1，ART

2，基本原理

3，计算过程

4，完成Python案例

（1）ART1网络二值输入

import numpy as np

class ART1:
    def __init__(self, rho=0.5, beta=0.5):
        self.rho = rho  # 匹配阈值
        self.beta = beta  # 学习率
        self.W = None  # 类别原型矩阵
        self.categories = 0  # 当前类别数

    def fit(self, X):
        n_samples, n_features = X.shape
        self.W = np.zeros((0, n_features))  # 初始化空类别

        for x in X:
            x_norm = x / np.sum(x)  # L1归一化
            if self.categories == 0:  # 第一个样本
                self.W = np.vstack([self.W, x_norm])
                self.categories += 1
            else:
                # 计算相似度
                similarities = np.dot(self.W, x_norm) / (np.sum(self.W, axis=1) + 1e-8)
                i_star = np.argmax(similarities)

                if similarities[i_star] >= self.rho:
                    # 更新类别原型
                    self.W[i_star] = self.beta * x_norm + (1 - self.beta) * self.W[i_star]
                else:
                    # 创建新类别
                    self.W = np.vstack([self.W, x_norm])
                    self.categories += 1

    def predict(self, X):
        predictions = []
        for x in X:
            x_norm = x / np.sum(x)
            similarities = np.dot(self.W, x_norm) / (np.sum(self.W, axis=1) + 1e-8)
            i_star = np.argmax(similarities)
            predictions.append(i_star)
        return np.array(predictions)

# 示例数据
X = np.array([
    [1, 0, 1, 0],
    [1, 1, 0, 0],
    [0, 0, 1, 1],
    [0, 1, 0, 1]
])

# 训练ART1网络
art = ART1(rho=0.6, beta=0.5)
art.fit(X)

# 预测
predictions = art.predict(X)
print("类别分配:", predictions)

5，Python案例的数学解释

完整数学运算过程