Logistic regression for classification

Beijing Institute of Technology | Ming-Jian Li

The following Python code is a companion code for the course on Artificial Intelligence and Simulation Science. It functions to establish a logistic regression model to classify the given data, with parameters optimized using the gradient descent method.

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import numpy as np
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import matplotlib.pyplot as plt
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# random seed
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np.random.seed(42)
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# mean value and covariance
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mean_1 = [2, 2]
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cov_1 = [[2, 0], [0, 2]]
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mean_2 = [-2, -2]
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cov_2 = [[1, 0], [0, 1]]
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# generate samples 
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X1 = np.random.multivariate_normal(mean_1, cov_1, 50)
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y1 = np.zeros(50)
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X2 = np.random.multivariate_normal(mean_2, cov_2, 50)
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y2 = np.ones(50)
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X = np.concatenate((X1, X2), axis=0)
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y = np.concatenate((y1, y2))
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plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Set1, edgecolor='k')
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plt.xlabel('Feature 1')
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plt.ylabel('Feature 2')
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plt.title('Logistic Regression Dataset')
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plt.show()
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def sigmoid(z):
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    y = 1.0/(1.0+np.exp(-z))
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    return y
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class LogisticRegression:
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    def __init__(self, learning_rate=0.01, num_iterations=1000):
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        self.learning_rate = learning_rate
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        self.num_iterations = num_iterations
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        self.weights = None
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        self.bias = None
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    def fit(self, X, y):
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        num_samples, num_features = X.shape
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        # initialize
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        self.weights = np.zeros(num_features)
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        self.bias = 0
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        # gradient descent
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        for _ in range(self.num_iterations):
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            linear_model = np.dot(X, self.weights) + self.bias
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            y_pred = sigmoid(linear_model)
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            dw = (1 / num_samples) * np.dot(X.T, (y_pred - y))
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            db = (1 / num_samples) * np.sum(y_pred - y)
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            self.weights -= self.learning_rate * dw
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            self.bias -= self.learning_rate * db
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    def predict_prob(self, X):
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        linear_model = np.dot(X, self.weights) + self.bias
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        y_pred = sigmoid(linear_model)
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        return y_pred
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    def predict(self, X, threshold=0.5):
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        y_pred_prob = self.predict_prob(X)
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        y_pred = np.zeros_like(y_pred_prob)
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        y_pred[y_pred_prob >= threshold] = 1
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        return y_pred
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logreg = LogisticRegression()
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logreg.fit(X, y)
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X_new = np.array([[2.5, 2.5], [-6.0, -4.0]])
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y_pred_prob = logreg.predict_prob(X_new)
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y_pred = logreg.predict(X_new)
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print("Predicted Labels:", y_pred)

The dataset is as follows:

The classification results for the given two points [2.5, 2.5] and [-6.0, -4.0] are:

Predicted Labels: [0. 1.]