Statistical Learning
Concept
- mean 数学期望（均值）
以下三者的区别：https://www.cnblogs.com/bigmonkey/p/11097322.html
- variance 方差
- https://en.wikipedia.org/wiki/Variance
- root-mean-square deviation, root-mean-square error, RMSD, RMSE（均方差，标准差）
- 开根与原数据差别大，开根之后更利于观察
Non-singular A matrix Inverse and Singular A matrix minimun solution
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import numpy.linalg as la
import scipy.linalg as spla
import numpy as np
A=np.random.rand(10,10)
x_real=np.arange(1,11)
b=A.dot(x_real)
print(A,x_real,b)
Q, R = la.qr(A)
print(Q,R)
qr_x=spla.solve_triangular(R, Q.T.dot(b),lower=False)
print(qr_x)
inverse_component_matrix = np.linalg.inv(A)
print(inverse_component_matrix.dot(b))
PCA
X是去平均值的 Consider an nxp data matrix, X, with column-wise zero empirical mean (the sample mean of each column has been shifted to zero), where each of the n rows represents a different repetition of the experiment, and each of the p columns gives a particular kind of feature (say, the results from a particular sensor).
用于降维。找到一个方向上，这个方向上all samples’ variation最大，即该方向上所有数据点（observations)projection的方差最大。大的方差意味能表达更多的信息。
定义
reference
https://zh.wikipedia.org/wiki/%E4%B8%BB%E6%88%90%E5%88%86%E5%88%86%E6%9E%90
