Two-way functional data consist of a data matrix whose row and column domains are both structured, for example, temporally or spatially, as when the data are time series collected at different locations in space. We extend one-way functional principal component analysis (PCA) to two-way functional data by introducing regularization of both left and right singular vectors in the singular value d...

In this paper, we present four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture. We particularly emphasize Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left-and right-singular vectors) for sparse matrices arising from two pra...

A recent image quality measure, M-SVD, can express the quality of distorted images either numerically or graphically. Based on the Singular Value Decomposition (SVD), it consistently measures the distortion across different distortion types and within a given distortion type at different distortion levels. The SVD decomposes every real matrix into a product of three matrices A = USV, where U an...

Let A 2 R mn be a matrix with known singular values and singular vectors, and let A 0 be the matrix obtained by appending a row to A. We present stable and fast algorithms for computing the singular values and the singular vectors of A 0 in O ? (m + n) min(m;n) log 2 2 oating point operations, where is the machine precision. Previous algorithms can be unstable and compute the singular values an...

In this paper, we tackle the two-dimensional (2-D) parameter estimation problem for a sum of K ≥ 2 real/complex damped sinusoids in additive white Gaussian noise. According to the rank-K property of the 2-D noise-free data matrix, the damping factor and frequency information is contained in the K dominant left and right singular vectors. Using the sinusoidal linear prediction property of these ...

In this paper, we propose an implicitly restarted block Lanczos bidiagonalization (IRBLB) method for computing a few extreme or interior singular values and associated right and left singular vectors of a large matrix A. Our method combines the advantages of a block routine, implicit shifting, and the application of Leja points as shifts in the accelerating polynomial. The method neither requir...

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) finding the left and right singular vectors corresponding to the largest singular value of a cer...

Repositories of motion captured (MoCap) data can be reused for human motion analysis in physical medicine, biomechanics and animation related entertainment industry. MoCap data expressed as a matrix Mm x n can be subject to tampering from shuffling of its elements or change in element values due to motion editing operations. Tampering of archived motion data intentionally or due to machine/huma...

The Topological N=2 Superconformal algebra has 29 different types of singular vectors (in complete Verma modules) distinguished by the relative U(1) charge and the BRST-invariance properties of the vector and of the primary on which it is built. Whereas one of these types only exists at level zero, the remaining 28 types exist for general levels and can be constructed already at level 1. In thi...

In this paper we propose a variant of the Rayleigh quotient method to compute an eigenvalue and corresponding eigenvectors of a matrix. It is based on the observation that eigenvectors of a matrix with eigenvalue zero are also singular vectors corresponding to zero singular values. Instead of computing eigenvector approximations by the inverse power method, we take them to be the singular vecto...