Modelling sparse and large data sets is highly in demand yet challenging in recommender systems. With the computation only on the non-zero ratings, Poisson Factorization (PF) enabled by variational inference has shown its high efficiency in scalable recommendation, e.g., modeling millions of ratings. However, as PF learns the ratings by individual users on items with the Gamma distribution, it cannot capture the coupling relations between users (items) and the rating popularity (i.e., favorable rating scores that are given to one item) and rating sparsity (i.e., those users (items) with many zero ratings) for one item (user). This work proposes Coupled Poisson Factorization (CPF) to learn the couplings between users (items), and the user/item attributes (i.e., metadata) are integrated into CPF to form the Metadata-integrated CPF (mCPF) to not only handle sparse but also popular ratings in very large-scale data. Our empirical results show that the proposed models significantly outperform PF and address the key limitations in PF for scalable recommendation.

Matrix Factorization (MF) is widely used in Recommender Systems (RSs) for estimating missing ratings in the rating matrix. MF faces major challenges of handling very sparse and large data. Poisson Factorization (PF) as an MF variant addresses these challenges with high efficiency by only computing on those non-missing elements. However, ignoring the missing elements in computation makes PF weak or incapable for dealing with columns or rows with very few observations (corresponding to sparse items or users). In this work, Metadata-dependent Poisson Factorization (MPF) is invented to address the user/item sparsity by integrating user/item metadata into PF. MPF adds the metadata-based observed entries to the factorized PF matrices. In addition, similar to MF, choosing the suitable number of latent components for PF is very expensive on very large datasets. Accordingly, we further extend MPF to Metadata-dependent Infinite Poisson Factorization (MIPF) that integrates Bayesian Nonparametric (BNP) technique to automatically tune the number of latent components. Our empirical results show that, by integrating metadata, MPF/MIPF significantly outperform the state-of-the-art PF models for sparse and large datasets. MIPF also effectively estimates the number of latent components.

A conjugate Gamma-Poisson model for Dynamic Matrix Factorization incorporated with metadata influence (mGDMF for short) is proposed to effectively and efficiently model massive, sparse and dynamic data in recommendations. Modeling recommendation problems with a massive number of ratings and very sparse or even no ratings on some users/items in a dynamic setting is very demanding and poses critical challenges to well-studied matrix factorization models due to the large-scale, sparse and dynamic nature of the data. Our proposed mGDMF tackles these challenges by introducing three strategies: (1) constructing a stable Gamma-Markov chain model that smoothly drifts over time by combining both static and dynamic latent features of data; (2) incorporating the user/item metadata into the model to tackle sparse ratings; and (3) undertaking stochastic variational inference to efficiently handle massive data. mGDMF is conjugate, dynamic and scalable. Experiments show that mGDMF significantly (both effectively and efficiently) outperforms the state-of-the-art static and dynamic models on large, sparse and dynamic data.

Numerical data (e.g., DNA micro-array data, sensor data) pose a challenging problem to existing frequent pattern mining methods which hardly handle them. In this framework, gradual patterns have been recently proposed to extract covariations of attributes, such as: "When X increases, Y decreases". There exist some algorithms for mining frequent gradual patterns, but they cannot scale to real-world databases. We present in this paper GLCM, the first algorithm for mining closed frequent gradual patterns, which proposes strong complexity guarantees: the mining time is linear with the number of closed frequent gradual item sets. Our experimental study shows that GLCM is two orders of magnitude faster than the state of the art, with a constant low memory usage. We also present PGLCM, a parallelization of GLCM capable of exploiting multicore processors, with good scale-up properties on complex datasets. These algorithms are the first algorithms capable of mining large real world datasets to discover gradual patterns.