145 lines
4.7 KiB
Python
145 lines
4.7 KiB
Python
__author__ = 'm.bashari'
|
|
import numpy as np
|
|
from sklearn import datasets, linear_model
|
|
import matplotlib.pyplot as plt
|
|
|
|
|
|
class Config:
|
|
nn_input_dim = 2 # input layer dimensionality
|
|
nn_output_dim = 2 # output layer dimensionality
|
|
# Gradient descent parameters (I picked these by hand)
|
|
epsilon = 0.01 # learning rate for gradient descent
|
|
reg_lambda = 0.01 # regularization strength
|
|
|
|
|
|
def generate_data():
|
|
np.random.seed(0)
|
|
X, y = datasets.make_moons(200, noise=0.20)
|
|
return X, y
|
|
|
|
|
|
def visualize(X, y, model):
|
|
# plt.scatter(X[:, 0], X[:, 1], s=40, c=y, cmap=plt.cm.Spectral)
|
|
# plt.show()
|
|
plot_decision_boundary(lambda x:predict(model,x), X, y)
|
|
plt.title("Logistic Regression")
|
|
|
|
|
|
def plot_decision_boundary(pred_func, X, y):
|
|
# Set min and max values and give it some padding
|
|
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
|
|
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
|
|
h = 0.01
|
|
# Generate a grid of points with distance h between them
|
|
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
|
|
# Predict the function value for the whole gid
|
|
Z = pred_func(np.c_[xx.ravel(), yy.ravel()])
|
|
Z = Z.reshape(xx.shape)
|
|
# Plot the contour and training examples
|
|
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
|
|
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)
|
|
plt.show()
|
|
|
|
|
|
# Helper function to evaluate the total loss on the dataset
|
|
def calculate_loss(model, X, y):
|
|
num_examples = len(X) # training set size
|
|
W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
|
|
# Forward propagation to calculate our predictions
|
|
z1 = X.dot(W1) + b1
|
|
a1 = np.tanh(z1)
|
|
z2 = a1.dot(W2) + b2
|
|
exp_scores = np.exp(z2)
|
|
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
|
|
# Calculating the loss
|
|
corect_logprobs = -np.log(probs[range(num_examples), y])
|
|
data_loss = np.sum(corect_logprobs)
|
|
# Add regulatization term to loss (optional)
|
|
data_loss += Config.reg_lambda / 2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
|
|
return 1. / num_examples * data_loss
|
|
|
|
|
|
def predict(model, x):
|
|
W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
|
|
# Forward propagation
|
|
z1 = x.dot(W1) + b1
|
|
a1 = np.tanh(z1)
|
|
z2 = a1.dot(W2) + b2
|
|
exp_scores = np.exp(z2)
|
|
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
|
|
return np.argmax(probs, axis=1)
|
|
|
|
|
|
# This function learns parameters for the neural network and returns the model.
|
|
# - nn_hdim: Number of nodes in the hidden layer
|
|
# - num_passes: Number of passes through the training data for gradient descent
|
|
# - print_loss: If True, print the loss every 1000 iterations
|
|
def build_model(X, y, nn_hdim, num_passes=20000, print_loss=False):
|
|
# Initialize the parameters to random values. We need to learn these.
|
|
num_examples = len(X)
|
|
np.random.seed(0)
|
|
W1 = np.random.randn(Config.nn_input_dim, nn_hdim) / np.sqrt(Config.nn_input_dim)
|
|
b1 = np.zeros((1, nn_hdim))
|
|
W2 = np.random.randn(nn_hdim, Config.nn_output_dim) / np.sqrt(nn_hdim)
|
|
b2 = np.zeros((1, Config.nn_output_dim))
|
|
|
|
# This is what we return at the end
|
|
model = {}
|
|
|
|
# Gradient descent. For each batch...
|
|
for i in range(0, num_passes):
|
|
|
|
# Forward propagation
|
|
z1 = X.dot(W1) + b1
|
|
a1 = np.tanh(z1)
|
|
z2 = a1.dot(W2) + b2
|
|
exp_scores = np.exp(z2)
|
|
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
|
|
|
|
# Backpropagation
|
|
delta3 = probs
|
|
delta3[range(num_examples), y] -= 1
|
|
dW2 = (a1.T).dot(delta3)
|
|
db2 = np.sum(delta3, axis=0, keepdims=True)
|
|
delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
|
|
dW1 = np.dot(X.T, delta2)
|
|
db1 = np.sum(delta2, axis=0)
|
|
|
|
# Add regularization terms (b1 and b2 don't have regularization terms)
|
|
dW2 += Config.reg_lambda * W2
|
|
dW1 += Config.reg_lambda * W1
|
|
|
|
# Gradient descent parameter update
|
|
W1 += -Config.epsilon * dW1
|
|
b1 += -Config.epsilon * db1
|
|
W2 += -Config.epsilon * dW2
|
|
b2 += -Config.epsilon * db2
|
|
|
|
# Assign new parameters to the model
|
|
model = {'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}
|
|
|
|
# Optionally print the loss.
|
|
# This is expensive because it uses the whole dataset, so we don't want to do it too often.
|
|
if print_loss and i % 1000 == 0:
|
|
print("Loss after iteration %i: %f" % (i, calculate_loss(model, X, y)))
|
|
|
|
return model
|
|
|
|
|
|
def classify(X, y):
|
|
# clf = linear_model.LogisticRegressionCV()
|
|
# clf.fit(X, y)
|
|
# return clf
|
|
|
|
pass
|
|
|
|
|
|
def main():
|
|
X, y = generate_data()
|
|
model = build_model(X, y, 3, print_loss=True)
|
|
visualize(X, y, model)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
main()
|