AdaptiveLinearNeuron.py

# 梯度相反的方向是学习速率最快的方向

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from matplotlib.colors import ListedColormap

class AdaLinNeuGD(object):
    def __init__(self, eta=0.01, n_iter=50):
        self.eta = eta
        self.n_iter = n_iter

    def fit(self, X, y):
        '''
        Fit training data
        :param X: shape = [n_samples, n_features]
        :param y: shape = n_sample
        :return: self: Object
        '''
        self.w_ = np.zeros(1 + X.shape[1])   # Initial weights
        self.cost_ = []

        for i in range(self.n_iter):
            output = self.net_input(X)
            errors = y - output
            self.w_[1:] += self.eta * X.T.dot(errors)   # Update weights
            self.w_[0] += self.eta * errors.sum()
            cost = (errors ** 2).sum() / 2.0    # Check whether convergence
            self.cost_.append(cost)
        return self

    def net_input(self, X):
        return np.dot(X, self.w_[1:]) + self.w_[0]

    def activation(self, X):
        return self.net_input(X)

    def predict(self, X):
        return np.where(self.activation(X) >= 0.0, 1, 0)


def plot_decision_region(X, y, classifier, resolution=0.02):
    # Set up marker generator and color map
    markers = ['s', 'x', 'o', '^', 'v']
    colors = ['red', 'blue', 'lightgreen', 'gray', 'cyan']
    cmap = ListedColormap(colors[:len(np.unique(y))])

    # Plot the decision surface
    x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1
    x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1
    xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),
                           np.arange(x2_min, x2_max, resolution))
    Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
    Z = Z.reshape(xx1.shape)
    plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)
    plt.xlim(xx1.min(), xx1.max())
    plt.ylim(xx2.min(), xx2.max())

    # Plot class samples
    for idx, cl in enumerate(np.unique(y)):
        plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1],
                    alpha=0.8, c=cmap(idx), marker=markers[idx], label=cl)


def plot_adjust_parameters_curve(X, y):
    fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(8, 4))
    ada1 = AdaLinNeuGD(n_iter=10, eta=0.01).fit(X, y)
    ax[0].plot(range(1, len(ada1.cost_)+1), np.log10(ada1.cost_), marker='o')
    ax[0].set_xlabel('Epochs')
    ax[0].set_ylabel('Log(Sum-squared-error')
    ax[0].set_title('Adaline-Learning rate 0.01')

    ada2 = AdaLinNeuGD(n_iter=10, eta=0.0001).fit(X, y)
    ax[1].plot(range(1, len(ada2.cost_)+1), ada2.cost_, marker='o')
    ax[1].set_xlabel('Epochs')
    ax[1].set_ylabel('Sum-squared-error')
    ax[1].set_title('Adaline-Learning rate 0.0001')
    plt.show()

    return


# adaptive linear neuron stochastic gradient descent
class AdalineSGD(object):
    def __init__(self, eta=0.01, n_iter=10, shuffle=True, random_state=None):
        self.eta = eta    # 学习速率
        self.n_iter = n_iter
        self.w_initialized = False
        self.shuffle = shuffle
        if random_state:
            np.random.seed(random_state)

    def fit(self, X, y):
        self._initialize_weights(X.shape[1])
        self.cost_ = []
        for i in range(self.n_iter):
            if self.shuffle:
                X, y = self._shuffle(X, y)
            cost = []
            for xi, target in zip(X, y):
                cost.append(self._update_weights(xi, target))
            avg_cost = np.sum(cost) / len(y)
            self.cost_.append(avg_cost)
        return self

    def partial_fit(self, X, y):
        if not self.w_initialized:
            self._initialize_weights(X.shape[1])

        if y.ravel().shape[0] > 1:
            for xi, target in zip(X, y):
                self._update_weights(xi, target)
        else:
            self._update_weights(X, y)
        return self

    def _shuffle(self, X, y):
        '''
        Shuffle training data
        '''
        r = np.random.permutation(len(y))
        return X[r], y[r]

    def _initialize_weights(self, m):
        '''
        Initialize weights to zeros
        '''
        self.w_ = np.zeros(1 + m)
        self.w_initialized = True

    def _update_weights(self, xi, target):
        '''
        Apply Adaline learning rule to update the weights
        '''
        output = self.net_input(xi)
        error = target - output
        self.w_[1:] += self.eta * xi.dot(error)
        self.w_[0] = self.eta * error
        cost = 0.5 * error ** 2
        return cost

    def net_input(self, X):
        return np.dot(X, self.w_[1:]) + self.w_[0]

    def activation(self, X):
        return self.net_input(X)

    def predict(self, X):
        return np.where(self.activation(X) >= 0.0, 1, 0)


data = load_iris()
df = pd.DataFrame(np.c_[data['data'], data['target']])
y = df.iloc[0:100, 4].values
X = df.iloc[:100, [0, 2]].values
plt.scatter(X[:50, 0], X[:50, 1], color='red', marker='o', label='setosa')
plt.scatter(X[50:100, 0], X[50:100, 1], color='blue', marker='x', label='versicolor')
plt.xlabel('petal length')
plt.ylabel('sepal length')
plt.legend(loc='upper left')
plt.show()

eta1, eta2 = 0.01, 0.0001
ada1 = AdaLinNeuGD(n_iter=10, eta=eta1).fit(X, y)

fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(8, 4))
ax[0].plot(range(1, len(ada1.cost_)+1), np.log10(ada1.cost_), marker='o') 
ax[0].set_xlabel('Epochs')
ax[0].set_ylabel('log(Sum-squared-error)')
ax[0].set_title('Adaline-Learning rate {}'.format(eta1))

ada2 = AdaLinNeuGD(n_iter=10, eta=eta2).fit(X, y)
ax[1].plot(range(1, len(ada1.cost_)+1), ada2.cost_, marker='o') 
ax[1].set_xlabel('Epochs')
ax[1].set_ylabel('Sum-squared-error')
ax[1].set_title('Adaline-Learning rate {}'.format(eta2))

plt.show()

# Feature Scaling
X_std = np.copy(X)
X_std[:, 0] = (X[:, 0] - X[:, 0].mean()) / X[:, 0].std()
X_std[:, 1] = (X[:, 1] - X[:, 1].mean()) / X[:, 1].std()

ada = AdaLinNeuGD(n_iter=15, eta=0.01)
ada.fit(X_std, y)

plot_decision_region(X_std, y, classifier=ada)
plt.title('Adaline - Gradient Descent`')
plt.xlabel('sepal length [Standardized]')
plt.ylabel('petal length [Standardized]')
plt.legend(loc='upper left')
plt.show()

plt.plot(range(1, len(ada.cost_)+1), ada.cost_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('Sum-squared-error')
plt.show()

sgd_ada = AdalineSGD(n_iter=15, eta=0.01, random_state=1)
sgd_ada.fit(X_std, y)
plot_decision_region(X_std, y, classifier=sgd_ada)
plt.title('Adaline - Stochastic Gradient Descent')
plt.xlabel('Sepal length [standardized]')
plt.ylabel('petal length [Standardized]')
plt.legend(loc='upper left')
plt.show()

plt.plot(range(1, len(sgd_ada.cost_)+1), sgd_ada.cost_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('Average Cost')
plt.show()