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As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
Non-negative Matrix Factorization (NMF) is a useful method to extract features from multivariate data, but an important and sometimes neglected concern is that NMF can result in non-unique solutions. Often, there exist a Set of Feasible…
Matrix factorization is a simple and effective solution to the recommendation problem. It has been extensively employed in the industry and has attracted much attention from the academia. However, it is unclear what the low-dimensional…
Many matrices associated with fast transforms posess a certain low-rank property characterized by the existence of several block partitionings of the matrix, where each block is of low rank. Provided that these partitionings are known,…
Much work on social media opinion polarization focuses on a flat categorization of stances (or orthogonal beliefs) of different communities from media traces. We extend in this work in two important respects. First, we detect not only…
User and item features of side information are crucial for accurate recommendation. However, the large number of feature dimensions, e.g., usually larger than 10^7, results in expensive storage and computational cost. This prohibits fast…
Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…
Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error…
Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including topic modeling, recommender systems and bioinformatics. Due to the compute-intensive nature of…
In continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose…
Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute.…
Computational drug repositioning aims to discover new therapeutic diseases for marketed drugs and has the advantages of low cost, short development cycle, and high controllability compared to traditional drug development. The matrix…
We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to…
We consider the following Stochastic Boolean Function Evaluation problem, which is closely related to several problems from the literature. A matroid $\mathcal{M}$ (in compact representation) on ground set $E$ is given, and each element…
Matrix factorization is a key component of collaborative filtering-based recommendation systems because it allows us to complete sparse user-by-item ratings matrices under a low-rank assumption that encodes the belief that similar users…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Many computer vision problems can be posed as learning a low-dimensional subspace from high dimensional data. The low rank matrix factorization (LRMF) represents a commonly utilized subspace learning strategy. Most of the current LRMF…
Collaborative filtering models based on matrix factorization and learned similarities using Artificial Neural Networks (ANNs) have gained significant attention in recent years. This is, in part, because ANNs have demonstrated good results…
Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative…
Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality. Making predictions on these time series has become a critical challenge due…