Constructing and Comparing User Mobility Profiles for Location-based Services

Transcription

1 Constrcting and Comparing User Mobility Profiles for Location-based Services Xihi Chen Interdisciplinary Centre for Secrity, Reliability and Trst, University of Lxemborg Jn Pang Compter Science and Commnications, University of Lxemborg Ran Xe University of Lxemborg & Shandong University ABSTRACT With the increasing availability of location-acqisition technologies, we have better access to collections of large spatio-temporal datasets. This brings new opportnities to location-based services (LBS), especially when knowledge of sers movement behavior (i.e., mobility profiles) can be extracted from sch datasets. For instance, in social networks, friends can be recommended according to similarity scores between ser mobility profiles. In this paper, we propose a new approach to constrct sers mobility profiles and calclate the mobility similarities between sers. We model mobility profiles as traces of places that sers freqently visit and se freqent seqential pattern mining technologies to extract them. To compare sers mobility profiles, we first discss the weakness of a similarity measrement in the literatre and then propose or new measrement. We evalate or work sing a real-life dataset pblished by Microsoft Research Asia and the experimental reslts show that or approach otperforms the existing works on different aspects. Categories and Sbject Descriptors H.3.4 [Systems and Software]: General User profiles and alert services protection; H..8 [Database Management]: Data Applications Data mining, Spatial databases and GIS General Terms Algorithms, measrement Keywords Mobility profiles, pattern mining, similarity. INTRODUCTION In the past decades, there has been a large increase on the poplarity and diversity of devices capable of location-acqisition. With this increase, a new type of virtal commnities location-based Spported by the National Research Fnd, Lxemborg (SE- CLOC 79436). Permission to make digital or hard copies of all or part of this work for personal or classroom se is granted withot fee provided that copies are not made or distribted for profit or commercial advantage and that copies bear this notice and the fll citation on the first page. To copy otherwise, to repblish, to post on servers or to redistribte to lists, reqires prior specific permission and/or a fee. SAC 3 March 8-, 03, Coimbra, Portgal. Copyright 03 ACM /3/03...$. social networks (LBSN) have emerged, e.g., Forsqare and Bikely. In LBSNs people can share their otdoor activities with friends, monitor travel distance and dration, or even pload photos tagging a rote. By leveraging ser similarity in terms of interest revealed by their whereabots, LBSNs can provide better services. For instance, the most basic service friend recommendation can be easily enhanced or improved by ranking sers according to sch similarities. Frthermore, once ser mobility profiles are available, we can recommend not only friends bt also new places from the ones that similar sers are interested in. De to the poplarity of recommendation services, mobility profile constrction and comparison have been attracting a lot of attention in the literatre. One common interpretation of mobility profiles is sers reglar moving behavior in terms of space and time. More specifically, space refers to the places freqently visited by sers and time indicates the typical transition time between two consective places. For example, a stdent in Lxemborg takes 0 mintes every day to transfer from the central train station to Hamilis, the central bs stop from which he spends another 5 mintes to get to the camps Kirchberg. This daily rotine can be described as one of the stdent s reglar movements: Central Train Station 0 min 5 min Hamilis Kirchberg. This interpretation leads to many mobility profile constrction methods and mobility similarity measrements. Related work. We classify the related works in the literatre into two grops one on mobility profile constrction and the other on ser similarity comptation for recommender systems. Giannotti et al. [5] introdce the concept of trajectory patterns to represent a set of sers trajectories inclding the same seqence of places referred to as regions of interest (RoI), with similar transition time. They redce the problem of trajectory pattern mining to the typical freqent seqential