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...

This paper proposes a neural network approach based on Error Back Propagation (EBP) for classification of different eye images. To reduce the complexity of layered neural network the dimensions of input vectors are optimized using Singular Value Decomposition (SVD). The main objective of this work is to prove usefulness of SVD to form a compact set of features for classification by EBP algorith...

We explore the use of the singular value decomposition (SVD) in image compression. We link the SVD and the multiresolution algorithms. In [22] it is derived a multiresolution representation of the SVD decomposition, and in [15] the SVD algorithm and Wavelets are linked, proposing a mixed algorithm which roughly consist on applying firstly a discrete Wavelet transform and secondly the SVD algori...

The Matrix Factorization models, sometimes called the latent factor models, are a family of methods in the recommender system research area to (1) generate the latent factors for the users and the items and (2) predict users’ ratings on items based on their latent factors. However, current Matrix Factorization models presume that all the latent factors are equally weighted, which may not always...

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...

Singular-value decomposition (SVD)-based multiple-input multiple-output (MIMO) systems have attracted a lot of attention in the wireless community. However, applying SVD to frequency-selective MIMO channels results in unequally weighted single-input single-output (SISO) channels requiring complex resource allocation techniques for optimizing the channel performance. Therefore, a different appro...

It is possible for Singular Value Decomposition (SVD) watermark embedding to have a quasi-one-way functionality. While basic SVD embedding has the drawback of being non-reversible, an advanced SVD method which uses a reversible relation only works one-way. When embedding takes place, the decomposing matrix obtained from the original image differs from the one obtained from the embedded image. T...

The text retrieval method using Latent Semantic Indexing (LSI) with the truncated Singular Value Decomposition (SVD) has been intensively studied in recent years. The term-document matrices after SVD are full matrices, although the rank is reduced substantially. To reduce memory consumption, we examine some strategies to sparsify the truncated SVD matrices. After applying the sparsification str...

In this paper, we extend the well known QR-updating scheme to a similar but more versatile and generally applicable scheme for updating the singular value decomposition (SVD). This is done by supplementing the QR-updating with a Jacobi-type SVD procedure, where apparently only a few SVD steps after each QR-update su ce in order to restore an acceptable approximation for the SVD. This then resul...

Watermarking is an operation to hide important information. In this paper, a new watermarking algorithm using Shearlet transform and GWO optimization algorithm as well as SVD transform is presented. The results of this paper show the improvement of robustness and transparency of the new algorithm.