Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse...

You want to find a linear combination of the x coordinates that correlates well over the data with an (in general, different) linear combination of the y coordinates. In fact, you want to find the best such matched pair of linear combinations on the x and y sides, that is, the one yielding the largest coefficient of correlation. But why stop there? Once you have the best pair, you can ask for t...

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...

High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data analysis. Existing methods, aimed at signal reconstruction and deconvolution...

The singular value decomposition, or SVD , has been studied in the past as a tool for detecting and understanding patterns in a collection of documents. We show how the matrices produced by the SVD calculation can be interpreted, allowing us to spot patterns of characters that indicate particular topics in a corpus. A test collection, consisting of two days of AP newswire tra c, is used as a ru...

In this paper, we propose a novel technique for video summarization based on the Singular Value Decomposition (SVD). For the input video sequence, we create a feature-frame matrix A, and perform the SVD on it. From this SVD, we are able to not only derive the reened feature space to better cluster visually similar frames, but also deene a metric to measure the amount of visual content contained...

Singular value decomposition has been used in signal processing, image processing, principal component analysis, robotics and my other real time applications. These applications demand fast processing of large datasets. SVD needs large amount of computation. In this paper, we present the parallel implementation of Singular Value Decomposition in FGPA. SVD is implemented using two sided Jacobi a...

High complexity of lattice construction algorithms and uneasy way of visualising lattices are two important problems connected with the formal concept analysis. Algorithm complexity plays significant role when computing all concepts from a huge incidence matrix. In this paper we try to modify an incidence matrix using matrix decomposition, creating a new matrix with fewer dimensions as an input...

Let A be an m × n matrix with m ≥ n. Then one form of the singular-value decomposition of A is A = UΣV, where U and V are orthogonal and Σ is square diagonal. That is, UUT = Irank(A), V V T = Irank(A), U is rank(A)×m, V is rank(A)× n and Σ =   σ1 0 · · · 0 0 0 σ2 · · · 0 0 .. .. . . . .. .. 0 0 · · · σrank(A)−1 0 0 0 · · · 0 σrank(A)   is a rank(A)× rank(A) diagonal matrix. In add...

This paper proposes a novel signature based on singular value decomposition (SVD) for video sequence matching. By considering the input image as a matrix, a partition procedure is first performed to separate the matrix into non-overlapping sub-images of a fixed size. The SVD process then individually decomposes each partitioned sub-image into an singular value and the corresponding singular vec...