pattern (FSP) problem []. Many algorithms have been proposed for FSP among which PrefixSpan [8] is one of the most efficient and widely sed algorithms. Giannotti et al. [4] extend PrefixSpan to mine seqences with typical temporal annotations (TAS). Trajectory patterns are defined as an extension of TASs in [5]. The elements in a pattern are no longer events bt RoIs that a ser often visits. RoIs are detected by merging dense spatial cells, which are contained by many trajectories. By transforming GPS points into RoIs, trajectory pattern mining is redced to TAS mining. Throgh experiments, we find that the RoIs generated by this method [4] cannot be sed as a precise representation of sers meaningfl areas de to their large area. Zheng et al. propose and implement a personalised friend and location recommender system called GeoLife [4]. GPS points are groped into stay points which stand for the places where sers hang ot and spend a certain amont of time. A density-based al-

2 gorithm is then sed to hierarchically clster the stay points into RoIs. Once all ses trajectories are transformed into seqences of RoIs, the longest common sbseqence (LCS) is extracted for any pair of sers and sed to measre their similarities. Xiao et al. [9] propose a similar approach bt make se of the semantics of places. They model a GPS trajectory with a seqence of semantic locations, sch as msems and restarants. In this way, the semantic meanings of RoIs are considered. However, both of the two approaches [4, 9] work on trajectories, which may contain some places rarely visited. These places will enlarge the area of ROIs as otliers dring the clstering process. Ying et al. also propose an approach to recommend friends based on sers semantic trajectories bt on the level of trajectory patterns []. They se PrefixSpan to mine freqent semantic trajectory patterns and define a measrement called maximal semantic trajectory pattern similarity (MSTP-similarity) in order to compte the similarity between two sers. However, Ying et al. ignore transition time and their measrement enconters a problem when comparing two identical ses (see Sect. 4). Or contribtions. In this paper, we propose a new approach to constrct ser mobility profiles and calclate the similarity scores between sers based on their mobility profiles. First, we improve the mobility profile constrction procedre by Giannotti et al. [5] to find more precise meaningfl places (RoIs) of sers. The se of trajectory patterns in or approach allows s to focs on sers reglar movements. Second, we show that the ser similarity measrement proposed by Ying et al. [9] is incorrect and we define a new measrement. Since we also consider transition time, or measrement is more accrate to compte ser similarities. We make se of a real-life dataset pblished by Microsoft Research Asia in or experiments. The reslts show that or profile constrction process otperforms the existing works in the literatre and or new similarity measrement is qite effective.. PRELIMINARIES We refer to a GPS point as a location on the earth and denote it by (lat, lng) indicating the latitde and longitde. A region represents an area and can be considered as a set of GPS points. We se a region of interest (RoI) to denote a meaningfl region for a ser where he has performed an activity. For the stdent in Lxemborg in Sect., the central train station and Hamilis are two RoIs. GPS trajectories are paths that moving objects follow throgh space in certain time periods. They record sers otdoor movements by logging time-stamped geographic points. DEFINITION (GPS TRAJECTORY). A GPS trajectory is a seqence of chronologically ordered spatio-temporal points, i.e., (p 0,..., p n) where p i = lat i, lng i, t i (0 i n) with t i as a time point and (lat i, lng i) as a GPS point. A stay point stands for a geographic region, where a ser stays over a time threshold θ t and within a distance threshold θ d [7]. Let dis(p, p ) be the Eclidean distance between two points p and p. The definition of stay points can be formlated as follows: DEFINITION (STAY POINT). A stay point s of a given trajectory T = (p 0,..., p n) corresponds to a sbseqence T of T. If T = (p j,..., p j+m) where 0 < x m, dis(p j, p j+x) θ d, dis(p j, p j+m+) > θ d and t j+m t j θ t, then we have s = mx=0 lat mx=0 (lat, lng, t a, t e) where lat = j+x lng, lng = j+x m+ m+ stand for the average latitde and longitde of the