chore: import upstream snapshot with attribution
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wehub-resource-sync
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# Python Machine Learning by Sebastian Raschka, Packt Publishing Ltd. 2015
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# Code Repository: https://github.com/rasbt/python-machine-learning-book
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# Code License: MIT License
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import numpy as np
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from scipy.special import expit
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import sys
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class NeuralNetMLP(object):
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""" Feedforward neural network / Multi-layer perceptron classifier.
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Parameters
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------------
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n_output : int
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Number of output units, should be equal to the
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number of unique class labels.
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n_features : int
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Number of features (dimensions) in the target dataset.
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Should be equal to the number of columns in the X array.
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n_hidden : int (default: 30)
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Number of hidden units.
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l1 : float (default: 0.0)
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Lambda value for L1-regularization.
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No regularization if l1=0.0 (default)
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l2 : float (default: 0.0)
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Lambda value for L2-regularization.
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No regularization if l2=0.0 (default)
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epochs : int (default: 500)
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Number of passes over the training set.
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eta : float (default: 0.001)
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Learning rate.
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alpha : float (default: 0.0)
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Momentum constant. Factor multiplied with the
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gradient of the previous epoch t-1 to improve
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learning speed
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w(t) := w(t) - (grad(t) + alpha*grad(t-1))
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decrease_const : float (default: 0.0)
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Decrease constant. Shrinks the learning rate
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after each epoch via eta / (1 + epoch*decrease_const)
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shuffle : bool (default: True)
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Shuffles training data every epoch if True to prevent circles.
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minibatches : int (default: 1)
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Divides training data into k minibatches for efficiency.
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Normal gradient descent learning if k=1 (default).
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random_state : int (default: None)
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Set random state for shuffling and initializing the weights.
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Attributes
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-----------
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cost_ : list
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Sum of squared errors after each epoch.
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"""
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def __init__(self, n_output, n_features, n_hidden=30,
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l1=0.0, l2=0.0, epochs=500, eta=0.001,
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alpha=0.0, decrease_const=0.0, shuffle=True,
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minibatches=1, random_state=None):
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np.random.seed(random_state)
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self.n_output = n_output
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self.n_features = n_features
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self.n_hidden = n_hidden
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self.w1, self.w2 = self._initialize_weights()
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self.l1 = l1
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self.l2 = l2
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self.epochs = epochs
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self.eta = eta
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self.alpha = alpha
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self.decrease_const = decrease_const
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self.shuffle = shuffle
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self.minibatches = minibatches
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def _encode_labels(self, y, k):
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"""Encode labels into one-hot representation
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Parameters
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------------
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y : array, shape = [n_samples]
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Target values.
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Returns
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-----------
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onehot : array, shape = (n_labels, n_samples)
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"""
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onehot = np.zeros((k, y.shape[0]))
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for idx, val in enumerate(y):
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onehot[val, idx] = 1.0
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return onehot
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def _initialize_weights(self):
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"""Initialize weights with small random numbers."""
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w1 = np.random.uniform(-1.0, 1.0,
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size=self.n_hidden*(self.n_features + 1))
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w1 = w1.reshape(self.n_hidden, self.n_features + 1)
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w2 = np.random.uniform(-1.0, 1.0,
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size=self.n_output*(self.n_hidden + 1))
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w2 = w2.reshape(self.n_output, self.n_hidden + 1)
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return w1, w2
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def _sigmoid(self, z):
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"""Compute logistic function (sigmoid)
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Uses scipy.special.expit to avoid overflow
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error for very small input values z.
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"""
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# return 1.0 / (1.0 + np.exp(-z))
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return expit(z)
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def _sigmoid_gradient(self, z):
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"""Compute gradient of the logistic function"""
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sg = self._sigmoid(z)
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return sg * (1.0 - sg)
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def _add_bias_unit(self, X, how='column'):
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"""Add bias unit (column or row of 1s) to array at index 0"""
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if how == 'column':
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X_new = np.ones((X.shape[0], X.shape[1] + 1))
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X_new[:, 1:] = X
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elif how == 'row':
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X_new = np.ones((X.shape[0] + 1, X.shape[1]))
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X_new[1:, :] = X
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else:
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raise AttributeError('`how` must be `column` or `row`')
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return X_new
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def _feedforward(self, X, w1, w2):
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"""Compute feedforward step
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Parameters
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-----------
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X : array, shape = [n_samples, n_features]
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Input layer with original features.
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w1 : array, shape = [n_hidden_units, n_features]
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Weight matrix for input layer -> hidden layer.
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w2 : array, shape = [n_output_units, n_hidden_units]
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Weight matrix for hidden layer -> output layer.
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Returns
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----------
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a1 : array, shape = [n_samples, n_features+1]
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Input values with bias unit.
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z2 : array, shape = [n_hidden, n_samples]
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Net input of hidden layer.
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a2 : array, shape = [n_hidden+1, n_samples]
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Activation of hidden layer.
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z3 : array, shape = [n_output_units, n_samples]
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Net input of output layer.
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a3 : array, shape = [n_output_units, n_samples]
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Activation of output layer.
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"""
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a1 = self._add_bias_unit(X, how='column')
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z2 = w1.dot(a1.T)
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a2 = self._sigmoid(z2)
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a2 = self._add_bias_unit(a2, how='row')
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z3 = w2.dot(a2)
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a3 = self._sigmoid(z3)
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return a1, z2, a2, z3, a3
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def _L2_reg(self, lambda_, w1, w2):
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"""Compute L2-regularization cost"""
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return (lambda_/2.0) * (np.sum(w1[:, 1:] ** 2) +
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np.sum(w2[:, 1:] ** 2))
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def _L1_reg(self, lambda_, w1, w2):
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"""Compute L1-regularization cost"""
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return (lambda_/2.0) * (np.abs(w1[:, 1:]).sum() +
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np.abs(w2[:, 1:]).sum())
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def _get_cost(self, y_enc, output, w1, w2):
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"""Compute cost function.
