Context has been recognized as an important factor to consider in personalized recommender systems. Particularly in location-based services (LBSs), a fundamental task is to recommend to a mobile user where he/she could be interested to visit next at the right time. Additionally, location-based social networks (LBSNs) allow users to share location-embedded information with friends who often co-occur in the same or nearby points-of-interest (POIs) or share similar POI visiting histories, due to the social homophily theory and Tobler’s first law of geography. So, both the time information and LBSN friendship relations should be utilized for POI recommendation.
Tensor completion has recently gained some attention in time-aware recommender systems. The problem decomposes a user-item-time tensor into low-rank embedding matrices of users, items and times using its observed entries, so that the underlying low-rank subspace structure can be tracked to fill the missing entries for time-aware recommendation. However, these tensor completion methods ignore the social-spatial context information available in LBSNs, which is important for POI recommendation since people tend to share their preferences with their friends, and near things are more related than distant things. In this paper, we utilize the side information of social networks and POI locations to enhance the tensor completion model paradigm for more effective time-aware POI recommendation. Specifically, we propose a regularization loss head based on a novel social Hausdorff distance function to optimize the reconstructed tensor. We also quantify the popularity of different POIs with location entropy to prevent very popular POIs from being over-represented hence suppressing the appearance of other more diverse POIs. To address the sensitivity of negative sampling, we train the model on the whole data by treating all unlabeled entries in the observed tensor as negative, and rewriting the loss function in a smart way to reduce the computational cost. Through extensive experiments on real datasets, we demonstrate the superiority of our model over state-of-the-art tensor completion methods.
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HOSVD-Based Algorithm for Weighted Tensor Completion
Matrix completion, the problem of completing missing entries in a data matrix with low-dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog that attempts to impute missing tensor entries from similar low-rank type assumptions. In this paper, we study the tensor completion problem when the sampling pattern is deterministic and possibly non-uniform. We first propose an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm for the recovery of the underlying low-rank tensor from noisy observations and then derive the error bounds under a properly weighted metric. Additionally, the efficiency and accuracy of our algorithm are both tested using synthetic and real datasets in numerical simulations.
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- Award ID(s):
- 1934319
- NSF-PAR ID:
- 10294115
- Date Published:
- Journal Name:
- Journal of Imaging
- Volume:
- 7
- Issue:
- 7
- ISSN:
- 2313-433X
- Page Range / eLocation ID:
- 110
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/jimaging7070110