points in T, t a = t j is the arriving time at s and t e = t j+m is the exiting time. From the trajectory dataset pblished by Microsoft [5], we have observed that a ser tends to start and end a trajectory with one of his meaningfl places, e.g., home or offices. Therefore, besides the stay points representing regions, we also consider the first and the last point of a trajectory as stay points. However, if they are close to other region representative stay points and the distance is smaller than a threshold, i.e., θ m, we merge them into one stay point, which is the middle point of the line connecting them. A trajectory pattern of a ser represents one of the ser s reglar mobility trace. It is sally denoted as seqences of RoIs with transition time annotated [5]. DEFINITION 3 (TRAJECTORY PATTERN). A trajectory pattern (T-pattern for short) is a pair (S, A) where S = (R 0,..., R n) (n 0) is a seqence of RoIs and A = (,..., n) is the temporal annotation of the seqence. It can be represented as (S, A) = R 0... n R n. If a ser seqentially travels all the RoIs of a T-pattern in a trajectory and spends similar time to transfer between regions, then we say this pattern is spatio-temporally contained in this trajectory. DEFINITION 4 (SPATIO-TEMPORAL CONTAINMENT). Given a trajectory T, time tolerance τ and a T-pattern (S, A) = R 0... n Rn, we say that (S, A) is spatio-temporally contained in T (denoted by (S, A) τ T ) if and only if there exists a sbseqence of T, i.e., T = ( x 0, y 0, t 0,..., x n, y n, t n ) sch that: 0 i n, x i, y i R i and i i τ where i = t i t i. When T-pattern (S, A) is spatio-temporally contained in a trajectory, we say that the T-pattern has an occrrence. A T-pattern sally has mltiple occrrences in a spatio-temporal dataset. We se spport vale (spport T τ (S, A)) to represent the percentage of the trajectories containing (S, A) in dataset T when the time interval tolerance is set to τ. If the spport vale of a T-pattern is larger than a given minimm spport, then we call the pattern a freqent T-pattern. The problem of trajectory pattern mining is how to find freqent T-patterns in a given spatio-temporal dataset. The reslt is a set of T-patterns, called freqent pattern set. DEFINITION 5 (FREQUENT PATTERN SET). For a set of trajectories T, time tolerance τ and a minimm spport vale σ, the (τ, σ)-freqent pattern set of T is PS T τ,σ = {(S, A) spport T τ (S, A) σ}. A mobility profile describes a ser s reglar movement, i.e., the traces of places that the ser often visits. Sch traces have a natral correspondence with freqent T-patterns when the places are interpreted as RoIs. Moreover, as a ser s movement is represented by a collection of trajectories, we can model his mobility profile by the freqent pattern set of his trajectories and se trajectory pattern mining techniqes to constrct it. Let T be the trajectories taken by ser in a dataset T. We call PS T τ,σ the mobility profile of. In the following discssion, we se PS to denote s mobility profile for short by assming τ and σ have been defined and T is clear from the context. With the same rle applied, the spport vale spport T τ (S, A) is denoted by spport (S, A) instead. 3. CONSTRUCTING MOBILITY PROFILES Given ser s trajectories T, we constrct his mobility profile throgh the following for seqential steps:. Compte the stay points of each trajectory in T sing stay point detection & merging algorithm;

3 (a) Trajectories & stay points. (b) RoIs with otliers. (c) RoIs withot otliers. (d) RoIs by the T-pattern miner. Figre : An example of RoI constrction.. Remove the noisy stay points and apply a hierarchical clstering algorithm on remaining stay points to generate RoIs; 3. Transform the GPS trajectories in T into RoI trajectories sing the RoIs compted at step ; 4. Use the trajectory pattern miner [5] to compte freqent trajectory patterns from the RoI trajectories obtained at step 3. The first two steps are abot constrcting RoIs. Fig. shows an example of the RoI constrction for a ser. We se the ble lines to depict the ser s trajectories. The extraction of stay points eliminates the points collected dring transition between places and enables s to only focs on sers meaningfl places. Fig. a displays the extracted stay points in yellow dots. Since GPS trajectories can be different even if they are collected from an identical rote, the stay points vary from trajectory to trajectory. However, from