感知器的三种算法用Python实现

感知器的三种算法是原始形式、对偶形式和对称形式。以下是使用Python实现这三种算法的示例代码：

1. 原始形式

import numpy as np

class Perceptron():
    def __init__(self, learning_rate=0.01, n_iterations=100):
        self.learning_rate = learning_rate
        self.n_iterations = n_iterations

    def fit(self, X, y):
        n_samples, n_features = X.shape

        # Initializing weights and bias
        self.weights = np.zeros(n_features)
        self.bias = 0

        for _ in range(self.n_iterations):
            for idx, sample in enumerate(X):
                linear_output = np.dot(sample, self.weights) + self.bias
                predicted_output = np.where(linear_output >= 0, 1, -1)

                # Updating weights and bias
                update = self.learning_rate * (y[idx] - predicted_output)
                self.weights += update * sample
                self.bias += update

    def predict(self, X):
        linear_output = np.dot(X, self.weights) + self.bias
        predicted_output = np.where(linear_output >= 0, 1, -1)
        return predicted_output

2. 对偶形式

import numpy as np

class DualPerceptron():
    def __init__(self, learning_rate=0.01, n_iterations=100):
        self.learning_rate = learning_rate
        self.n_iterations = n_iterations

    def fit(self, X, y):
        n_samples, n_features = X.shape

        # Initializing alpha, bias and Gram matrix
        self.alpha = np.zeros(n_samples)
        self.bias = 0
        gram_matrix = np.dot(X, X.T)

        for _ in range(self.n_iterations):
            for idx in range(n_samples):
                linear_output = np.sum(self.alpha * y * gram_matrix[:, idx]) + self.bias
                predicted_output = np.where(linear_output >= 0, 1, -1)

                # Updating alpha and bias
                update = self.learning_rate * (y[idx] - predicted_output)
                self.alpha[idx] += update
                self.bias += update * y[idx]

    def predict(self, X):
        gram_matrix = np.dot(X, X.T)
        linear_output = np.sum(self.alpha * self.y_train * gram_matrix, axis=1) + self.bias
        predicted_output = np.where(linear_output >= 0, 1, -1)
        return predicted_output

3. 对称形式

import numpy as np

class SymmetricPerceptron():
    def __init__(self, learning_rate=0.01, n_iterations=100):
        self.learning_rate = learning_rate
        self.n_iterations = n_iterations

    def fit(self, X, y):
        n_samples, n_features = X.shape

        # Initializing weights, bias and v
        self.weights = np.zeros(n_features)
        self.bias = 0
        self.v = np.zeros(n_features)

        for _ in range(self.n_iterations):
            for idx, sample in enumerate(X):
                linear_output = np.dot(sample, self.weights) + self.bias
                predicted_output = np.where(linear_output >= 0, 1, -1)

                # Updating weights, bias and v
                if y[idx] * predicted_output <= 0:
                    self.weights += self.learning_rate * (y[idx] - predicted_output) * sample + self.v
                    self.bias += self.learning_rate * (y[idx] - predicted_output)
                    self.v = self.learning_rate * (y[idx] - predicted_output) * sample

    def predict(self, X):
        linear_output = np.dot(X, self.weights) + self.bias
        predicted_output = np.where(linear_output >= 0, 1, -1)
        return predicted_output