# American Institute of Mathematical Sciences

February  2018, 1(1): 11-48. doi: 10.3934/mfc.2018002

## Exploring timeliness for accurate recommendation in location-based social networks

 1 Gianforte School of Computing, Montana State University, Bozeman, MT 59717, USA 2 Department of Computer Science and Engineering, University of North Texas, Denton, TX 76207, USA 3 School of Computer Science and Technology, Harbin Institute of Technology, Weihai, Shandong 264209, China

Received  September 2017 Revised  November 2017 Published  February 2018

An individual's location history in the real world implies his or her interests and behaviors. This paper analyzes and understands the process of Collaborative Filtering (CF) approach, which mines an individual's preference from his/her geographic location histories and recommends locations based on the similarities between the user and others. We find that a CF-based recommendation process can be summarized as a sequence of multiplications between a transition matrix and visited-location matrix. The transition matrix is usually approximated by the user's interest matrix that reflect the similarity among users, regarding to their interest in visiting different locations. The visited-location matrix provides the history of visited locations of all users, which is currently available to the recommendation system. We find that recommendation results will converge if and only if the transition matrix remains unchanged; otherwise, the recommendations will be valid for only a certain period of time. Based on our analysis, a novel location-based accurate recommendation (LAR) method is proposed, which considers the semantic meaning and category information of locations, as well as the timeliness of recommending results, to make accurate recommendations. We evaluated the precision and recall rates of LAR, using a large-scale real-world data set collected from Brightkite. Evaluation results confirm that LAR offers more accurate recommendations, comparing to the state-of-art approaches.

Citation: Yi Xu, Qing Yang, Dianhui Chu. Exploring timeliness for accurate recommendation in location-based social networks. Mathematical Foundations of Computing, 2018, 1 (1) : 11-48. doi: 10.3934/mfc.2018002
##### References:

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##### References:
Overview a location-based social network
Influence of training size to the precision
Cosine similarity between the transition and similarity matrix
Average number of new visited location changes through each month
Cumulative distribution function (CDF) of time interval between timelinesss
Precision and recall of CF with or without K-means clustering and SVD
Influence of data sparsity and category to the recommendation rate (recall ratio) where number of recommendations $k = 20$
Influence of constant and dynamic similarity to the recommendation rate (precision ratio) where $N$ is number of multiplications
Recommendation timeliness comparison for constant similarity matrix and dynamic similarity matrix
Similarity of the eigenvector of transition matrix and similarity matrix comparisons of our method and the three benchmarks
The recommendation rate of our method and the three baseline varying in the recommendation timeliness (month)
The empirical CDF of time intervals of our method and the three benchmarks except CF varying in the recommendation period time (month)
Precisions and recalls of LAR, CF, LGS and GeoSoCa
An example of user-item matrix
 Apple Pear Grape Watermelon Alice Like Like Dislike Dislike Bob Dislike Like Like Chris Dislike Like Tony Like Dislike
 Apple Pear Grape Watermelon Alice Like Like Dislike Dislike Bob Dislike Like Like Chris Dislike Like Tony Like Dislike
A summary of precision and recall ratios of the four approaches
 Models Precision Recall Avg.Precision Avg.Recall CF 0.51 0.69 0.3573 0.6395 LGS 0.59 0.77 0.3682 0.6762 GeoSoCa 0.58 0.76 0.3657 0.6684 LAR 0.62 0.83 0.4582 0.7523
 Models Precision Recall Avg.Precision Avg.Recall CF 0.51 0.69 0.3573 0.6395 LGS 0.59 0.77 0.3682 0.6762 GeoSoCa 0.58 0.76 0.3657 0.6684 LAR 0.62 0.83 0.4582 0.7523
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