Fig. a, we can observe that the stay points in an RoI are sally close to each other. Ths we can apply clstering algorithms to atomatically detect nearby stay points. In this paper, we se the minimm rectanglar area which covers a clster of stay points to represent an RoI. Another observation is that there exist otlying stay points which sers visit occasionally (see the points in red circles in Fig. a). Sch points degrade the qality of generated RoIs, e.g., enlarging area or compting infreqent places [6]. We introdce LOF (Local Otlier Factor) [3] to measre the extent of each stay point to which it is isolated from others. Based on the reslts, we discard a certain percentage (called deletion percentage) of the points with the largest LOF vales. Fig. b and c show the RoIs generated by the hierarchical clstering algorithm with and withot otlying points, respectively. It is clear that if the otliers are not removed, a nmber of small regions are compted and they only have a few points inside. Sch regions shold not be considered as RoIs where sers sally visit. After removing the otliers, we can see that the RoIs have a relative large nmber of stay points inside and have smaller area compared to the ones in Fig. b. The last two steps focs on mining the freqent pattern set. With the stay points compted in the step, we first transform each trajectory into a seqence of stay points. Sbseqently we transform this stay point trajectory into an RoI trajectory by replacing any stay point with the RoI where it lies in. In the end, we give the RoI trajectories to the trajectory mining tool [4] and compte the T-patterns that satisfy given minimm spport and time tolerance. With regards to the RoI constrction, there exist other methods in the literatre. Zheng et al. [4] se a density-based clstering algorithm OPTICS [] to compte RoIs from stay points bt withot removing otliers. We have illstrated the shortcoming of this method by Fig. b and c. In the trajectory pattern miner, Giannotti et al. [5] also implement an RoI constrction algorithm. Space is divided into a grid, each cell of which is assigned a density vale according to the nmber of GPS trajectories passing throgh. Af- terwards, a region growing procedre starts from dense cells by merging nearby dense cells. The procedre contines ntil the average density of the region is below a threshold. We do not se this method becase: () the density measres the freqency of a ser passing by a cell bt not staying in the cell; () the poplarity of an RoI is determined only by density and stay time is ignored. Therefore, the generated RoIs tend to have large areas, particlarly when sers own large nmbers of fine-grained trajectories. Fig. d shows the RoIs compted by the tool, which covers almost the whole area. In the following we present an example of mobility profiles. E XAMPLE. Sppose after trajectory transformation (i.e., step 3), ser has three RoI trajectories: T : A B D C T3 : A B F C. T : 5 A B E C For the sake of being concise, we label the transition time between RoIs explicitly. Assme the minimm spport σ = 0.5 and time tolerance τ =. We find that a seqence of RoIs may correspond to infinitely many B always has T-patterns. For instance, when 0 4, A two occrrences and spport (A B) = 3 > 0.5. For these T-patterns, we can se the interval [0, 4] to represent the transi[0,4] tion time between A and B, and ths A B is the set of all T-patterns with the seqence of RoIs (A, B) and transition time between 0 and 4. Ths, in Exa. the ser s mobility profile can be represented as follows: [0,4] [6,] [6,8] P S ={A, B, C, A B, A C, B C, [0,4] [6,8] A B C}. 4. COMPARING MOBILITY PROFILES In this section, we first focs on comparing mobility profiles withot considering transition time and then give or method to take transition time into accont. When transition time is ignored, given a ser s mobility profile PS we get a simpler mobility profile (called seqence pattern set) PS = {S (S, A) PS }. The spport vale of a seqence pattern S (spport (S)) eqals to the spport vale of any (S, A) PS when τ is set to +, i.e., spport T+ (S, A). In the seqence pattern set, we have all the freqent seqences of RoIs. In Exa., PS = {A, B, C, A B, A C, B C, A B C}. We notice that some of these seqence patterns have dplicated information. For instance, in Exa., if we know A B is a seqence pattern, then A and B are also his seqence patterns.

