We consider the problem of matrix approximation and denoising induced by the Kronecker
product decomposition. Specifically, we propose to approximate a given matrix by the sum of …

Singular values of a data in a matrix form provide insights on the structure of the data, the
effective dimensionality, and the choice of hyper-parameters on higher-level data analysis …

We introduce a “learning-based” algorithm for the low-rank decomposition problem: given
an $ n\times d $ matrix $ A $, and a parameter $ k $, compute a rank-$ k $ matrix $ A'$ that …

Kernel matrices that encode the distance (or similarity) between data points are widely used
throughout the computational sciences for classification, clustering, and dimensionality …

The CUR matrix decomposition and the Nyström approximation are two important low-rank
matrix approximation techniques. The Nyström method approximates a symmetric positive …

We study the Kronecker product regression problem, in which the design matrix is a
Kronecker product of two or more matrices. Formally, given $ A_i\in\R^{n_i\times d_i} $ for …

Low-rank matrix recovery problems involving high-dimensional and heterogeneous data
appear in applications throughout statistics and machine learning. The contribution of this …

In multi-response regression, pursuit of two different types of structures is essential to battle
the curse of dimensionality. In this paper, we seek a sparsest decomposition representation …

Kernel methods are powerful tools for modeling nonlinear data. However, the amount of
computation and memory required for kernel methods becomes the bottleneck when dealing …

The kernel trick concept, formulated as an inner product in a feature space, facilitates
powerful extensions to many well-known algorithms. While the kernel matrix involves inner …