Singular Value Decomposition

奇異值分解( SVD )的主要應用就是「對特定資料集合做拆解，以便找出相對數量少卻富含重要資訊的要素組成新資料集合，並以此來近似原先的資料集合」，達到以簡馭繁或是減少雜訊的目的( a low-dimensional representation of a high-dimensional matrix )。

Eigenvalues play an important role in situations where the matrix is a transformation from one vector space onto itself.＂

＂Singular values play an important role where the matrix is a transformation from one vector space to a different vector space, possibly with a different dimension.＂

影音說明1(YouTube)

影音說明2(YouTube)

影音說明3(YouTube)

影音說明4(YouTube)

影音說明5(YouTube)

svdFull.ipynb(link)

svdReduced.ipynb(link)

import numpy as np

import numpy.linalg as la

np.set_printoptions(precision=4, suppress=True)

A= np.array([[1,2,3,4], [1,1,2,3],[0,1,1,0]])

u, s, vt = la.svd(A, full_matrices=True)

import numpy as np

import numpy.linalg as la

np.set_printoptions(precision=4, suppress=True)

A= np.array([[1,2,3,4], [1,1,2,3],[0,1,1,0]])

u, s, vt = la.svd(A, full_matrices=False)