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Proof of the Singular Value Decomposition

Proof of the Singular Value Decomposition
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Gilbert Strang , Singular Value Decomposition , Matrix Factorization , Principal Components Analysis , Data Analysis , Statistical Modeling , Machine Learning ,

SVD Image Compression, Explained

Singular Value Decomposition (SVD) is a fundamental concept in linear algebra, and it is particularly important in the field of machine learning for tasks such as dimensionality reduction, data compression, and noise reduction. ....

Singular Value Decomposition ,

"Visualising Departures from Symmetry and Bowker's X<sup>2</sup> Statis" by Eric J. Beh and Rosaria Lombardo

Sometimes, the same categorical variable is studied over different time periods or across different cohorts at the same time. One may consider, for example, a study of voting behaviour of different age groups across different elections, or the study of the same variable exposed to a child and a parent. For such studies, it is interesting to investigate how similar, or different, the variable is between the two time points or cohorts and so a study of the departure from symmetry of the variable is important. In this paper, we present a method of visualising any departures from symmetry using correspondence analysis. Typically, correspondence analysis uses Pearson’s chi-squared statistic as the foundation for all of its numerical and visual features. In the case of studying the symmetry of a variable, Bowker’s chi-squared statistic, presented in 1948, provides a simple numerical means of assessing symmetry. Therefore, this paper shall discuss how a correspondence analysis can be perf ....

Michael Greenacre , Bowkers Chi Squared Statistic , Correspondence Analysis , Singular Value Decomposition , Skew Symmetric Matrix ,