Low rank matrix completion has been applied successfully in a wide range of machine learning applications, such as collaborative filtering, image inpainting and Microarray data imputation. However, many existing algorithms are not scalable to large-scale problems, as they involve computing singular value decomposition. In this paper, we present an efficient and scalable algorithm for matrix com...

Plant structure is utilized for the simpli cation of system analysis and controller synthesis. For plants where the directionality is independent of frequency, the singular value decomposition (SVD) is used to decouple the system into nominally independent subsystems of lower dimension. In H2and H1-optimal control, the controller synthesis can thereafter be performed for each of these subsystem...

We consider a residue form for a singular hypersurface K with isolated singularities. Suppose there are neighbourhoods of the singular points with coordinates in which hypersurface is described by quasihomogeneous polynomials. We find a condition on the weights under which the norm of the Leray residue form is square integrable. For dim K ≥ 2 all simple singularities satisfy this condition. The...

In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear norm regularizes all singular values equally, which is however not flexible enough to fit real scenarios. Weighted nuclear norm minimization (WNNM) is a natu...

Let Ai for i = 1, 2 be an expansive dilation, respectively, on R n and R and ~ A ≡ (A1, A2). Denote by A∞(R × R; ~ A) the class of Muckenhoupt weights associated with ~ A. The authors introduce a class of anisotropic singular integrals on R×R, whose kernels are adapted to ~ A in the sense of Bownik and have vanishing moments defined via bump functions in the sense of Stein. Then the authors est...

Conventional gene selection methods based on principal component analysis (PCA) use only the first principal component (PC) of PCA or sparse PCA to select characteristic genes. These methods indeed assume that the first PC plays a dominant role in gene selection. However, in a number of cases this assumption is not satisfied, so the conventional PCA-based methods usually provide poor selection ...

Low rank modeling has found applications in a wide range of machine learning and data mining tasks, such as matrix completion, dimensionality reduction, compressed sensing, multi-class and multi-task learning. Recently, significant efforts have been devoted to the low rank matrix completion problem, as it has important applications in many domains including collaborative filtering, Microarray d...

This study reports novel hybrid computational methods for the solutions of nonlinear singular Lane-Emden type differential equation arising in astrophysics models by exploiting the strength of unsupervised neural network models and stochastic optimization techniques. In the scheme the neural network, sub-part of large field called soft computing, is exploited for modelling of the equation in an...

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...