Low-rank modeling generally refers to a class of methods that solves problems by
representing variables of interest as low-rank matrices. It has achieved great success in …

Principal components analysis (PCA) is a well-known technique for approximating a tabular
data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets …

Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric
spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is …

Machine learning and data mining algorithms are becoming increasingly important in
analyzing large volume, multi-relational and multi--modal datasets, which are often …

In recent years, low-rank based tensor completion, which is a higher order extension of
matrix completion, has received considerable attention. However, the low-rank assumption …

Sparse models are particularly useful in scientific applications, such as biomarker discovery
in genetic or neuroimaging data, where the interpretability of a predictive model is essential …

We address the rectangular matrix completion problem by lifting the unknown matrix to a
positive semidefinite matrix in higher dimension, and optimizing a nonconvex objective over …

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to
speed up matrix problems including matrix completion, subspace tracking, and SDP …

Let us consider a case where all of the elements in some continuous slices are missing in
tensor data. In this case, the nuclear-norm and total variation regularization methods usually …

Motivated principally by the low-rank matrix completion problem, we present an extension of
the Frank--Wolfe method that is designed to induce near-optimal solutions on low …