def nnGradient(nn_params, *args):
input_size, hidden_size, n_labels, X, y, lmbda = args
W1_size = hidden_size * (input_size + 1)
W1 = np.reshape(nn_params[0:W1_size], (hidden_size, input_size + 1),
order='F')
W2 = np.reshape(nn_params[W1_size:], (n_labels, hidden_size + 1),
order='F')
###############################################################################
# Part 1: Feed forward the neural network and return the cost in the
# variable J.
###############################################################################
n = X.shape[0]
a1 = np.hstack((np.ones((n, 1)), X))
z2 = a1.dot(np.transpose(W1))
a2 = sigmoid(z2)
a2 = np.hstack((np.ones((a2.shape[0], 1)), a2))
z3 = a2.dot(np.transpose(W2))
a3 = sigmoid(z3)
Y = np.eye(n_labels)[y, :]
W1_nobias = W1[:, 1:]
W2_nobias = W2[:, 1:]
# calculate J
delta_3 = a3 - Y
delta_2 = np.dot(delta_3, W2) * np.hstack((np.ones(
(z2.shape[0], 1)), sigmoidGradient(z2)))
delta_2 = delta_2[:, 1:]
# accumulate gradients
D2 = np.dot(np.transpose(delta_3), a2)
D1 = np.dot(np.transpose(delta_2), a1)
# calculate regularized gradient
g2 = lmbda * 1.0 / n * np.hstack((np.zeros((W2.shape[0], 1)), W2_nobias))
g1 = lmbda * 1.0 / n * np.hstack((np.zeros((W1.shape[0], 1)), W1_nobias))
W1_grad = D1 / n + g1
W2_grad = D2 / n + g2
grad = np.hstack((W1_grad.T.ravel(), W2_grad.T.ravel()))
return grad
def nnGradient(nn_params, *args):
input_size, hidden_size, n_labels, X, y, lmbda = args
W1_size = hidden_size * (input_size + 1)
W1 = np.reshape(nn_params[0 : W1_size], (hidden_size, input_size + 1), order = 'F')
W2 = np.reshape(nn_params[W1_size : ], (n_labels, hidden_size + 1), order = 'F')
###############################################################################
# Part 1: Feed forward the neural network and return the cost in the
# variable J.
###############################################################################
n = X.shape[0]
a1 = np.hstack((np.ones((n, 1)), X))
z2 = a1.dot(np.transpose(W1))
a2 = sigmoid(z2)
a2 = np.hstack((np.ones((a2.shape[0], 1)), a2))
z3 = a2.dot(np.transpose(W2))
a3 = sigmoid(z3)
Y = np.eye(n_labels)[y, :]
W1_nobias = W1[:, 1:]
W2_nobias = W2[:, 1:]
# calculate J
delta_3 = a3 - Y
delta_2 = np.dot(delta_3, W2) * np.hstack((np.ones((z2.shape[0], 1)), sigmoidGradient(z2)))
delta_2 = delta_2[:, 1:]
# accumulate gradients
D2 = np.dot(np.transpose(delta_3), a2)
D1 = np.dot(np.transpose(delta_2), a1)
# calculate regularized gradient
g2 = lmbda * 1.0 / n * np.hstack((np.zeros((W2.shape[0], 1)), W2_nobias))
g1 = lmbda * 1.0 / n * np.hstack((np.zeros((W1.shape[0], 1)), W1_nobias))
W1_grad = D1 / n + g1
W2_grad = D2 / n + g2
grad = np.hstack((W1_grad.T.ravel(), W2_grad.T.ravel()))
return grad
def nnCostFunction(nn_params, input_size, hidden_size, n_labels, X, y, lmbda):
"""
Implements the neural network cost function for a two layer neural network
which performs classification
Computes the cost and gradient of the neural network. The parameters for
the neural network are "unrolled" into the vector nn_params and need to be
converted back into the weight matrices.
The returned parameter grad should be an "unrolled" vector of the partial
derivatives of the neural network.
@param
@return J cost
@return grad gradient
"""
# X: n x m
# w1: h x (m+1)
# w2: o x (h+1)
# Reshaping the input into W1 and W2
print('\tReshaping ...')
W1_size = hidden_size * (input_size + 1)
W1 = np.reshape(nn_params[0 : W1_size], (hidden_size, input_size + 1), order = 'F')
"""
print '\nW1 =================================='
print 'w1.shape: ', W1.shape
print 'w1.size: ', W1_size
print 'w1 ', W1[0, 0:5]
print '\n'
"""
W2 = np.reshape(nn_params[W1_size : ], (n_labels, hidden_size + 1), order = 'F')
###############################################################################
# Part 1: Feed forward the neural network and return the cost in the
# variable J.
###############################################################################
n = X.shape[0]
print('\tComputing hidden layer input ...')
a1 = np.hstack((np.ones((n, 1)), X))
z2 = a1.dot(np.transpose(W1))
print('\tComputing output layer ...')
a2 = sigmoid(z2)
a2 = np.hstack((np.ones((a2.shape[0], 1)), a2))
z3 = a2.dot(np.transpose(W2))
a3 = sigmoid(z3)
Y = np.eye(n_labels)[y, :]
W1_nobias = W1[:, 1:]
W2_nobias = W2[:, 1:]
# calculate J
print('\tCalculating cost ...')
