Applications of singular-value decomposition (SVD)
نویسندگان
چکیده
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 addition σ1 ≥ σ2 ≥ · · · ≥ σrank(A) > 0. The σi’s are called the singular values of A and their number is equal to the rank of A. The ratio σ1 σrank(A) can be regarded as a condition number of the matrix A. It is easily verified that the singular-value decomposition can be also written as
منابع مشابه
Graph Clustering by Hierarchical Singular Value Decomposition with Selectable Range for Number of Clusters Members
Graphs have so many applications in real world problems. When we deal with huge volume of data, analyzing data is difficult or sometimes impossible. In big data problems, clustering data is a useful tool for data analysis. Singular value decomposition(SVD) is one of the best algorithms for clustering graph but we do not have any choice to select the number of clusters and the number of members ...
متن کاملFace Recognition Based Rank Reduction SVD Approach
Standard face recognition algorithms that use standard feature extraction techniques always suffer from image performance degradation. Recently, singular value decomposition and low-rank matrix are applied in many applications,including pattern recognition and feature extraction. The main objective of this research is to design an efficient face recognition approach by combining many tech...
متن کاملFeature Extraction of Visual Evoked Potentials Using Wavelet Transform and Singular Value Decomposition
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...
متن کاملSingular Value Decomposition based Steganography Technique for JPEG2000 Compressed Images
In this paper, a steganography technique for JPEG2000 compressed images using singular value decomposition in wavelet transform domain is proposed. In this technique, DWT is applied on the cover image to get wavelet coefficients and SVD is applied on these wavelet coefficients to get the singular values. Then secret data is embedded into these singular values using scaling factor. Different com...
متن کاملSynthesis, characterization and spectroscopic properties of new azo dyes derived from aniline derivatives based on acetylacetone and azo-metal (II) complexes and singular value decomposition (SVD) investigation
Four new azo-dyes, 3-phenyl azopentane-2,4-dion (LA), 3-(4-nitro phenyl azo)-pentane-2,4-dion (LP), 3-(2-nitro phenyl azo)-pentane-2,4-dion (LO) and 4-(1-acetyle-2-oxo-propyl azo)-benzene sulfonate sodium (LS), were synthesized from, aniline, 4-nitroaniline, 2-nitroaniline and sulfanilic acid with acetylacetone, respectively. Reaction of these new dyes with acetate salts of copper(II), nickel(I...
متن کاملA Note on Singular Value Decomposition∗
This note is intended to summarize the definition, properties, interpretation and applications of Singular Value Decomposition (SVD) described by Strang [?], Shilov [?], Johnson and Wichern [?] and Will [?]. 1 Definition Singular Value Decomposition (SVD) technique decomposes a m × n matrix A into the following factored form :
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Mathematics and Computers in Simulation
دوره 67 شماره
صفحات -
تاریخ انتشار 2004