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, eta=0.1, n_iter=10):
        self.eta = eta
        self.n_iter = n_iter

    def fit(self, X, y):
        self.w_ = np.zeros(1 + X.shape[1])
        self.errors_ = []

        for _ in range(self.n_iter):
            errors = 0
            for xi, target in zip(X, y):
                update = self.eta * (target - self.predict(xi))
                self.w_[1:] += update * xi
                self.w_[0] += update
                errors += int(update != 0.0)
            self.errors_.append(errors)
        return self

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

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

2. 对偶形式

import numpy as np

class DualPerceptron:
    def __init__(self, eta=0.1, n_iter=10):
        self.eta = eta
        self.n_iter = n_iter

    def fit(self, X, y):
        self.alpha_ = np.zeros(X.shape[0])
        self.b_ = 0

        gram_matrix = np.dot(X, X.T)

        for _ in range(self.n_iter):
            errors = 0
            for i in range(X.shape[0]):
                if y[i] * (np.sum(self.alpha_ * y * gram_matrix[i]) + self.b_) <= 0:
                    self.alpha_[i] += self.eta
                    self.b_ += self.eta * y[i]
                    errors += 1
            if errors == 0:
                break

        self.w_ = np.sum(self.alpha_ * y * X.T, axis=1)
        return self

    def predict(self, X):
        return np.where(np.dot(X, self.w_) + self.b_ >= 0, 1, -1)

3. 对称形式

import numpy as np

class SymmetricPerceptron:
    def __init__(self, eta=0.1, n_iter=10):
        self.eta = eta
        self.n_iter = n_iter

    def fit(self, X, y):
        self.w_ = np.zeros(X.shape[1])
        self.b_ = 0
        self.v_ = np.zeros(X.shape[1])

        for _ in range(self.n_iter):
            errors = 0
            for xi, target in zip(X, y):
                if target * (np.dot(xi, self.w_) + self.b_) <= 0:
                    self.w_ += self.eta * target * xi + self.v_
                    self.b_ += self.eta * target
                    self.v_ = self.eta * target * xi
                    errors += 1
            if errors == 0:
                break

        return self

    def predict(self, X):
        return np.where(np.dot(X, self.w_) + self.b_ >= 0, 1, -1)