【Python 代码】CS231n中Softmax线性分类器、非线性分类器对比举例（含python绘图显示结果）

1 #CS231n中线性、非线性分类器举例（Softmax）
#注意其中反向传播的计算 # -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
N = 100 # number of points per class
D = 2 # dimensionality
K = 3 # number of classes
X = np.zeros((N*K,D)) # data matrix (each row = single example)
y = np.zeros(N*K, dtype='uint8') # class labels
for j in xrange(K):
ix = range(N*j,N*(j+1))
r = np.linspace(0.0,1,N) # radius
t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta
X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
y[ix] = j
# lets visualize the data:
plt.xlim([-1, 1])
plt.ylim([-1, 1])
plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
plt.show() # initialize parameters randomly
# 线性分类器
W = 0.01 * np.random.randn(D,K)
b = np.zeros((1,K)) # some hyperparameters
step_size = 1e-0
reg = 1e-3 # regularization strength # gradient descent loop
num_examples = X.shape[0]
for i in xrange(200): # evaluate class scores, [N x K]
scores = np.dot(X, W) + b # compute the class probabilities
exp_scores = np.exp(scores)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K] # compute the loss: average cross-entropy loss and regularization
corect_logprobs = -np.log(probs[range(num_examples),y])
data_loss = np.sum(corect_logprobs)/num_examples
reg_loss = 0.5*reg*np.sum(W*W)
loss = data_loss + reg_loss
if i % 10 == 0:
print "iteration %d: loss %f" % (i, loss) # compute the gradient on scores
dscores = probs
dscores[range(num_examples),y] -= 1
dscores /= num_examples # backpropate the gradient to the parameters (W,b)
dW = np.dot(X.T, dscores)
db = np.sum(dscores, axis=0, keepdims=True) dW += reg*W # regularization gradient # perform a parameter update
W += -step_size * dW
b += -step_size * db # evaluate training set accuracy
scores = np.dot(X, W) + b
predicted_class = np.argmax(scores, axis=1)
print 'training accuracy: %.2f' % (np.mean(predicted_class == y)) # plot the resulting classifier
h = 0.02
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b
Z = np.argmax(Z, axis=1)
Z = Z.reshape(xx.shape)
fig = plt.figure()
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)
plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max()) ## initialize parameters randomly
# 含一个隐层的非线性分类器 使用ReLU
h = 100 # size of hidden layer
W = 0.01 * np.random.randn(D,h)
b = np.zeros((1,h))
W2 = 0.01 * np.random.randn(h,K)
b2 = np.zeros((1,K)) # some hyperparameters
step_size = 1e-0
reg = 1e-3 # regularization strength # gradient descent loop
num_examples = X.shape[0]
for i in xrange(10000): # evaluate class scores, [N x K]
hidden_layer = np.maximum(0, np.dot(X, W) + b) # note, ReLU activation
scores = np.dot(hidden_layer, W2) + b2 # compute the class probabilities
exp_scores = np.exp(scores)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K] # compute the loss: average cross-entropy loss and regularization
corect_logprobs = -np.log(probs[range(num_examples),y])
data_loss = np.sum(corect_logprobs)/num_examples
reg_loss = 0.5*reg*np.sum(W*W) + 0.5*reg*np.sum(W2*W2)
loss = data_loss + reg_loss
if i % 1000 == 0:
print "iteration %d: loss %f" % (i, loss) # compute the gradient on scores
dscores = probs
dscores[range(num_examples),y] -= 1
dscores /= num_examples # backpropate the gradient to the parameters
# first backprop into parameters W2 and b2
dW2 = np.dot(hidden_layer.T, dscores)
db2 = np.sum(dscores, axis=0, keepdims=True)
# next backprop into hidden layer
dhidden = np.dot(dscores, W2.T)
# backprop the ReLU non-linearity
dhidden[hidden_layer <= 0] = 0
# finally into W,b
dW = np.dot(X.T, dhidden)
db = np.sum(dhidden, axis=0, keepdims=True) # add regularization gradient contribution
dW2 += reg * W2
dW += reg * W # perform a parameter update
W += -step_size * dW
b += -step_size * db
W2 += -step_size * dW2
b2 += -step_size * db2
# evaluate training set accuracy
hidden_layer = np.maximum(0, np.dot(X, W) + b)
scores = np.dot(hidden_layer, W2) + b2
predicted_class = np.argmax(scores, axis=1)
print 'training accuracy: %.2f' % (np.mean(predicted_class == y))
# plot the resulting classifier
h = 0.02
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = np.dot(np.maximum(0, np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b), W2) + b2
Z = np.argmax(Z, axis=1)
Z = Z.reshape(xx.shape)
fig = plt.figure()
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)
plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())