The Singular Value Decomposition (SVD) is a fundamental algorithm used to understand the structure of data by providing insight into the relationship between the row and column factors. SVD aims to approximate a rectangular data matrix, given some rank restriction, especially lower rank approximation. In practical data analysis, however, outliers and missing values maybe exist that restrict the...

Singular value decomposition (SVD) is a useful multivariate technique for dimension reduction. It has been successfully applied to analyze microarray data, where the eigen vectors are called eigen-genes/arrays. One weakness associated with the SVD is the interpretation. The eigen-genes are essentially linear combinations of all the genes. It is desirable to have sparse SVD, which retains the di...

We demonstrate an implementation for an approximate rank-k SVD factorization, combiningwell-known randomized projection techniques with previously implemented map/reduce solutions in order to compute steps of the random projection based SVD procedure, such QR and SVD. We structure the problem in a way that it reduces to Cholesky and SVD factorizations on k× k matrices computed on a single machi...

In this work we consider algorithms based on the Singular Value Decomposition (SVD) to approximate Lyapunov and Exponential Dichotomy spectra of dynamical systems. We review existing contributions, and propose new algorithms of the continuous SVD method. We present implementation details for the continuous SVD method, and illustrate on several examples the behavior of continuous (and also discr...

The text retrieval method using latent semantic indexing (LSI) technique with truncated singular value decomposition (SVD) has been intensively studied in recent years. The SVD reduces the noise contained in the original representation of the term–document matrix and improves the information retrieval accuracy. Recent studies indicate that SVD is mostly useful for small homogeneous data collect...

Singular Value Decomposition (SVD) is of great significance in theory development of mathematics and statistics. In this paper we propose the SVD for 3-dimensional (3-D) matrices and extend it to the general Multidimensional Matrices (MM). We use the basic operations associated with MM introduced by Solo to define some additional aspects of MM. We achieve SVD for 3-D matrix through these MM ope...

The text retrieval method using Latent Semantic Indexing (LSI) technique with truncated Singular Value Decomposition (SVD) has been intensively studied in recent years. The SVD reduces the noise contained in the original representation of the term-document matrix and improves the information retrieval accuracy. Recent studies indicate that SVD is mostly useful for small homogeneous data collect...

Introduction: Brain visual evoked potential (VEP) signals are commonly known to be accompanied by high levels of background noise typically from the spontaneous background brain activity of electroencephalography (EEG) signals. Material and Methods: A model based on dyadic filter bank, discrete wavelet transform (DWT), and singular value decomposition (SVD) was developed to analyze the raw data...

The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and then show the central role of SVD in matrices. Using majorization theory, we consider variational principles of singular values and eigenvalues. Built on SVD...