Profile Likelihood Biclustering

Biclustering, the process of simultaneously clustering the rows and columns of a data matrix, is a popular and effective tool for finding structure in a high-dimensional dataset. Many biclustering procedures appear to work well in practice, but most do not have associated consistency guarantees. To address this shortcoming, we propose a new biclustering procedure based on profile likelihood. The procedure applies to a broad range of data modalities, including binary, count, and continuous observations. We prove that the procedure recovers the true row and column classes when the dimensions of the data matrix tend to infinity, even if the functional form of the data distribution is misspecified. The procedure requires computing a combinatorial search, which can be expensive in practice. Rather than performing this search directly, we propose a new heuristic optimization procedure based on the Kernighan-Lin heuristic, which has nice computational properties and performs well in simulations. We demonstrate our procedure with applications to congressional voting records, and microarray analysis.Comment: 40 pages, 11 figures; R package in development at https://github.com/patperry/biclustp

User-Specific Bicluster-based Collaborative Filtering

Tese de mestrado, Ciência de Dados, Universidade de Lisboa, Faculdade de Ciências, 2020Collaborative Filtering is one of the most popular and successful approaches for Recommender Systems. However, some challenges limit the effectiveness of Collaborative Filtering approaches when dealing with recommendation data, mainly due to the vast amounts of data and their sparse nature. In order to improve the scalability and performance of Collaborative Filtering approaches, several authors proposed successful approaches combining Collaborative Filtering with clustering techniques. In this work, we study the effectiveness of biclustering, an advanced clustering technique that groups rows and columns simultaneously, in Collaborative Filtering. When applied to the classic U-I interaction matrices, biclustering considers the duality relations between users and items, creating clusters of users who are similar under a particular group of items. We propose USBCF, a novel biclustering-based Collaborative Filtering approach that creates user specific models to improve the scalability of traditional CF approaches. Using a realworld dataset, we conduct a set of experiments to objectively evaluate the performance of the proposed approach, comparing it against baseline and state-of-the-art Collaborative Filtering methods. Our results show that the proposed approach can successfully suppress the main limitation of the previously proposed state-of-the-art biclustering-based Collaborative Filtering (BBCF) since BBCF can only output predictions for a small subset of the system users and item (lack of coverage). Moreover, USBCF produces rating predictions with quality comparable to the state-of-the-art approaches

A reinforcement learning recommender system using bi-clustering and Markov Decision Process

Collaborative filtering (CF) recommender systems are static in nature and does not adapt well with changing user preferences. User preferences may change after interaction with a system or after buying a product. Conventional CF clustering algorithms only identifies the distribution of patterns and hidden correlations globally. However, the impossibility of discovering local patterns by these algorithms, headed to the popularization of bi-clustering algorithms. Bi-clustering algorithms can analyze all dataset dimensions simultaneously and consequently, discover local patterns that deliver a better understanding of the underlying hidden correlations. In this paper, we modelled the recommendation problem as a sequential decision-making problem using Markov Decision Processes (MDP). To perform state representation for MDP, we first converted user-item votings matrix to a binary matrix. Then we performed bi-clustering on this binary matrix to determine a subset of similar rows and columns. A bi-cluster merging algorithm is designed to merge similar and overlapping bi-clusters. These bi-clusters are then mapped to a squared grid (SG). RL is applied on this SG to determine best policy to give recommendation to users. Start state is determined using Improved Triangle Similarity (ITR similarity measure. Reward function is computed as grid state overlapping in terms of users and items in current and prospective next state. A thorough comparative analysis was conducted, encompassing a diverse array of methodologies, including RL-based, pure Collaborative Filtering (CF), and clustering methods. The results demonstrate that our proposed method outperforms its competitors in terms of precision, recall, and optimal policy learning