class pca init

CH16/README.md

@@ -28,6 +28,7 @@
 - 书中有提到在实际问题中，不同变量可能有不同的量纲，直接求主成分有时会产生不合理的结果。**消除这个影响**常对各个随机变量实施规范化，使其均值为0，方差为1。
 - 关于主成分的性质，规范化的变量总体主成分主要是围绕特征值和特征向量展开的。
 - 关于总体和样本的说明可以参考一下Strang的书[^1]中第十二章部分说明。
+- 关于$k$的选择，2000年有一个文章自动选择[^2]。
 
 ## 内容
 
@@ -152,4 +153,6 @@ $$
 
 ## 参考
 
-[^1]: [Introduction to Linear Algebra](https://github.com/J-Mourad/Introduction-to-Linear-Algebra-5th-Edition---EE16A/raw/master/Ed%205%2C%20Gilbert%20Strang%20-%20Introduction%20to%20Linear%20Algebra%20(2016%2C%20Wellesley-Cambridge%20Press).pdf)
+[^1]: [Introduction to Linear Algebra](https://github.com/J-Mourad/Introduction-to-Linear-Algebra-5th-Edition---EE16A/raw/master/Ed%205%2C%20Gilbert%20Strang%20-%20Introduction%20to%20Linear%20Algebra%20(2016%2C%20Wellesley-Cambridge%20Press).pdf)
+[^2]: [Automatic choice of dimensionality for PCA](https://papers.nips.cc/paper/1853-automatic-choice-of-dimensionality-for-pca.pdf)
+

CH16/pca.py

@@ -0,0 +1,27 @@
+#! /usr/bin/env python
+#! -*- coding=utf-8 -*-
+# Project:  Lihang
+# Filename: pca
+# Date: 5/31/19
+# Author: 😏 <smirk dot cao at gmail dot com>
+# from svd import SVD # someday
+import numpy as np
+
+
+class PCA(object):
+    def __init__(self, n_components=2):
+        self.n_components_ = n_components
+        self.explained_variance_ratio_ = None
+        self.singular_values_ = None
+
+    def __str__(self,):
+        rst = "PCA algorithms:\n"
+        rst += "n_components: " + str(self.n_components_)
+        return rst
+
+    def fit(self, x):
+        # check n_components and min(n_samples, n_features)
+        pass
+
+    def fit_transform(x):
+        return x

CH16/unit_test.py

@@ -9,6 +9,8 @@
 # Ref to : https://code.visualstudio.com/docs/python/unit-testing
 import unittest
 from sklearn import datasets
+from pca import PCA as smirkpca
+from sklearn.decomposition import PCA as skpca
 import matplotlib.pyplot as plt
 import numpy as np
 
@@ -108,3 +110,21 @@ def test_ex1601(self):
         # plt.scatter(rst[:, 0], rst[:, 1])
         # plt.show()
 
+    def test_pca(self):
+        # raw data
+        x = np.array([[2, 3, 3, 4, 5, 7],
+                      [2, 4, 5, 5, 6, 8]])
+        # for sklearn x.shape == (n_samples, n_features)
+        pca_sklearn = skpca(n_components=2)
+        pca_sklearn.fit(x.T)
+        print("\n")
+        print(40*"*"+"sklearn_pca"+40*"*")
+        print(pca_sklearn.explained_variance_ratio_)
+        print(pca_sklearn.singular_values_)
+
+        print(40*"*"+"smirk_pca"+40*"*")
+        pca_test = smirkpca(n_components=2)
+        print(pca_test)
+
+    def test_pca_get_fig(self):
+        pass