From 9b85dce4fd17a1de302ff7866282cd9557aeeaa3 Mon Sep 17 00:00:00 2001 From: pxae954wu <29792637378@qq.com> Date: Sun, 31 Aug 2025 15:21:13 +0800 Subject: [PATCH] ADD file via upload --- kernel_LR_perceptron.py | 177 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 177 insertions(+) create mode 100644 kernel_LR_perceptron.py diff --git a/kernel_LR_perceptron.py b/kernel_LR_perceptron.py new file mode 100644 index 0000000..4605571 --- /dev/null +++ b/kernel_LR_perceptron.py @@ -0,0 +1,177 @@ +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +import matplotlib.colors as colors +from mpl_toolkits.mplot3d import Axes3D + +class Kernel(object): + def __init__(self, gamma=1.0, coef0=1, degree=3): + self.gamma, self.coef0, self.degree = gamma, coef0, degree + + def linear(self, X1, X2): + return np.dot(X1, X2.T) + + def poly(self, X1, X2): + return (self.gamma * np.dot(X1, X2.T) + self.coef0)**self.degree + + def gaussian(self, X1, X2): + X1_norm_sq = np.sum(X1**2, axis=1) + X2_norm_sq = np.sum(X2**2, axis=1) + dot_product = np.dot(X1, X2.T) + dist_sq = X1_norm_sq[:, np.newaxis] - 2 * dot_product + X2_norm_sq + dist_sq = np.maximum(dist_sq, 0) + return np.exp(-self.gamma * dist_sq) + + def laplace(self, X1, X2): + mat = np.zeros([len(X1), len(X2)]) + for i in range(len(X1)): + for j in range(len(X2)): + mat[i, j] = np.exp(-self.gamma * np.linalg.norm(X1[i] - X2[j])) + return mat + +class KPerceptron(object): + def __init__(self, ker='poly', gamma=1, coef0=1, degree=2, eta0=1.0, max_iter=100): + kernel_obj = Kernel(gamma=gamma, coef0=coef0, degree=degree) + + self.kernel_func = getattr(kernel_obj, ker if ker != 'rbf' else 'gaussian') + self.eta0, self.max_iter = eta0, max_iter + + def decision_function(self, Z): + Z = np.atleast_2d(Z) + if not hasattr(self, 'sv_index') or not self.sv_index.any(): + return np.zeros(len(Z)) + k_values = self.kernel_func(Z, self.sv[self.sv_index]) + return np.dot(k_values, self.alpha[self.sv_index]) + + def fit(self, X, y): + m = X.shape[0]; self.alpha = np.zeros(m) + self.sv_index = np.zeros(m, dtype=bool); self.sv = X + for _ in range(self.max_iter): + indexes = np.random.permutation(m); stop = True + for i in indexes: + xi, yi = X[i:i+1], y[i] + if yi * self.decision_function(xi) <= 0: + self.alpha[i] += yi * self.eta0 + self.sv_index[i] = (self.alpha[i] != 0) + stop = False + if stop: return + + def predict(self, Z): + return np.sign(self.decision_function(Z)) + +class LogisticRegression(object): + def __init__(self, kernel_name='linear', gamma=1.0, degree=3, coef0=1): + kernel_obj = Kernel(gamma=gamma, degree=degree, coef0=coef0) + self.kernel_func = getattr(kernel_obj, kernel_name) + + @staticmethod + def _sigmoid(z): + z = np.clip(z, -250, 250); return 1 / (1 + np.exp(-z)) + def _cost(self, K, y, a): + pred = np.dot(a, K); pred = np.clip(pred, -50, 50) + return -np.dot(y, pred) + np.sum(np.log(1 + np.exp(pred))) + def _gradient(self, K, y, a): + return -np.dot(K, y - self._sigmoid(np.dot(a, K))) + def fit(self, X, y, max_rate=100, min_rate=0.001, gd_step=10, epsilon=1e-4): + self.X_train = X; m = len(X); K = self.kernel_func(X, X) + self.a = np.zeros(m); prev_cost = 0; next_cost = self._cost(K, y, self.a) + for _ in range(1000): + if np.abs(prev_cost - next_cost) <= epsilon and _ > 0: break + neg_grad = -self._gradient(K, y, self.a) + best_rate, min_cost_for_step = 0, self._cost(K, y, self.a) + rate = max_rate + while rate >= min_rate: + cost = self._cost(K, y, self.a + neg_grad * rate) + if cost < min_cost_for_step: min_cost_for_step, best_rate = cost, rate + rate /= gd_step + self.a += neg_grad * best_rate; prev_cost, next_cost = next_cost, min_cost_for_step + def predict(self, X): + X = np.atleast_2d(X) + K_pred = self.kernel_func(X, self.X_train) + return self._sigmoid(np.dot(K_pred, self.a)) + + +def run_xor_kperceptron_experiment(ker_name, degree_param=2): + + X = np.array([[1, 1], [1, 0], [0, 1], [0, 0]]) + y = np.array([-1, 1, 1, -1]) + np.random.seed(1) + + + fig = plt.figure(figsize=(10, 5)) + + with plt.style.context('Solarize_Light2'): + x_min, x_max, y_min, y_max = -0.2, 1.2, -0.2, 1.2 + h = .02 + xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) + grid_points = np.c_[xx.ravel(), yy.ravel()] + + + ax1 = fig.add_subplot(1, 2, 1) + ax1.set_xlim(xx.min(), xx.max()); ax1.set_ylim(yy.min(), yy.max()) + ax1.set_xticks(()); ax1.set_yticks(()) + + + kp = KPerceptron(ker=ker_name, gamma=1, coef0=1, degree=degree_param, eta0=0.5) + kp.fit(X, y) + Z = kp.decision_function(grid_points).reshape(xx.shape) + + contours = ax1.contour(xx, yy, Z, 16, alpha=.8) + ax1.clabel(contours) + ax1.scatter(X[:, 0], X[:, 1], s=50, c=y, edgecolors='#002b36') + title_str = f'{ker_name} {degree_param}' if ker_name == 'poly' else f'{ker_name}' + ax1.set_title(title_str, color='#586e75') + + ax2 = fig.add_subplot(1, 2, 2, projection='3d') + ax2.plot_surface(xx, yy, Z) + ax2.set_xlabel(r'$x_1$'); ax2.set_ylabel(r'$x_2$') + + plt.tight_layout() + plt.show() + +def run_watermelon_logreg_experiment(kernel_name): + + try: data = pd.read_csv('data3.0.csv') + except FileNotFoundError: print("错误：找不到'data3.0.csv'！"); return + + X = np.array(data[['密度', '含糖率']]) + y = (np.array(data['好瓜']) == '是').astype(int) + + + model = None + title = '' + if kernel_name == 'poly': + model = LogisticRegression(kernel_name='linear') + title = '线性核' + elif kernel_name == 'gaussian': + model = LogisticRegression(kernel_name='gaussian', gamma=50) + title = '高斯核，σ=0.1' + elif kernel_name == 'laplace': + model = LogisticRegression(kernel_name='laplace', gamma=10) + title = '拉普拉斯核，σ=0.1' + else: + print(f"错误：未知的核函数名称 '{kernel_name}'") + return + + model.fit(X, y) + + cmap = colors.LinearSegmentedColormap.from_list('watermelon', ['red', 'green']) + xx, yy = np.meshgrid(np.arange(0.2, 0.8, 0.01), np.arange(0.0, 0.5, 0.01)) + Z = model.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape) + + plt.figure() + plt.contourf(xx, yy, Z, cmap=cmap, alpha=0.3, antialiased=True) + plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap) + plt.xlabel('密度'); plt.ylabel('含糖率'); plt.title(title) + plt.show() + + +if __name__ == '__main__': + plt.rcParams['font.sans-serif'] = ['SimHei', 'Microsoft YaHei'] + plt.rcParams['axes.unicode_minus'] = False + + run_xor_kperceptron_experiment(ker_name='poly', degree_param=2) + # run_xor_kperceptron_experiment(ker_name='rbf') + + run_watermelon_logreg_experiment(kernel_name='gaussian') + # run_watermelon_logreg_experiment(kernel_name='poly') \ No newline at end of file