| # Install on Terminal of MacOS # 1. NumPy #pip3 install -U numpy # 2. pandas #pip3 install -U pandas # 3. matplotlib #pip3 install -U matplotlib # 4. scikit-learn (sklearn) #pip3 install -U scikit-learn # 5. seaborn #pip3 install -U seaborn |
1_MacOS_Terminal.txt
| ########## Run Terminal on MacOS and execute ### TO UPDATE cd "YOUR_WORKING_DIRECTORY" python3 pca01.py X.csv 2 x1 x2 |
Input data files
X.csv
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0.39864720557220024,0.02318655255760607 |
Python files
pca01.py
| #################### Principal Component Analysis in Python #################### #Run this script on Terminal of MacOS as follows: # #python3 pca01.py X.csv 2 x1 x2 #python3 pca01.py (X file that includes columns x1 and x2) (number of PCA components) (column x1) (column x2) #Reference # #In Depth: Principal Component Analysis #https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html ########## import import sys # #print(sys.argv[0]) #pca01.py # Xfilename = sys.argv[1] n = int(sys.argv[2]) x1name = sys.argv[3] x2name = sys.argv[4] import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns; sns.set() from sklearn.decomposition import PCA ########## ########## raw data plotting #rng = np.random.RandomState(1) # #X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T # # #print(type(X)) #<class 'numpy.ndarray'> #print(X.shape) # #colnames=['x1', 'x2'] #pd.DataFrame(X).to_csv('X.csv', header=False, index=False) # #add x1, x2 to the columns of X.csv X = pd.read_csv(Xfilename, header=0) # #print(X) #print(X[x1name]) #print(X[x2name]) #plt.scatter(X[:, 0], X[:, 1]) plt.scatter(X[x1name], X[x2name]) plt.xlabel(x1name) plt.ylabel(x2name) plt.axis('equal') plt.savefig('Fig_1.png') plt.show() plt.close() ########## ########## PCA fitting pca = PCA(n_components=n) pca.fit(X) print(pca.components_) ''' [[-0.94446029 -0.32862557] [-0.32862557 0.94446029]] ''' ''' x1 x2 pc1 -0.94446029 -0.32862557 pc2 -0.32862557 0.94446029 Namely, pc1 (calculated) = ((-0.94446029) * x1) + ((-0.32862557) * x2)) pc2 (calculated) = ((-0.32862557) * x1) + (( 0.94446029) * x2)) ''' print(pca.explained_variance_) #[0.7625315 0.0184779] print(pca.explained_variance_ratio_) #[0.97634101 0.02365899] print(np.cumsum(pca.explained_variance_ratio_)) #[0.97634101 1. ] ########## vector drawing function def draw_vector(v0, v1, ax=None): ax = ax or plt.gca() arrowprops=dict(arrowstyle='->', linewidth=2, color='k', shrinkA=0, shrinkB=0) ax.annotate('', v1, v0, arrowprops=arrowprops) ########## ########## plot data x1 & x2 and principal components PC1 & PC2 fig, ax = plt.subplots(1, 2, figsize=(16, 6)) fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1) ##### PCA X_pca = pca.transform(X) #print(type(X_pca[:, 0])) #<class 'numpy.ndarray'> # #print(max(X_pca[:, 0])) #2.6580358349697173 # #print(np.argmax(X_pca[:, 0])) #50 # #print(X_pca[:, 0][np.argmax(X_pca[:, 0])]) #2.6580358349697173 # #print(max(X_pca[:, 1])) #0.393203001154575 # #print(X_pca[:, 1][np.argmax(X_pca[:, 1])]) #0.393203001154575 ##### raw data #X[:, 0] #print(X[x1name][np.argmax(X_pca[:, 0])]) #-2.488382767219812 # #print(X[x2name][np.argmax(X_pca[:, 0])]) #-0.844571248983918 #X[:, 1] #print(X[x1name][np.argmax(X_pca[:, 1])]) #-0.3526694737890958 # #print(X[x2name][np.argmax(X_pca[:, 1])]) #0.2778729045016903 ##### validation: PCA data and raw data ###pc1 # #print(((X[x1name][np.argmax(X_pca[:, 0])]) ** 2) + ((X[x2name][np.argmax(X_pca[:, 0])]) ** 2)) #6.905349390806785 #(-2.488382767219812) ** 2 + (-0.844571248983918) ** 2 # #print(max(X_pca[:, 0]) ** 2) #7.065154499983162 #(2.6580358349697173) ** 2 ###pc2 # #print(((X[x1name][np.argmax(X_pca[:, 1])]) ** 2) + ((X[x2name][np.argmax(X_pca[:, 1])]) ** 2)) #0.2015891087988832 #(-0.3526694737890958) ** 2 + (0.2778729045016903) ** 2 # #print((max(X_pca[:, 1])) ** 2) #0.15460860011696473 #(0.393203001154575) ** 2 ##### plot raw data #ax[0].scatter(X[:, 0], X[:, 1], alpha=0.2) ax[0].scatter(X[x1name], X[x2name], alpha=0.2) for length, vector in zip(pca.explained_variance_, pca.components_): v = vector * 3 * np.sqrt(length) draw_vector(pca.mean_, pca.mean_ + v, ax=ax[0]) # ax[0].axis('equal') #ax[0].set(xlabel='x', ylabel='y', title='input') ax[0].set(xlabel=x1name, ylabel=x2name, title='Raw Data') # ax[0].text(X[x1name][np.argmax(X_pca[:, 0])] * 1.00, X[x2name][np.argmax(X_pca[:, 0])] * 1.15, '(' + str(X[x1name][np.argmax(X_pca[:, 0])]) + ', ' + str(X[x2name][np.argmax(X_pca[:, 0])]) + ')') ax[0].text(X[x1name][np.argmax(X_pca[:, 1])] * 1.10, X[x2name][np.argmax(X_pca[:, 1])] * 1.30, '(' + str(X[x1name][np.argmax(X_pca[:, 1])]) + ', ' + str(X[x2name][np.argmax(X_pca[:, 1])]) + ')') # ##### plot principal components ax[1].scatter(X_pca[:, 0], X_pca[:, 1], alpha=0.2) # #draw_vector([0, 0], [0, 3], ax=ax[1]) draw_vector([0, 0], [0, max(X_pca[:, 1])], ax=ax[1]) # #draw_vector([0, 0], [3, 0], ax=ax[1]) draw_vector([0, 0], [max(X_pca[:, 0]),0], ax=ax[1]) # ax[1].axis('equal') ''' ax[1].set(xlabel='PC1', ylabel='PC2', title='Principal Components', xlim=(-5, 5), ylim=(-3, 3.1)) ''' #print(max(X_pca[:, 0])) #print(min(X_pca[:, 0])) #print(max(X_pca[:, 1])) #print(min(X_pca[:, 1])) # ax[1].set( xlabel='PC1', ylabel='PC2', title='Principal Components', xlim=(min(X_pca[:, 0]), max(X_pca[:, 0])), ylim=(min(X_pca[:, 1]), max(X_pca[:, 1])) ) # ax[1].text(max(X_pca[:, 0])/2, 0.05, '(' + str(max(X_pca[:, 0])) + ', 0)') ax[1].text(0.05, max(X_pca[:, 1])/2, '(0, ' + str(max(X_pca[:, 1])) + ')') # plt.savefig('Fig_2.png') plt.show() plt.close() ########## output ##### output principal components pc1 = pd.DataFrame(X_pca[:, 0]) pc1.rename({0:'pc1'},axis=1,inplace=True) pc2 = pd.DataFrame(X_pca[:, 1]) pc2.rename({0:'pc2'},axis=1,inplace=True) Xpca = pd.concat( [ pc1, pc2 ], axis=1 ) #print(Xpca) Xpca.to_csv('Xpca.csv', header=True, index=False) ##### output raw data and principal components XXpca = pd.concat( [ X, Xpca ], axis=1 ) #print(XXpca) XXpca.to_csv('XXpca.csv', header=True, index=False) |
Figures
Fig_1.png
Fig_2.png
References
In Depth: Principal Component Analysis
https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html
https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html
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