4 If we compare two sers mobility profiles sing the whole seqence pattern set, some behavior will be considered more than once. Therefore, we se the maximal pattern set to compare sers mobility profiles which consist of only the patterns that are not contained in other patterns. Given P = (R 0,..., R n) and Q = (R 0,..., R m), we call Q a sbseqence of P (denoted by Q P ) if there exists j <...<j m sch that R i = R ji (0 i m). We define the maximal seqence pattern set as follows: DEFINITION 6 (MAXIMAL SEQUENCE PATTERN SET). Given ser s seqence pattern set PS, the maximal seqence pattern set of is M(PS ) = {P PS P PS (P P )}. In the following discssion, we first give a brief introdction to a similarity measrement [] in the literatre and show that it is incorrect throgh examples. Afterwards, we define or own measrement and extend it to take transition time into accont. 4. A similarity measrement by Ying et al. Ying et al. define a ser similarity measrement [] according to semantic trajectory patterns. By semantics they mean the fnction of the places, sch as parks, schools or hospitals. For instance, the trajectory pattern of the stdent in Lxemborg in Sect. corresponds to semantic pattern train station bs stop school. To compte two sers similarity, they first propose a similarity measrement between maximal semantic pattens (MSTP-similarity). Then based on pattern similarity, sers profiles which consist of all maximal semantic patterns are compared. Althogh maximal semantic patterns are defined on the level of location semantics, they have the same form as seqence patterns syntactically. So we can apply it on maximal seqence patterns as well. Given two maximal seqence patterns, the argment is that the more similar they are, the longer common part they share. We se longest common seqences (LCS) to represent the longest common part. For example, seqence patterns P = A E B H D and Q = E A B D have two longest common seqences E B D and A B D. They form the set of the longest common seqences of P and Q, denoted by lcs(p, Q). Let lenlcs(p, Q) be the length of the longest common seqences in lcs(p, Q) and len(p ) be the length of P. According to the weighted average trajectory pattern similarity in [], the similarity between P and Q is calclated as follows: sim(p, Q) = lenlcs(p, Q) len(p ) + len(q). In the previos example, with lenlcs(p, Q) = 3 and len(p ) = len(q) = 4, sim(p, Q) = 3 = The similarity between sers is compted based on MSTP-similarity. The idea is to compte the weighted average of all possible similarities between maximal patterns. In this paper, we se spport vales of patterns to constrct the weighting fnction. Given two sers and, the similarity between them is calclated as follows: w(p i, Q j) sim(p i, Q j) sim(, ) = P i M(PS ) Q j M(PS ) P i M(PS ) Q j M(PS ) w(p i, Q j) where w(p i, Q j) = spport (P i )+spport (Q j ). We find that the similarity between sers calclated by this measrement is conter-intitive and inconsistent with common sense in certain cases. We illstrate the inconsistency throgh the following example. EXAMPLE. Given three seqence patterns P = A B, P = C D and P 3 = E F and for sers,, and 3, we want to calclate the similarity of to other three sers. The ser has the same maximal seqence pattern set as 3, which is {P, P, P 3} while the maximal seqence pattern sets of and are {P } and {P, P }, respectively. The pattern similarity between any two patterns is shown in Tab.. For the sake of simplicity, we assme patterns have the same spport vale 0.. Table : Example of similarity comptation with Ying et al. s method. M(PS ) M(PS ) M(PS ) M(PS 3 ) P P P P P P 3 P P P We see that shares one common pattern with, two with and three with 3. So intitively, the similarity of to shold be the smallest and the similarity between and 3 shold be as they are identical. However, with the measrement, we get sim(, ) = = ; sim(, ) = = ; sim(, 3) = =. The reslts say that is the same similar to the three sers, which is clearly not what we expect. 4. Or method From Exa., we learn that the weighted average of pattern similarities is not the proper measrement for ser similarity. Or idea is to only consider the most similar pattern of each maximal seqence pattern instead of all the maximal patterns of another ser. Given two sers and, we se fnction ψ, : M(PS ) M(PS ) to map a maximal pattern of to the most similar maximal pattern in M(PS ). Specifically, for each P i M(PS ), ψ, (P i) = arg max Q j M(PS ) sim(p i, Q j) w(p i, Q j). Then for each ser, we compte his relative similarity to the other one. The relative similarity of to is sim( P ) = i M(PS ) sim(pi, ψ, (Pi)) w(pi, ψ, (Pi)) P i M(PS ) w(pi, ψ, (Pi)). Similarly, we can also compte the relative similarity of to, i.e., sim( ). As the relation of similarity is symmetric, we take the average of the two relative similarity as the similarity score between and : sim(, ) = sim( ) + sim( ). EXAMPLE 3. Sppose we have the same sers as in Exa.. We take as an example to show the calclation process. First, for each pattern of, we find the corresponding pattern of with the maximal similarity score, i.e., ψ, (P ) = P, ψ, (P ) = P ψ, (P 3) = P /P. So sim( ) = = 0.67.

