def remove_component(X):
"""Remove components of already obtained eigen vectors from X."""
X_m = X[:m]
X_n = X[m:]
for eivec in eivec_m:
coeff = dotproduct(X_m, eivec)
X_m = [x1 - coeff * x2 for x1, x2 in zip(X_m, eivec)]
for eivec in eivec_n:
coeff = dotproduct(X_n, eivec)
X_n = [x1 - coeff * x2 for x1, x2 in zip(X_n, eivec)]
return X_m + X_n
def predict(example):
o_nodes = learned_net[1]
# Forward pass
for node in o_nodes:
in_val = dotproduct(example, node.weights)
node.value = node.activation(in_val)
# Hypothesis
return find_max_node(o_nodes)
def LinearLearner(dataset, learning_rate=0.01, epochs=100):
"""Define with learner = LinearLearner(data); infer with learner(x)."""
idx_i = dataset.inputs
idx_t = dataset.target # As of now, dataset.target gives only one index.
examples = dataset.examples
num_examples = len(examples)
# X transpose
X_col = [dataset.values[i] for i in idx_i] # vertical columns of X
# Add dummy
ones = [1 for _ in range(len(examples))]
X_col = [ones] + X_col
# Initialize random weigts
num_weights = len(idx_i) + 1
w = random_weights(min_value=-0.5, max_value=0.5, num_weights=num_weights)
for epoch in range(epochs):
err = []
# Pass over all examples
for example in examples:
x = [1] + example
y = dotproduct(w, x)
t = example[idx_t]
err.append(t - y)
# update weights
for i in range(len(w)):
w[i] = w[i] + learning_rate * (dotproduct(err, X_col[i]) /
num_examples)
def predict(example):
x = [1] + example
return dotproduct(w, x)
return predict
def predict(example):
# Input nodes
i_nodes = learned_net[0]
# Activate input layer
for v, n in zip(example, i_nodes):
n.value = v
# Forward pass
for layer in learned_net[1:]:
for node in layer:
inc = [n.value for n in node.inputs]
in_val = dotproduct(inc, node.weights)
node.value = node.activation(in_val)
# Hypothesis
o_nodes = learned_net[-1]
prediction = find_max_node(o_nodes)
return prediction
def predict(example):
x = [1] + example
return dotproduct(w, x)
def BackPropagationLearner(dataset,
net,
learning_rate,
epochs,
activation=sigmoid):
"""[Figure 18.23] The back-propagation algorithm for multilayer networks"""
# Initialise weights
for layer in net:
for node in layer:
node.weights = random_weights(min_value=-0.5,
max_value=0.5,
num_weights=len(node.weights))
examples = dataset.examples
'''
As of now dataset.target gives an int instead of list,
Changing dataset class will have effect on all the learners.
Will be taken care of later.
'''
o_nodes = net[-1]
i_nodes = net[0]
o_units = len(o_nodes)
idx_t = dataset.target
idx_i = dataset.inputs
n_layers = len(net)
inputs, targets = init_examples(examples, idx_i, idx_t, o_units)
for epoch in range(epochs):
# Iterate over each example
for e in range(len(examples)):
i_val = inputs[e]
t_val = targets[e]
# Activate input layer
for v, n in zip(i_val, i_nodes):
n.value = v
# Forward pass
for layer in net[1:]:
for node in layer:
inc = [n.value for n in node.inputs]
in_val = dotproduct(inc, node.weights)
node.value = node.activation(in_val)
# Initialize delta
delta = [[] for _ in range(n_layers)]
# Compute outer layer delta
# Error for the MSE cost function
err = [t_val[i] - o_nodes[i].value for i in range(o_units)]
# The activation function used is relu or sigmoid function
if node.activation == sigmoid:
delta[-1] = [
sigmoid_derivative(o_nodes[i].value) * err[i]
for i in range(o_units)
]
elif node.activation == relu:
delta[-1] = [
relu_derivative(o_nodes[i].value) * err[i]
for i in range(o_units)
]
elif node.activation == tanh:
delta[-1] = [
tanh_derivative(o_nodes[i].value) * err[i]
for i in range(o_units)
]
elif node.activation == elu:
delta[-1] = [
elu_derivative(o_nodes[i].value) * err[i]
for i in range(o_units)
]
else:
delta[-1] = [
leaky_relu_derivative(o_nodes[i].value) * err[i]
for i in range(o_units)
]
# Backward pass
h_layers = n_layers - 2
for i in range(h_layers, 0, -1):
layer = net[i]
h_units = len(layer)
nx_layer = net[i + 1]
# weights from each ith layer node to each i + 1th layer node
w = [[node.weights[k] for node in nx_layer]
for k in range(h_units)]
if activation == sigmoid:
delta[i] = [
sigmoid_derivative(layer[j].value) *
dotproduct(w[j], delta[i + 1]) for j in range(h_units)
]
elif activation == relu:
delta[i] = [
relu_derivative(layer[j].value) *
dotproduct(w[j], delta[i + 1]) for j in range(h_units)
]
elif activation == tanh:
delta[i] = [
tanh_derivative(layer[j].value) *
dotproduct(w[j], delta[i + 1]) for j in range(h_units)
]
elif activation == elu:
delta[i] = [
elu_derivative(layer[j].value) *
dotproduct(w[j], delta[i + 1]) for j in range(h_units)
]
else:
delta[i] = [
leaky_relu_derivative(layer[j].value) *
dotproduct(w[j], delta[i + 1]) for j in range(h_units)
]
# Update weights
for i in range(1, n_layers):
layer = net[i]
inc = [node.value for node in net[i - 1]]
units = len(layer)
for j in range(units):
layer[j].weights = vector_add(
layer[j].weights,
scalar_vector_product(learning_rate * delta[i][j],
inc))
return net