J = -1.0 / n * np.sum((Y * 1.0 * np.log(a3) + (1.0 - Y) * np.log(1.0 - a3)).T.ravel())
reg = lmbda * 1.0 / (2 * n) * (np.linalg.norm(W1_nobias.T.ravel())**2
+ np.linalg.norm(W2_nobias.T.ravel())**2)
J = J + reg
###############################################################################
# Part 2: Implement the backpropagation algorithm to compute the gradients
# W1_grad and W2_grad. You should return the partial derivative of
# the cost function with respect to W1 and W2 in W1_grad and W2_grad,
# respectively.
#
# Note: The vector y passed into the function is a vector of labels
# containing values from 1..K. You need to map this vector into a
# binary vector of 1's and 0's to be used with the neural
# network cost function.
###############################################################################
# error at output layer
# delta_3 n_input x n_labels
# W2 n_hidden x n_labels
# delta_2 n_input x n_hidden
# W1 n_input x n_hidden
delta_3 = a3 - Y
delta_2 = np.dot(delta_3, W2) * np.hstack((np.ones((z2.shape[0], 1)), sigmoidGradient(z2)))
delta_2 = delta_2[:, 1:]
# accumulate gradients
# a2 n_input x n_hidden
# delta_3 n_input x n_labels
D2 = np.dot(np.transpose(delta_3), a2)
D1 = np.dot(np.transpose(delta_2), a1)
# calculate regularized gradient
g2 = lmbda * 1.0 / n * np.hstack((np.zeros((W2.shape[0], 1)), W2_nobias))
g1 = lmbda * 1.0 / n * np.hstack((np.zeros((W1.shape[0], 1)), W1_nobias))
W1_grad = D1 / n + g1
W2_grad = D2 / n + g2
grad = np.hstack((W1_grad.T.ravel(), W2_grad.T.ravel()))
return (J, grad)
def nnCostFunction(nn_params, input_size, hidden_size, n_labels, X, y, lmbda):
"""
Implements the neural network cost function for a two layer neural network
which performs classification
Computes the cost and gradient of the neural network. The parameters for
the neural network are "unrolled" into the vector nn_params and need to be
converted back into the weight matrices.
The returned parameter grad should be an "unrolled" vector of the partial
derivatives of the neural network.
@param
@return J cost
@return grad gradient
"""
# X: n x m
# w1: h x (m+1)
# w2: o x (h+1)
# Reshaping the input into W1 and W2
print('\tReshaping ...')
W1_size = hidden_size * (input_size + 1)
W1 = np.reshape(nn_params[0:W1_size], (hidden_size, input_size + 1),
order='F')
"""
print '\nW1 =================================='
print 'w1.shape: ', W1.shape
print 'w1.size: ', W1_size
print 'w1 ', W1[0, 0:5]
print '\n'
"""
W2 = np.reshape(nn_params[W1_size:], (n_labels, hidden_size + 1),
order='F')
###############################################################################
# Part 1: Feed forward the neural network and return the cost in the
# variable J.
###############################################################################
n = X.shape[0]
print('\tComputing hidden layer input ...')
a1 = np.hstack((np.ones((n, 1)), X))
z2 = a1.dot(np.transpose(W1))
print('\tComputing output layer ...')
a2 = sigmoid(z2)
a2 = np.hstack((np.ones((a2.shape[0], 1)), a2))
z3 = a2.dot(np.transpose(W2))
a3 = sigmoid(z3)
Y = np.eye(n_labels)[y, :]
W1_nobias = W1[:, 1:]
W2_nobias = W2[:, 1:]
# calculate J
print('\tCalculating cost ...')
J = -1.0 / n * np.sum(
(Y * 1.0 * np.log(a3) + (1.0 - Y) * np.log(1.0 - a3)).T.ravel())
reg = lmbda * 1.0 / (2 * n) * (np.linalg.norm(W1_nobias.T.ravel())**2 +
np.linalg.norm(W2_nobias.T.ravel())**2)
J = J + reg
###############################################################################
# Part 2: Implement the backpropagation algorithm to compute the gradients
# W1_grad and W2_grad. You should return the partial derivative of
# the cost function with respect to W1 and W2 in W1_grad and W2_grad,
# respectively.
#
# Note: The vector y passed into the function is a vector of labels
# containing values from 1..K. You need to map this vector into a
# binary vector of 1's and 0's to be used with the neural
# network cost function.
###############################################################################
# error at output layer
# delta_3 n_input x n_labels
# W2 n_hidden x n_labels
# delta_2 n_input x n_hidden
# W1 n_input x n_hidden
delta_3 = a3 - Y
delta_2 = np.dot(delta_3, W2) * np.hstack((np.ones(
(z2.shape[0], 1)), sigmoidGradient(z2)))
delta_2 = delta_2[:, 1:]
# accumulate gradients
# a2 n_input x n_hidden
# delta_3 n_input x n_labels
D2 = np.dot(np.transpose(delta_3), a2)
D1 = np.dot(np.transpose(delta_2), a1)
# calculate regularized gradient
g2 = lmbda * 1.0 / n * np.hstack((np.zeros((W2.shape[0], 1)), W2_nobias))
g1 = lmbda * 1.0 / n * np.hstack((np.zeros((W1.shape[0], 1)), W1_nobias))
W1_grad = D1 / n + g1
W2_grad = D2 / n + g2
grad = np.hstack((W1_grad.T.ravel(), W2_grad.T.ravel()))
return (J, grad)