5 With the same process, we obtain sim( ) = =. So sim(, ) = Tab. lists calclated similarities. The similarity of with is 0.67 which is the smallest and has the largest similarity to 3. The reslts are consistent with what we wold expect. Table : Example of similarity comptation with or method. i 3 sim( i) 0.67 sim( i ) sim(, i) We can see that or method can clearly distingish the similarity degrees of to the three sers. More importantly, for identical sers, or method always gives a degree of. 4.3 Adding transition time In this section, we take transition time into accont in ser similarity measrement. The argment is that if two sers are similar, in addition to longer common seqences of RoIs, transition time between consective RoIs shold also be close. Or idea is to pdate the similarity measrement between maximal patterns by taking comparison of transition time into accont. The more similar the given sers are, the longer common seqences they share and the closer the transition times on common seqences are. Sppose that we have two maximal patterns P M(PS ) and Q M(PS ), and one of their longest common seqence S = (R 0,..., R n) (S lcs(p, Q)). For any two consective RoIs R i and R i (0 < i n), the typical transition time of ser between them is the nion of all transition time appearing in a T-pattern with S in the ser s profile. Let trant S(i) be the nion, then we have trant S(i) = { i (S, A) PS s.t. A = (,..., n)}. In the same way, we can obtain the corresponding set of transition time of ser, i.e., trant S (i). Recall that we can se intervals to represent transition time in Exa.. Ths trant S(i) can be represented as the nion of intervals, e.g., [x, y ]... [x k, y k ]. Then we can compte the overlapping transition time of the sers and all the occrring transition time by calclating the intersection and nion of trant S(i) and trant S (i). Sppose trant S (i) trant S(i) = [x, y ]... [x k, y k ] and trant S (i) trant S(i) = [x, y ]... [x m, y m]. Then we can calclate ot, S R i to R i between and, by (i), the ratio of overlapping time from i m y i x i i k y i x i. We se the average of all transition time similarities in all longest common seqences to measre the transition time similarity between two maximal patterns, called time-overlap-fraction. DEFINITION 7 (TIME-OVERLAP-FRACTION). Let P and Q be two maximal seqence patterns of and, respectively. Then the time-overlap-fraction of P and Q, denoted by tof (P, Q) can be calclated as: len(s) S lcs(p,q) i= ot, S (i) tof (P, Q) = lcs(p, Q) (lenlcs(p, Q) ). The similarity of P and Q can ths be calclated as follows: sim(p, Q) = lenlcs(p, Q) tof (P, Q). len(p ) + len(q) 5. EXPERIMENTS We se the GPS trajectory dataset collected in Geolife project of Microsoft Research Aisa [3] to evalate or work. 5. Setting The dataset. The Geolife dataset consists of 7,6 trajectories from 78 sers in a period of over for years (from April 007 to October 0). The trajectories cover a total length of,5,654 km and a total dration of 48,03 hors. Moreover, the GPS positions are collected with a high freqency. Over 90% of the positions are recorded less than every 5 seconds with a distance less than 0 meters from their previos positions. The trajectories also reflect a diverse collection of sers otdoor movements, not restricted to only daily activities. Almost all trajectories are located in Beijing (China) althogh the GPS positions are distribted in over 30 cities. The trajectory dataset does not provide sers personal information sch as gender or affiliation de to privacy protection. So we have no access to the grond trth abot the similarity between sers. Althogh Zheng et al. constrct the volnteers similarity which works as the grond trth in [7], we cannot obtain and se