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Parameters
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----------
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y_enc : array, shape = (n_labels, n_samples)
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one-hot encoded class labels.
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output : array, shape = [n_output_units, n_samples]
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Activation of the output layer (feedforward)
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w1 : array, shape = [n_hidden_units, n_features]
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Weight matrix for input layer -> hidden layer.
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w2 : array, shape = [n_output_units, n_hidden_units]
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Weight matrix for hidden layer -> output layer.
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Returns
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---------
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cost : float
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Regularized cost.
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"""
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term1 = -y_enc * (np.log(output))
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term2 = (1.0 - y_enc) * np.log(1.0 - output)
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cost = np.sum(term1 - term2)
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L1_term = self._L1_reg(self.l1, w1, w2)
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L2_term = self._L2_reg(self.l2, w1, w2)
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cost = cost + L1_term + L2_term
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return cost
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def _get_gradient(self, a1, a2, a3, z2, y_enc, w1, w2):
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""" Compute gradient step using backpropagation.
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Parameters
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------------
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a1 : array, shape = [n_samples, n_features+1]
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Input values with bias unit.
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a2 : array, shape = [n_hidden+1, n_samples]
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Activation of hidden layer.
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a3 : array, shape = [n_output_units, n_samples]
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Activation of output layer.
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z2 : array, shape = [n_hidden, n_samples]
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Net input of hidden layer.
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y_enc : array, shape = (n_labels, n_samples)
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one-hot encoded class labels.
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w1 : array, shape = [n_hidden_units, n_features]
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Weight matrix for input layer -> hidden layer.
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w2 : array, shape = [n_output_units, n_hidden_units]
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Weight matrix for hidden layer -> output layer.
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Returns
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---------
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grad1 : array, shape = [n_hidden_units, n_features]
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Gradient of the weight matrix w1.
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grad2 : array, shape = [n_output_units, n_hidden_units]
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Gradient of the weight matrix w2.
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"""
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# backpropagation
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sigma3 = a3 - y_enc
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z2 = self._add_bias_unit(z2, how='row')
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sigma2 = w2.T.dot(sigma3) * self._sigmoid_gradient(z2)
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sigma2 = sigma2[1:, :]
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grad1 = sigma2.dot(a1)
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grad2 = sigma3.dot(a2.T)
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# regularize
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grad1[:, 1:] += self.l2 * w1[:, 1:]
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grad1[:, 1:] += self.l1 * np.sign(w1[:, 1:])
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grad2[:, 1:] += self.l2 * w2[:, 1:]
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grad2[:, 1:] += self.l1 * np.sign(w2[:, 1:])
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return grad1, grad2
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def predict(self, X):
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"""Predict class labels
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Parameters
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-----------
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X : array, shape = [n_samples, n_features]
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Input layer with original features.
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Returns:
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----------
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y_pred : array, shape = [n_samples]
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Predicted class labels.
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"""
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if len(X.shape) != 2:
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raise AttributeError('X must be a [n_samples, n_features] array.\n'
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'Use X[:,None] for 1-feature classification,'
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'\nor X[[i]] for 1-sample classification')
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a1, z2, a2, z3, a3 = self._feedforward(X, self.w1, self.w2)
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y_pred = np.argmax(z3, axis=0)
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return y_pred
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def fit(self, X, y, print_progress=False):
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""" Learn weights from training data.
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Parameters
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-----------
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X : array, shape = [n_samples, n_features]
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Input layer with original features.
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y : array, shape = [n_samples]
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Target class labels.
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print_progress : bool (default: False)
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Prints progress as the number of epochs
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to stderr.
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Returns:
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----------
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self
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"""
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self.cost_ = []
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X_data, y_data = X.copy(), y.copy()
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y_enc = self._encode_labels(y, self.n_output)
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delta_w1_prev = np.zeros(self.w1.shape)
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delta_w2_prev = np.zeros(self.w2.shape)
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for i in range(self.epochs):
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# adaptive learning rate
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self.eta /= (1 + self.decrease_const*i)
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if print_progress:
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sys.stderr.write('\rEpoch: %d/%d' % (i+1, self.epochs))
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sys.stderr.flush()
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if self.shuffle:
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idx = np.random.permutation(y_data.shape[0])
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X_data, y_enc = X_data[idx], y_enc[:, idx]
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mini = np.array_split(range(y_data.shape[0]), self.minibatches)
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for idx in mini:
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# feedforward
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a1, z2, a2, z3, a3 = self._feedforward(X_data[idx],
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self.w1,
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self.w2)
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cost = self._get_cost(y_enc=y_enc[:, idx],
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output=a3,
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w1=self.w1,
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w2=self.w2)
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self.cost_.append(cost)
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# compute gradient via backpropagation
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grad1, grad2 = self._get_gradient(a1=a1, a2=a2,
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a3=a3, z2=z2,
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y_enc=y_enc[:, idx],
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w1=self.w1,
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w2=self.w2)
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delta_w1, delta_w2 = self.eta * grad1, self.eta * grad2
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self.w1 -= (delta_w1 + (self.alpha * delta_w1_prev))
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self.w2 -= (delta_w2 + (self.alpha * delta_w2_prev))
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delta_w1_prev, delta_w2_prev = delta_w1, delta_w2
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return self
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