SVD.md

SVD (Singular Value Decomposition)

for more: wikipedia, machinelearningmastery.com, statbot.co

• Allows to achieve variable reduction for ML computation.

• Can also be used for least sqaure linear regression, image compression and denoising data.

• Offers various useful applications in signal processing, psychology, sociology, climate, atomospheric science, statistics and astronomy.

• SVD is a matrix decomposition method. It's stable as all matrices have an SVD.

• It helps reduce a big matrix to it's constituent parts to make calculations simpler.

• SVD has been known under names like factor analysis, principal component decomposition and empirical orthogonal function; mathematically equivalent and need grip over matrix algebra and vector calculus.

• SVD decomposes a larger matrix into 3 matrices as A = USVᵀ

• A is main m x n matrix

• U is m x n orthogonal matrix; is left Singular Vector

• S Sigma is an n x n diagonal matrix; Si are called Singular Values

• V is n x n orthogonal matrix, transposed; is right Singular Vector

Identity Matrix is a square matrix with diagonal elements 1 and others 0. Diagonal Matrix has all entries other than diagonal as 0. Singular Matrix has determinant 0 or a sqaure matrix which doesn't have a matrix inverse.

• Sum of squares of Singular Values from diagonal matrix should be equal to toal variance in A. Truncated SVD can contain major portion of Variance.

• scipy provides with svd() and TruncatedSVD() methods to aid

• sample code

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