0.995

• KHU’s Observation Probabilities B

B=

0.000 0.001 0.999 0.000 0.000 0.0000.045 0.066 0.000 0.000 0.856 0.0330.000 0.001 0.999 0.000 0.000 0.0000.000 0.001 0.999 0.000 0.000 0.0000.000 0.000 0.000 1.000 0.000 0.000

• KHU’s Initial State Probabilities

π=[0.474 0.000 0.137 0.389 0.000

]


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Table 1: Clusters of KHU’s dataCluster # 1 Cluster # 2 Cluster # 3

Center latitude 37.55062150 Center latitude 37.50724912 Center latitude 37.53083248

Center longitude 126.92433107 Center longitude 126.73725146 Center longitude 126.74442818

Max Distance 1.276km Max Distance 1.623km Max Distance 0.020km

Mean Distance 0.130km Mean Distance 0.476km Mean Distance 0.002km

Mean Velocity 1.035km/h Mean Velocity 0.558km/h Mean Velocity 0.088km/h

Num of Data 36277 Num of Data 37017 Num of Data 246

Cluster # 4 Cluster # 5 Cluster # 6







Figure 3: Mobility Model for KHU

Figure 3 shows the corresponding Markov chain forΘKHU . The three places were notable one in KHU’smodel.

- Home- University- Other places

Each state has the following meaning.- state 1 : to University- state 2 : from University- state 3 : to Home

- state 4 : from Home- state 5 : other places- state 6 : at Home

From the model, KHU spend most of time athome and at university. State 3, 4 and 6 show his timeat home and state 1 and 2 show his time at school.His university is always the starting point of humanmobility as an interpretation of his mobility model.

For SHY’s mobility mode, ΘSHY is as follows:• SHY’s Hidden Markov Model ΘSHY

ΘSHY = (A,B, π)


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• SHY’s Observation Probability BB=

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.454 0.538 0.000 0.000 0.008 0.000 0.000 0.000 0.000

0.000 0.000 0.121 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.879 0.000 0.000 0.000

1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.003 0.934 0.000 0.000 0.000 0.045 0.017

0.000 0.685 0.000 0.002 0.280 0.000 0.002 0.008 0.000 0.010 0.000 0.000 0.000 0.000 0.013 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.454 0.538 0.000 0.000 0.008 0.000 0.000 0.000 0.000

• SHY’s State Transition Probability A

A=

0.137 0.000 0.001 0.000 0.001 0.8610.000 0.998 0.000 0.000 0.002 0.0000.000 0.000 0.999 0.000 0.001 0.0000.000 0.000 0.000 0.998 0.001 0.0010.001 0.001 0.000 0.001 0.997 0.0000.787 0.000 0.000 0.000 0.001 0.212

• SHY’s Initial State Probability π

π=[0.000 0.000 1.000 0.000 0.000 0.000

]Figure 4 visualizes SHY’s model as Markov chain andeach state has the following interpretation:

- state 3 : at Home- state 5 : at University or transient state- state 1, 6 : from Home or to Home- state 2, 4 : other places

Since SHY moves more frequently than KHU, his mo-bility model has more clusters and more complicatedinterpretations.

Figure 4: Mobility Model of SHY

5 ConclusionFor the automated process of human mobility modelconstruction from raw positioning data, we estab-lished human mobility model as intermediate resultsusing Hidden Markov Model. Our result can be usedfor related applications. Our human mobility model iswell fit for past locations however, it does not includetime information or seasonal patterns. Fully utiliz-ing time information in positioning data, we will drawout time information and will embed such information

into our human mobility model. For prediction of hu-man locations using human mobility model, anotherresearch is undergoing [8] and the embed of timingdata will show another possibility for better locationbased service.

The positioning data set is now constantly ex-panding for several persons, and the merit of HMMbased model establishment is clear that we can eas-ily calibrate the HMM based model incrementallywith newly collected positioning data set. In addition,group mobility model is another candidate for our fu-ture research.

Acknowledgements: This research was supported bythe National Research Foundation of Korea funded bythe Ministry of Education, Science and Technology(No. 20120007162 and No. 2012046473).

References:

[1] C. Song, Q. Zehui, B. Nicholas and B. Albert-laszio, Limits of Predictability in Human Mo-bility, Science 19, Vol. 327, No. 5968., 2010,pp. 1018–1021.

[2] Jie Yang, Yangsheng Xu and Chiou S.Chen,Human Action Learning via Hidden MarkovModel, IEEE Transantions on Systems,Man and Cybernetics–part A: System and Hu-mans, Vol. 27, No. 1, 1997.

[3] Garmin GPS device GPSmap62S,https://buy.garmin.com/shop/shop.do?pID=63801&ra=true

[4] Garmin EDGE 800, https://buy.garmin.com/shop/shop.do?cID=160&pID=69043

[5] Google Earth, http://www.google.com/intl/us/earth/index.html

[6] Hidden Markov Model (HMM) Software,http://www.kanungo.com/software/software.html#umdhmm

[7] Hyunuk Kim and Ha Yoon Song, FormulatingHuman Mobility Model in a Form of ContinuousTime Markov Chain, Procedia CS, Vol. 10, 2012,pp. 389–396.

[8] Seungyeon Kim, Ha Yoon Song andHoon Jung Koo, Probabilistically Predict-ing Location of Human with PsychologicalFactors, European Conference of COM-PUTER SCIENCE (ECCS ’12), Paris, France,December 2–4, 2012.


ISBN: 978-1-61804-150-0 123

Table 2: Clusters of SHY’s dataCluster # 1 Cluster # 2 Cluster # 3



































Cluster # 16 Cluster # 17

Center latitude 37.51157987 Center latitude 37.55425717

Center longitude 126.99701639 Center longitude 126.87533290

Max Distance 0.010km Max Distance 0.004km

Mean Distance 0.004km Mean Distance 0.003km

Mean Velocity 0.353km/h Mean Velocity 0.166km/h

Num of Data 317 Num of Data 127


ISBN: 978-1-61804-150-0 124

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Human Mobility Model Establishment with Hidden Markov Model · Human Mobility Model Establishment with Hidden Markov Model SEUNG HO RYU Hongik University Department of Computer Engineering