A new method for detecting shot boundaries in video sequences using singular value decomposition (SVD) is proposed. The method relies on performing singular value decomposition on the matrix A created from 3D histograms of single frames. We have used SVD for its capabilities to derive a low dimensional refined feature space from a high dimensional raw feature space, where pattern similarity can...

NOTE: I have not thoroughly proofread these notes!!! We recommend the reader review Weeks 9-11 of Linear Algebra: Foundations to Frontiers-Notes to LAFF With.

In this report, we investigate the truncated multilinear singular value decomposition (MLSVD), proposed in De Lathauwer et al. (2000). Truncating the MLSVD results in an approximation, with a prescribed multilinear rank, to a tensor. We present a new error expression for an approximate Tucker decomposition with orthogonal factor matrices. From this expression, new insights are obtained which le...

then σ is a singular value of A and u and v are corresponding left and right singular vectors, respectively. (For generality it is assumed that the matrices here are complex, although given these results, the analogs for real matrices are obvious.) If, for a given positive singular value, there are exactly t linearly independent corresponding right singular vectors and t linearly independent co...

Tomosynthesis is an emerging technique with potential to replace mammography, since it gives 3D information at a relatively small increase in dose and cost. We present an analytical singular-value decomposition of a tomosynthesis system, which provides the measurement component of any given object. The method is demonstrated on an example object. The measurement component can be used as a recon...

A new approach to low-complexity channel estimation in orthogonal-frequency division multiplexing (OFDM) systems is proposed. A lowrank approximation is applied to a linear minimum mean-squared error (LMMSE) estimator that uses the frequency correlation of the channel. By using the singular-value decomposition (SVD) an optimal low-rank estimator is derived, where performance is essentially pres...

The Higher-Order SVD (HOSVD) is a generalization of the Singular Value Decomposition (SVD) to higher-order tensors (i.e. arrays with more than two indices) and plays an important role in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a third-order tensor involves the computation of the SVD of three matrices, which are referred to as "modes"...

The task of digital image compression is the subject of many researches for many years. Up to now this task remains a topic of constant interest. The reason of such interest is that digital media and digital communication are becoming of growing significance worldwide. The subject of this paper is a new original approach to digital image compression. It is based on using singular value decompos...

In this paper we present the usage of singular value decomposition (SVD) in text summarization. Firstly, we mention the taxonomy of generic text summarization methods. Then we describe principles of the SVD and its possibilities to identify semantically important parts of a text. We propose a modification of the SVD-based summarization, which improves the quality of generated extracts. In the s...

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