feat(alg): add pca

Author: jessicayung

algorithms/load_data.py

@@ -0,0 +1,19 @@
+import pandas as pd
+from sklearn.preprocessing import StandardScaler
+
+def load_iris(std=False):
+    df = pd.read_csv(
+        filepath_or_buffer='https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data', 
+        header=None, 
+        sep=',')
+
+    df.columns=['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid', 'class']
+    df.dropna(how="all", inplace=True) # drops the empty line at file-end
+
+    X = df.ix[:,0:4].values
+    y = df.ix[:,4].values
+
+    if std:
+        X = StandardScaler().fit_transform(X)
+
+    return X, y

algorithms/pca.py

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+"""
+Principal Components Analysis (PCA) using NumPy
+
+Dataset: Iris dataset.
+Adapted from Plotly PCA tutorial
+https://plot.ly/ipython-notebooks/principal-component-analysis/
+"""
+
+from load_data import load_iris
+import numpy as np
+
+
+X_std, y = load_iris(std=True)
+
+
+def pca(X_std):
+
+    # 1. Calculate covariance matrix
+    mean_vec = np.mean(X_std, axis=0)
+    # same as np.cov(X_std.T)
+    N = X_std.shape[0]
+    cov_mat = (X_std - mean_vec).T.dot((X_std - mean_vec)) / (N-1)
+
+    # 2. Find eigenvectors and eigenvalues by SVD
+    u,s,v = np.linalg.svd(X_std.T)
+
+    eig_vals = s**2/(N-1)
+    eig_vecs = u
+
+    # Can also do by eigendecomposition -> less efficient, O(N^3) 
+    # vs O(min(M,N)MN).
+    # can also do for cor_mat1 = np.corrcoef(X_std.T)
+    # eig_vals, eig_vecs = np.linalg.eig(cov_mat)
+
+    # 3. Select PCs
+    # Make a list of (eigenvalue, eigenvector) tuples
+    eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]
+
+    # Sort the (eigenvalue, eigenvector) tuples from high to low
+    eig_pairs.sort()
+    eig_pairs.reverse()
+
+    # Visually confirm that the list is correctly sorted by decreasing eigenvalues
+    print('Eigenvalues and eigenectors, in descending order of eigenvalues:')
+    for i in eig_pairs:
+        print(i)
+    return eig_pairs
+
+eig_pairs = pca(X_std)