### Python 实现感知机算法对鸢尾花数据集进行多分类 感知机是一种线性分类模型，适用于二分类问题。为了将其扩展到多分类场景，可以采用“一对余”(One-vs-Rest, OvR) 或 “一对一” (One-vs-One, OvO) 的策略[^1]。 以下是基于 `sklearn` 中的鸢尾花数据集实现一个多分类感知机的代码示例： #### 数据加载与预处理 ```python from sklearn.datasets import load_iris from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler # 加载鸢尾花数据集 data = load_iris() X, y = data.data, data.target # 划分训练集和测试集 X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42) # 特征标准化 scaler = StandardScaler() X_train = scaler.fit_transform(X_train) X_test = scaler.transform(X_test) ``` #### 感知机模型定义 ```python import numpy as np class Perceptron: def __init__(self, learning_rate=0.01, epochs=100): self.learning_rate = learning_rate self.epochs = epochs def fit(self, X, y): n_samples, n_features = X.shape # 初始化权重和偏置 self.weights = np.zeros((len(np.unique(y)), n_features)) self.bias = np.zeros(len(np.unique(y))) # 将标签转换为 one-hot 编码 y_one_hot = np.eye(len(np.unique(y)))[y] for _ in range(self.epochs): for idx, x_i in enumerate(X): output = np.dot(x_i, self.weights.T) + self.bias predicted_class = np.argmax(output) if y[idx] != predicted_class: true_label = y_one_hot[idx] # 更新权重和偏置 self.weights -= self.learning_rate * (-true_label.reshape(-1, 1) @ x_i.reshape(1, -1)) self.bias -= self.learning_rate * (-true_label) def predict(self, X): outputs = np.dot(X, self.weights.T) + self.bias return np.argmax(outputs, axis=1) ``` #### 训练与评估 ```python # 创建并训练感知机模型 perceptron = Perceptron(learning_rate=0.01, epochs=1000) perceptron.fit(X_train, y_train) # 进行预测 y_pred = perceptron.predict(X_test) # 输出准确率 accuracy = np.mean(y_pred == y_test) print(f"Accuracy: {accuracy:.2f}") ``` 此代码实现了多分类感知机的核心逻辑，并通过 One-vs-All 策略完成对鸢尾花数据集的分类任务[^2]。 ---