Nowadays, deep representations have been attracting much attention owing to the great performance in various tasks. However, the interpretability of deep representations poses a vast challenge on real-world applications. To alleviate the challenge, a deep matrix factorization method with non-negative constraints is proposed to learn deep part-based representations of interpretability for big data in this paper. Specifically, a deep architecture with a supervisor network suppressing noise in data and a student network learning deep representations of interpretability is designed, which is an end-to-end framework for pattern mining. Furthermore, to train the deep matrix factorization architecture, an interpretability loss is defined, including a symmetric loss, an apposition loss, and a non-negative constraint loss, which can ensure the knowledge transfer from the supervisor network to the student network, enhancing the robustness of deep representations. Finally, extensive experimental results on two benchmark datasets demonstrate the superiority of the deep matrix factorization method.

With the rapid development of social network, intelligent terminal and automatic positioning technology, location-based social network (LBSN) service has become an important and valuable application. Point of interest (POI) recommendation is an important content in LBSN, which aims to recommend new locations of interest for users. It can not only alleviate the information overload problem faced by users in the era of big data, improve user experience, but also help merchants quickly find target users and achieve accurate marketing. Most of the works are based on users' check-in history and social network data to model users' personalized preferences for interest points, and recommend interest points through collaborative filtering and other recommendation technologies. However, in the check-in history, the multi-source heterogeneous information (including the position, category, popularity, social, reviews) describes user activity from different aspects which hides people's life style and personal preference. However, the above methods do not fully consider these factors' combined action. Considering the data privacy, it is difficult for individuals to share data with others with similar preferences. In this paper, we propose a privacy protection point of interest recommendation algorithm based on multi-exploring locality sensitive hashing (LSH). This algorithm studies the POI recommendation problem under distributed system. This paper introduces a multi-exploring method to improve the LSH algorithm. On the one hand, it reduces the number of hash tables to decrease the memory overhead; On the other hand, the retrieval range on each hash table is increased to reduce the time retrieval overhead. Meanwhile, the retrieval quality is similar to the original algorithm. The proposed method uses modified LSH and homomorphic encryption technology to assist POI recommendation which can ensure the accuracy, privacy and efficiency of the recommendation algorithm, and it verifies feasibility through experiments on real data sets. In terms of root mean square error (RMSE), mean absolute error (MAE) and running time, the proposed method has a competitive advantage.