it becase of the legal rles abot pblishing data in Microsoft []. In order to validate or similarity measrement, we choose two sers who have a large nmber of trajectories and divide them into new sers. One is ser 6, who is divided into two sers (i.e., 6, 6 ) while the other one is ser 5, divided into three sers (i.e., 5,5,5 # ). Intitively, the new sers shold preserve the original sers behavior and ths have a higher degree of similarity. In addition, we choose another five sers from the rest of volnteers. In this way, we have a testing dataset with 0 sers and 55 different pair of sers for similarity comptation. In or experiments, a ser s movement in a day forms a trajectory. For the ten chosen sers, each has abot 300 trajectories on average containing over,50 stay points. Implementation. We se the bottom-p (also called agglomerative) hierarchical clstering algorithm to clster stay points. Compared to other clstering algorithms, it allows s to cstomise the termination condition sing the shortest distance between clsters and does not need to fix the nmber of clsters beforehand like k-means. The clstering process stops once the shortest distance between any two clsters is larger than a threshold, i.e., δ. This parameter also determines the longest diagonal of generated RoIs. To compare two sers, we first merge their trajectories and constrct their common RoIs. Then we transform each ser s trajectories sing these RoIs and generate his mobility profile. All related parameters need to be fixed before performing or evalation. The principle of setting their vales is to enforce a good qality of T-patterns. De to the page limit, we refer readers to [0] for the parameter settings. 5. Experimental reslts In Fig. we show the similarity between any pair of the 0 sers calclated by three similarity measrements. We se different grey levels to distingish the similarity scores between two sers. The darker the cell is, the more similar the corresponding two sers are. Fig. a and b show the ser similarities compted by the measrement of Ying et al. [] (MSTP) and or measrement withot transition time (MTP), respectively. The diagonal cells correspond to the similarity of a ser to himself which is expected to be one. However, from Fig. a it is clear that MSTP fails to captre this except for the sers who have only one maximal seqence patterns, i.e., ser 6 and 6. (These two sers originate from one volnteer, their maximal seqence patterns are the same. This leads to a similarity score of.00 between them.)

6 * * * * * * # * 5 5* 5# (a) User similarities compted by MSTP. 5# * 5 5* 5# (b) User similarities compted by MTP. 5# * 5 5* 5# (c) User similarities compted by MTP+TOF. Figre : User similarities by three methods. Recall that ser 5, 5 and 5 # are derived from the same volnteer. They shold have large common mobility patterns in their mobility profiles and ths have high similarity scores. However, measred by MSTP, the similarity scores are only abot 0.0. On the contrary, or method MTP sccessflly finds the similarity of these three sers. The average similarity score is over For the sers who do not share any common seqences, both of the two measrements give zero indicating their dissimilarity. From the above analysis, we can conclde that or measrement can give a better similarity comparison between sers mobility profiles, especially when they have mltiple maximal seqence patterns. Fig. c shows the similarity between sers when we add time overlapping fraction into or measrements (MTP+TOF). Compared to the vales in Fig. b, we find that the similarity vales between sers in general become smaller. That is becase the difference between transition time disconts the similarities. Even for sers 6 and 6 who have the