Exercise 3 included

ml2/spiral.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from math import cos, sin
+from scipy.constants import golden, pi
+
+def gen_spiral_dataset(n_examples=500, n_classes=2, a=None, b=None, pi_space=3):
+    n_spirals = n_classes
+    
+    # default: golden spiral
+    if a is None:
+        a = golden
+    if b is None:
+        b = 2/pi
+
+    theta = np.linspace(0,pi_space*pi, num=n_examples)
+    xy = np.zeros((n_examples,2))
+
+    # logaritmic spirals
+    x_golden_parametric = lambda a, b, theta: a**(theta*b) * cos(theta)
+    y_golden_parametric = lambda a, b, theta: a**(theta*b) * sin(theta)
+    x_golden_parametric = np.vectorize(x_golden_parametric)
+    y_golden_parametric = np.vectorize(y_golden_parametric)
+
+    # rotation matrix
+    gen_rotation = lambda theta: np.array([[cos(theta), -sin(theta)],[sin(theta), cos(theta)]])
+
+    # rotation angles
+    rot_division = (2*pi) / n_spirals
+    rot_thetas = [i * rot_division for i in range(n_spirals)]
+
+    XY = np.zeros((2, n_examples, n_spirals))
+    for i in range(n_spirals):
+        x = x_golden_parametric(a, b, theta)
+        y = y_golden_parametric(a, b, theta)
+        xy = np.vstack((x,y))
+        R = gen_rotation(rot_thetas[i])
+        xy_ = np.dot(R.T, xy)
+        XY[:,:,i] = xy_
+    
+    return XY
+
+def load_spiral_dataset(n_examples=300, n_classes=2):
+    XY = gen_spiral_dataset(n_examples, n_classes)
+    X_s = []
+    y_s = []
+    for i in range(XY.shape[2]):
+        X = XY[:,:,i].T
+        X_s.append(X)
+        y = np.array([i] * XY.shape[1]).T
+        y_s.append(y)
+    X = np.vstack(X_s)
+    y = np.hstack(y_s)
+    
+    return X, y
+
+def plot_dataset(X,y):
+    cm = plt.cm.RdBu
+    plt.scatter(X[:,0], X[:,1], c=y, cmap=cm, lw=.5, s=10)
+    
+def plot_decision_surface(X, y, classifier):
+    h = .02
+    cm = plt.cm.RdBu
+    
+    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
+    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
+    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
+                         np.arange(y_min, y_max, h))
+    
+
+    z = classifier.predict(np.c_[xx.ravel(), yy.ravel()])#[:, 1]
+    
+    z = z.reshape(xx.shape)
+    plt.contourf(xx, yy, z, cmap=cm, alpha=.8)
+    
+    plot_dataset(X, y)