Geographical and Temporal Similarity Measurement inLocation-based Social Networks

Chongqing University of Posts and Telecommunications

KTH – Royal Institute of Technology

Zhengwu Yuan

Yanli Jiang

Gyözö Gidofalvi

Outline

Introduction Related work A hierarchical spatio-temporal similarity measure in LBSN Empirical evaluations

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Introduction

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Mobile Internet technology

Internet technology

Space Location technology

Location-based Social NetworkLocation-based Social NetworkUser SimilarityUser Similarity

LBSN Applications

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Information Layout of LBSN

Gao at al. Data Analysis on Location-Based Social Networks. 2011

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Outline

Introduction Related work A hierarchical spatio-temporal similarity measure in LBSN Empirical evaluations

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Traditional: Cosine Similarity

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, ,

2 2, ,

( , ) AB

AB AB

A i B ii I

A i B ii I i I

R Rsim A B

R R

Given a set of commonly rated items IAB, the cosine similarity between two users A and B based on their respective ratings RA,i and RB,i on items i ϵ IAB is:

Traditional: Adjusted Cosine Similarity

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Given a set of commonly rated items IAB , the adjusted cosine similarity between two users A and B based on the sets of their individually rated items IA and IB and their average individual ratings on these items and is:

, ,

2 2, ,

( , )( )

( ) ( )

AB

A B

A i A B i Bi I

A i A B i Bi I i I

sim A BR R R R

R R R R

Traditional: Pearson Correlation Coefficient

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Given a set of commonly rated items IAB , the adjusted cosine similarity between two users A and B based on the sets of their individually rated items IA and IB and their average individual ratings on these items and is:

, ,

2 2, ,

( , )( )( )

( ) ( )

AB

AB AB

A i A B i Bi I

A i A B i Bi I i I

sim A BR R R R

R R R R

Similarity in LBSN

Similarity along (a combination of) different dimensions: Content layer, e.g.: Ye’11, McKenzie’13 Social layer, e.g.: Ye’12 Geographical layer, e.g.: Li’08 Semantic locations / categories of locations, e.g.: Xiao’10, Bao’12, Ye’11 Temporal sequential similarity, e.g.: Li’08 Check-in temporal similarity, e.g.: Ye’11

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Outline

Introduction Related work A hierarchical spatio-temporal similarity measure in LBSN Empirical evaluations

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A Hierarchical Spatial-Temporal Similarity Measure in LBSN

Assumptions about user similarity: The closer is the time and the geographical location that two users access the

more similar are the two users to each other The larger is the number of check-ins of two users in nearby locations at similar

times, the more similar are the two users to each other Similarity changes with the level of detail

Proposed method: Extract spatio-temporal clusters from user check-ins at different spatio-temporal

levels of detail For each ST level of detail, measure the cosine similarity between users using

the classical Vector Space Model (VSM) with vectors composed of the amount of user visits in different ST clusters

Calculate the weighted combination of similarities at different ST levels of detail

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Hierarchical Spatio-Temporal Clustering

Spatio-temporal variant of DBSCAN: ST-DBSCAN [Birant’07] An object is a core object if within its spatial (Eps_space) and temporal

(Eps_time) neighborhood the number of objects is at least MinPts. Definitions for Directly Density-Reachable (DDR), Density-Reachable (DR), and

Density-Connected are straight forward extensions.

Clusters at different levels of detail:

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Vector Space Model

Define the user-location matrix within a certain period as

where m is the total number of users, n is the number of ST clusters discovered by ST-DBSCAN(Eps_space, Eps_time, MinPts), Vij is the number of check-ins by user i in the ST cluster j, and l is the level of detail in the clustering hierarchy.

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1,1 1,2 1, 1 1,

2,1 2,2 2, 1 2,( )

,1 ,2 , 1 ,

n n

n nl m n

m m m n m n

V V V V

V V V VV

V V V V

User Similarity

User similarity at a given cluster hierarchy level is according to the cosine similarity of the location vectors of the users:

The overall similarity of users is calculated across the cluster hierarchy levels as follows:

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( , ) cos( , ) A BA B

A B

U Usim A B U U

U U

1

N

overall ii

sim sim

1

( )

iN

ii

Outline

Introduction Related work A hierarchical spatio-temporal similarity measure in LBSN Empirical evaluations

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Dataset

Check-in datasets from Gowalla from the Stanford Network Analysis project for the US cities:

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Evaluation Metrics

Precision and recall (“relative overlap”) of the visits of a user ur and its most similar user u to the Top-N ST clusters / POIs:

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Results

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ST generalization at different levels of detail improves performance Combining similarity measures

at different ST levels of detail improves precision and recall and outperforms the fine-grained method (see ST-DBSCAN)

Considering the amount (not only the existence) of check-in at different ST clusters improves performance (see Jaccard)

Conclusions

We have proposed a new method to calculate the user similarity on LBSN based on the spatial and temporal properties of the user check-in data.

The method can be applied to recommend location or friends in LBSN, because the key of a recommendation system is the similarity measurement of user or item.

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Thank you for your attention!

Q/A?

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