same maximal seqence pattern, their similarity decreases from.0 to We can also see that transition time does help identify similar sers. For example, by MTP, the similarity between sers 003 and 004 is 0.77 which is larger than the similarity between sers 5 and 5 # (0.7) even they are derived from the same volnteer. With transition time considered, the former similarity decreases to while the later still remains over 0.60, mainly becase sers 003 and 004 do not have similar transition time. Therefore, considering transition time leads s to a more accrate evalation of ser similarity. 6. CONCLUSION In this paper, we have accomplished two tasks. First, we propose a new method to constrct sers mobility patterns. Compared to the existing methods in the literatre, or method can detect more accrate RoIs for sers. This also ensres the precision of the sbseqent ser similarity comptation. Second, we showed that the ser similarity measrement proposed by Ying et al. is incorrect in some cases and we defined a new measrement to fix the problem. As transition time between RoIs are also part of sers mobility patterns, we frther took them into accont in or ser similarity measrement. We validated or work by experiments on a dataset of real-life trajectories. The reslts show that or measrement and ser profile constrction are effective. For ftre work, we will apply or similarity measrement to location privacy analysis. A high similarity between a given set of anonymised trajectories and a ser s mobility profile indicates a high probability for the ser to be the owner of the trajectories. It is also interesting to analyse sers similarity according to their trajectory logs posted on social networks. 7. REFERENCES [] AGRAWAL, R., AND SRIKANT, R. Mining seqential patterns. In Proc. ICDE (995), IEEE CS, pp [] ANKERST, M., BREUNIG, M. M., KRIEGEL, H.-P., AND SANDER, J. OPTICS: Ordering points to identify the clstering strctre. In Proc. SIGMOD (999), ACM Press, pp [3] BREUNIG, M., KRIEGEL, H.-P., NG, R. T., AND SANDER, J. LOF: Identifying density-based local otliers. In Proc. SIGMOD (000), ACM Press, pp [4] GIANNOTTI, F., NANNI, M., PEDRESCHI, D., AND PINELLI, F. Mining seqences with temporal annotations. In Proc. SAC (006), ACM Press, pp [5] GIANNOTTI, F., NANNI, M., PEDRESCHI, D., PINELLI, F., AND AXIAK, M. Trajectory pattern mining. In Proc. SIGKDD (007), ACM Press, pp [6] JAIN, A. K., AND DUBES, R. C. Algorithms for clstering data. Prentice-Hall, Inc., 988. [7] LI, Q., ZHENG, Y., XIE, X., CHEN, Y., LIU, W., AND MA, W.-Y. Mining ser similarity based on location history. In Proc. SIGSPATIAL (008), ACM Press, pp [8] PEI, J., HAN, J., MORTAZAVI-ASL, B., WANG, J., PINTO, H., CHEN, Q., DAYAL, U., AND HSU, M.-C. Mining seqential patterns by pattern-growth: the PrefixSpan approach. IEEE TKDE, 6 (004), [9] XIAO, X., ZHENG, Y., LUO, Q., AND XIE, X. Finding similar sers sing category-based location history. In Proc. SIGSPATIAL (00), ACM Press, pp [0] XUE, R. Constrcting and comparing ser mobility profiles for location-based services. Master s thesis, University of Lxemborg, 0. [] YING, J.-C., LU, H.-C., LEE, W.-C., WENG, T.-C., AND TSENG, S. Mining ser similarity from semantic trajectories. In Proc. SIGSPATIAL (00), ACM Press, pp [] ZHENG, Y. Personal commnication, 0. [3] ZHENG, Y., WANG, L., ZHANG, R., XIE, X., AND MA, W.-Y. GeoLife: Managing and nderstanding yor past life over maps. In Proc. MDM (008), IEEE CS, pp.. [4] ZHENG, Y., ZHANG, L., MA, Z., XIE, X., AND MA, W.-Y. Recommending friends and locations based on individal location history. ACM TWEB, (0), 44. [5] ZHENG, Y., ZHANG, L., XIE, X., AND MA, W.-Y. Mining interesting locations and travel seqences from GPS trajectories. In Proc. WWW (009), ACM Press, pp