This paper provides a classification methodology of Malayalam characters segmented from scanned document images. Optical Character Recognition (OCR) is one of the successful area which has wide variety of applications related to pattern recognition. This paper describes segmented character recognition using Singular Value Decomposition (SVD). Euclidean distance measure is used for finding the n...

The Singular Value Decomposition (SVD) is a longstanding standard for data approximation because it is optimal in the 2 and Frobenius norms. The SVD, nevertheless, suffers from many setbacks, including computational cost, loss of sparsity in the decomposition, and the inability to be updated easily when new information arrives. Additionally, the SVD provides limited information on data features...

A tutorial is presented on the Proper Orthogonal Decomposition (POD), which finds applications in computationally processing large amounts of high-dimensional data with the aim of obtaining low-dimensional descriptions that capture much of the phenomena of interest. The discrete version of the POD, which is the singular value decomposition (SVD) of matrices, is described in some detail. The con...

A data set with n measurements on p variables can be represented by an n × p data matrix X. In highdimensional settings where p is large, it is often desirable to work with a low-rank approximation to the data matrix. The most prevalent low-rank approximation is the singular value decomposition (SVD). Given X, an n × p data matrix, the SVD factorizes X as X = UDV ′, where U ∈ Rn×n and V ∈ Rp×p ...

A series of microarray experiments produces observations of differential expression for thousands of genes across multiple conditions. Principal component analysis(PCA) has been widely used in multivariate data analysis to reduce the dimensionality of the data in order to simplify subsequent analysis and allow for summarization of the data in a parsimonious manner. PCA, which can be implemented...

The focus of this work is to investigate the effects of applying the singular value decomposition (SVD), a linear algebra technique, to the domain of Genetic Algorithms. Empirical evidence, concerning document comparison, suggests that the SVD can be used to model information in such a way that provides both a saving in storage space and an improvement in information retrieval. It will be shown...

In this paper, a robust digital image watermarking scheme for copyright protection applications using the singular value decomposition (SVD) is proposed. In this scheme, an entropy masking model has been applied on the host image for the texture segmentation. Moreover, the local luminance and textures of the host image are considered for watermark embedding procedure to increase the robustness ...

Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics, the matrices are dense, but low-rank matrices. In these cases, a truncated SVD corresponding to the most significant singular values is sufficient. In this paper, we propose a tree based merge-and-truncate algorithm to ...

In this paper, we first discuss the singular value decomposition (SVD) of a quaternion matrix and propose an algorithm to calculate the SVD of a quaternion matrix using its equivalent complex matrix. The singular values of a quaternion matrix are still real and positive, but the two unitary matrices are quaternion matrices with quaternion entries. Then, applications for color image processing b...

We present a parallel software implementation for computing the singular value decomposition (SVD) of general, banded or bidiagonal matrices. First, the matrix is reduced to bidiagonal form. This reduction can be rearranged in a way that allows heavy use of matrix-matrix operations. Then the singular values are computed in an iterative process. Finally the singular vectors are computed independ...