Low rank approximation of matrices has been well studied in literature. Singular value
decomposition, QR decomposition with column pivoting, rank revealing QR factorization …

Constrained low-rank matrix approximations have been known for decades as powerful
linear dimensionality reduction techniques able to extract the information contained in large …

We consider a family of algorithms that successively sample and minimize simple stochastic
models of the objective function. We show that under reasonable conditions on …

X≈ WH, W∈ RM× R, H∈ RN× R,(1) to 'explain'the data matrix X, where W≥ 0, H≥ 0, and
R≤ min {M, N}. At first glance, NMF is nothing but an alternative factorization model to …

Understanding, modeling, and predicting student performance in higher education poses
significant challenges concerning the design of accurate and robust diagnostic models …

Topic modeling is a popular technique for exploring large document collections. It has
proven useful for this task, but its application poses a number of challenges. First, the …

We consider global efficiency of algorithms for minimizing a sum of a convex function and a
composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely …

The development of democratic systems is a crucial task as confirmed by its selection as one
of the Millennium Sustainable Development Goals by the United Nations. In this article, we …

Each day humans generate massive volumes of data in a variety of different forms (Lazer et
al., 2009). For example, digitized texts provide a rich source of political content through …

Identifying the underlying structure of a data set and extracting meaningful information is a
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …