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Implementing a perceptron learning algorithm in Python

Define a Class

import numpy as np class Perceptron(object):"""Perceptron classifier.Parameters------------eta : floatLearning rate (between 0.0 and 1.0)n_iter : intPasses over the training dataset.Attributes-----------w_ : 1d-arrayWeights after fitting.errors_ : listNumber of misclassifications (updates) in each epoch."""def __init__(self, eta=0.01, n_iter=10):self.eta = etaself.n_iter = n_iterdef fit(self, X, y):"""Fit training data.Parameters----------X : {array-like}, shape = [n_samples, n_features]Training vectors, where n_samples is the number of samples andn_features is the number of features.y : array-like, shape = [n_samples]Target values.Returns-------self : object"""self.w_ = np.zeros(1 + X.shape[1])self.errors_ = []for _ in range(self.n_iter):errors = 0for xi, target in zip(X, y):update = self.eta*(target - self.predict(xi))self.w_[1:] += update*xiself.w_[0] += updateerrors += int(update != 0.0)self.errors_.append(errors)return selfdef net_input(self, X):"""Calculate net input"""return np.dot(X, self.w_[1:]) + self.w_[0]def predict(self, X):"""Return class label after unit step"""return np.where(self.net_input(X) >= 0.0, 1, -1)

Training a perceptron model on the Iris dataset

import pandas as pd df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data', header=None) df.tail() 01234145146147148149

6.7	3.0	5.2	2.3	Iris-virginica
6.3	2.5	5.0	1.9	Iris-virginica
6.5	3.0	5.2	2.0	Iris-virginica
6.2	3.4	5.4	2.3	Iris-virginica
5.9	3.0	5.1	1.8	Iris-virginica

We extract the first 100 class labels that correspond to 50 Iris-Setosa and 50 Iris-Versicolor flowers.

%matplotlib inline import matplotlib.pyplot as plt import numpy as npy = df.iloc[0:100, 4].values y = np.where(y == 'Iris-setosa', -1, 1) X = df.iloc[0:100, [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()

To train our perceptron algorithm, plot the misclassification error

ppn = Perceptron(eta=0.1, n_iter=10) ppn.fit(X,y) plt.plot(range(1,len(ppn.errors_) + 1), ppn.errors_, marker='o') plt.xlabel('Epochs') plt.ylabel('Number of misclassifications') # plt.show()

Visualize the decision boundaries for 2D datasets

from matplotlib.colors import ListedColormapdef plot_decision_regions(X, y, classifier, resolution=0.02):# setup marker generator and color mapmarkers = ('s', 'x', 'o', '^', 'v')colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')cmap = ListedColormap(colors[:len(np.unique(y))])# plot the decision surfacex1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1xx1, 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 samplefor 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) plot_decision_regions(X, y, classifier=ppn) plt.xlabel('sepal lenght [cm]') plt.ylabel('petal length [cm]') plt.legend(loc='upper left') # plt.show()

Adaptive linear neurons and the convergence of learning

Implementing an Adaptive Linear Neuron in Python

class AdalineGD(object):"""ADAptive LInear NEuron classifier.Parameters-------------eta : floatLearning rate (between 0.0 and 1.0)n_iter : intPasses over the training dataset.Attributes-------------w_ : 1d-arrayWeights after fitting.errors_ : listNumber of misclassifications in every epoch."""def __init__(self, eta=0.01, n_iter=50):self.eta = etaself.n_iter = n_iterdef fit(self, X, y):""" Fit training data.Parameters------------X : {array-like5}, shape = [n_samples, n_features]Training vectors,where n_samples is the number of samples andn_features is the number of features.y　: array-like, shape = [n_samples]Target values.Returns------------self : object"""self.w_ = np.zeros(1 + X.shape[1])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)self.w_[0] += self.eta * errors.sum()cost = (errors**2).sum() / 2.0self.cost_.append(cost)return selfdef net_input(self, X):"""Calculate net input"""return np.dot(X, self.w_[1:]) + self.w_[0]def activation(self, X):"""Compute linear activation"""return self.net_input(X)def predict(self, X):"""Return class label after unit step"""return np.where(self.activation(X) >= 0.0, 1, -1) fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(8,4)) ada1 = AdalineGD(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 = AdalineGD(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()

standardization

X_std = np.copy(X) X_std[:,0] = (X_std[:,0] - X_std[:,0].mean()) / X_std[:,0].std() X_std[:,1] = (X_std[:,1] - X_std[:,1].mean()) / X_std[:,1].std() ada = AdalineGD(n_iter=15, eta=0.01) ada.fit(X_std, y) plot_decision_regions(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()

Large scale machine learning and stochastic gradient descent

from numpy.random import seedclass AdalineSGD(object):"""ADAptive LInear NEuron classifier.Parameters------------eta : floatLearning rate (between 0.0 and 1.0)n_iter : intPasses over the training dataset.Attributes------------w_ : 1d-arrayWeights after fitting.cost_ : listNumber of misclassifications in every epoch.shuffle : bool (default: True)Shuffles training data every epochif True to prevent cycles.random_state : int (default: None)Set random state for shufflingand initializing the weights."""def __init__(self, eta=0.01, n_iter=10, shuffle=True, random_state=None):self.eta = etaself.n_iter = n_iterself.w_initialized = Falseself.shuffle = shuffleif random_state:seed(random_state)def fit(self, X, y):"""Fit training data.Parameters------------X : {array-like}, shape = [n_samples, n_features]Training vector, where n_samplesis the number of samples andn_features is the number of features.y: arrary-like, shape = [n_samples]Target values.Returns------------self : object"""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 = sum(cost)/len(y)self.cost_.append(avg_cost)return selfdef partial_fit(self, X, y):"""Fit training data without reinitializing the weights"""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 selfdef _shuffle(self, X, y):"""Shuffle training data"""r = np.random.permutation(len(y))return X[r], y[r]def _initialize_weights(self, m):"""Initialize weighs to zeros"""self.w_ = np.zeros(1+m)self.w_initialized = Truedef _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*errorcost = 0.5 * error**2return costdef net_input(self, X):"""Calculate net input"""return np.dot(X, self.w_[1:]) + self.w_[0]def activation(self, X):"""Compute linear activation"""return self.net_input(X)def predict(self, X):"""Return class label after unit step"""return np.where(self.activation(X) >= 0.0, 1, -1) ada = AdalineSGD(n_iter=15, eta=0.01, random_state=1) ada.fit(X_std, y) plot_decision_regions(X_std, y, classifier=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(ada.cost_) + 1), ada.cost_, marker='o') plt.xlabel('Epochs') plt.ylabel('Average Cost') plt.show()

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