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Matrix factorization (MF) can extract the low-rank features and integrate theinformation of the data manifold distribution from high-dimensional data, whichcan consider the nonlinear neighbourhood information. Thus, MF has drawn wideattention for low-rank analysis of sparse big data, e.g., CollaborativeFiltering (CF) Recommender Systems, Social Networks, and Quality of Service.However, the following two problems exist: 1) huge computational overhead forthe construction of the Graph Similarity Matrix (GSM), and 2) huge memoryoverhead for the intermediate GSM. Therefore, GSM-based MF, e.g., kernel MF,graph regularized MF, etc., cannot be directly applied to the low-rank analysisof sparse big data on cloud and edge platforms. To solve this intractableproblem for sparse big data analysis, we propose Locality Sensitive Hashing(LSH) aggregated MF (LSH-MF), which can solve the following problems: 1) Theproposed probabilistic projection strategy of LSH-MF can avoid the constructionof the GSM. Furthermore, LSH-MF can satisfy the requirement for the accurateprojection of sparse big data. 2) To run LSH-MF for fine-grainedparallelization and online learning on GPUs, we also propose CULSH-MF, whichworks on CUDA parallelization. Experimental results show that CULSH-MF can notonly reduce the computational time and memory overhead but also obtain higheraccuracy. Compared with deep learning models, CULSH-MF can not only savetraining time but also achieve the same accuracy performance.

Locality Sensitive Hash Aggregated Nonlinear Neighbourhood Matrix Factorization for Online Sparse Big Data Analysis