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July 24, 2017 20:57
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| import numpy as np | |
| import matplotlib.pyplot as plt | |
| class NNet(object): | |
| def __init__(self, n_in, n_hidden, n_out): | |
| self.n_in = n_in | |
| self.n_hidden = n_hidden | |
| self.n_out = n_out | |
| self.W1 = np.random.randn(n_in, n_hidden) | |
| self.W2 = np.random.randn(n_hidden, n_out) | |
| self.b1 = np.random.randn(n_hidden,) | |
| self.b2 = np.random.randn(n_out,) | |
| def sigmoid(self, z): | |
| return 1/(1 + np.exp(-z)) | |
| def sig_prime(self, z): | |
| return (np.exp(-z))/((1+np.exp(-z))**2) | |
| def propagate_forward(self, X): | |
| self.z1 = np.dot(self.W1.T, X) + self.b1 | |
| self.a1 = self.sigmoid(self.z1) | |
| self.z2 = np.dot(self.W2.T, self.a1) + self.b2 | |
| self.a2 = self.sigmoid(self.z2) | |
| return self.a2 | |
| def cost(self, y, y_hat): | |
| #y_hat = np.round(y_hat) | |
| return np.mean((y - y_hat)**2) | |
| def accuracy(self, y, y_hat): | |
| y_hat = np.round(y_hat) | |
| return 100 - (np.sum((y - y_hat)**2)/len(y))*100 | |
| def cost_grad(self, X, y): | |
| y_hat = self.propagate_forward(X) | |
| d2 = np.multiply(self.sig_prime(self.z2), -(y - y_hat)) | |
| gJ_W2 = np.matrix(np.multiply(self.a1.T, d2)) | |
| d1 = np.dot(self.W2, d2)*self.sig_prime(self.z1) | |
| gJ_W1 = np.dot(np.matrix(X).T, np.matrix(d1)) | |
| return [gJ_W1, d1, gJ_W2, d2] | |
| m = 1000 | |
| n = 2 | |
| X = np.zeros((m, n)) | |
| y = np.zeros((m,1)) | |
| import random | |
| import math | |
| i = 0 | |
| for r, theta in zip(np.linspace(0, 5, num=m), np.linspace(0, 8 * math.pi, num=m)): | |
| r += random.random() | |
| X[i] = [r * math.cos(theta), r * math.sin(theta)] | |
| if i < 333: | |
| y[i] = 0 | |
| elif i < 666: | |
| y[i] = 1 | |
| else: | |
| y[i] = 1 | |
| i += 1 | |
| nnet = NNet(n, 5, 1) | |
| learning_rate = 0.08 | |
| improvement_threshold = 0.995 | |
| cost = np.inf | |
| xs = [] | |
| ys = [] | |
| accs = [] | |
| itera = 0 | |
| while cost > 0: | |
| cost = nnet.cost(y, [nnet.propagate_forward(x_train) for x_train in X]) | |
| acc = nnet.accuracy(y, [nnet.propagate_forward(x_train) for x_train in X]) | |
| if itera % 100 == 0: | |
| xs.append(itera) | |
| ys.append(cost) | |
| accs.append(acc) | |
| print("--- iter ",itera, " ---") | |
| print("Cost", cost) | |
| print("Acc:", acc ,"\n","-"*15) | |
| if itera >= 1000: | |
| print("Gradient descent is taking too long, giving up.") | |
| break | |
| cost_grads = [nnet.cost_grad(x_train, y_train) for x_train, y_train in zip(X, y)] | |
| gW1 = [grad[0] for grad in cost_grads] | |
| gb1 = [grad[1] for grad in cost_grads] | |
| gW2 = [grad[2] for grad in cost_grads] | |
| gb2 = [grad[3] for grad in cost_grads] | |
| nnet.W1 -= np.mean(gW1, axis=0)/2 * learning_rate | |
| nnet.b1 -= np.mean(gb1, axis=0)/2 * learning_rate | |
| nnet.W2 -= np.mean(gW2, axis=0).T/2 * learning_rate | |
| nnet.b2 -= np.mean(gb2, axis=0)/2 * learning_rate | |
| itera += 1 | |
| plt.plot(ys) | |
| plt.show() | |
| plt.plot(accs) | |
| plt.show() |
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