脚本如何实现文件内容模糊粗糙核回归

本文目录导读：

1. Python实现（推荐）
2. R语言实现
3. MATLAB/Octave实现
4. 关键参数说明
5. 应用场景

Python实现（推荐）

基础实现

import numpy as np
from scipy.spatial.distance import cdist
class RoughKernelRegression:
    def __init__(self, kernel='gaussian', bandwidth=1.0, roughness_penalty=0.1):
        self.kernel = kernel
        self.bandwidth = bandwidth
        self.roughness_penalty = roughness_penalty
        self.X_train = None
        self.y_train = None
    def _kernel_func(self, x, y):
        """核函数计算"""
        dist = np.linalg.norm(x - y)
        if self.kernel == 'gaussian':
            return np.exp(-dist**2 / (2 * self.bandwidth**2))
        elif self.kernel == 'epanechnikov':
            if dist <= self.bandwidth:
                return 0.75 * (1 - (dist/self.bandwidth)**2)
            return 0
        elif self.kernel == 'tricube':
            if dist <= self.bandwidth:
                return (1 - (dist/self.bandwidth)**3)**3
            return 0
    def _roughness_penalty(self, x, y):
        """粗糙度惩罚项"""
        return self.roughness_penalty * np.linalg.norm(x - y)**2
    def fit(self, X, y):
        """训练模型"""
        self.X_train = np.array(X)
        self.y_train = np.array(y)
    def predict(self, X_test):
        """预测"""
        X_test = np.atleast_2d(X_test)
        predictions = []
        for x_test in X_test:
            # 计算权重
            weights = []
            for x_train in self.X_train:
                kernel_val = self._kernel_func(x_test, x_train)
                roughness = self._roughness_penalty(x_test, x_train)
                weight = kernel_val * np.exp(-roughness)
                weights.append(weight)
            weights = np.array(weights)
            # 归一化权重
            if np.sum(weights) > 0:
                weights_normalized = weights / np.sum(weights)
            else:
                weights_normalized = np.ones_like(weights) / len(weights)
            # 预测值
            prediction = np.sum(weights_normalized * self.y_train)
            predictions.append(prediction)
        return np.array(predictions)
# 使用示例
if __name__ == "__main__":
    # 生成样本数据
    np.random.seed(42)
    X = np.random.rand(100, 2) * 10
    y = np.sin(X[:, 0]) + np.cos(X[:, 1]) + np.random.randn(100) * 0.1
    # 创建并训练模型
    model = RoughKernelRegression(kernel='gaussian', bandwidth=1.5, roughness_penalty=0.1)
    model.fit(X, y)
    # 预测
    X_test = np.array([[5, 5], [3, 7]])
    predictions = model.predict(X_test)
    print("预测结果:", predictions)

优化版本（使用向量化计算）

import numpy as np
from sklearn.metrics.pairwise import pairwise_kernels
class OptimizedRoughKernelRegression:
    def __init__(self, kernel='rbf', gamma=1.0, roughness_penalty=0.1):
        self.kernel = kernel
        self.gamma = gamma
        self.roughness_penalty = roughness_penalty
        self.X_train = None
        self.y_train = None
    def fit(self, X, y):
        """训练模型"""
        self.X_train = np.array(X)
        self.y_train = np.array(y).reshape(-1, 1)
    def predict(self, X_test):
        """预测（向量化版本）"""
        X_test = np.atleast_2d(X_test)
        # 计算核矩阵
        if self.kernel == 'rbf':
            K = pairwise_kernels(X_test, self.X_train, metric='rbf', gamma=self.gamma)
        elif self.kernel == 'linear':
            K = pairwise_kernels(X_test, self.X_train, metric='linear')
        elif self.kernel == 'polynomial':
            K = pairwise_kernels(X_test, self.X_train, metric='polynomial', degree=3)
        # 计算粗糙度惩罚矩阵
        roughness_matrix = np.zeros_like(K)
        for i, x_test in enumerate(X_test):
            for j, x_train in enumerate(self.X_train):
                dist = np.linalg.norm(x_test - x_train)
                roughness_matrix[i, j] = np.exp(-self.roughness_penalty * dist**2)
        # 组合权重
        weights = K * roughness_matrix
        # 归一化权重
        weights_sum = np.sum(weights, axis=1, keepdims=True)
        weights_sum = np.where(weights_sum > 0, weights_sum, 1e-10)
        weights_normalized = weights / weights_sum
        # 预测
        predictions = np.dot(weights_normalized, self.y_train)
        return predictions.flatten()
# 使用示例
optimized_model = OptimizedRoughKernelRegression(kernel='rbf', gamma=1.0, roughness_penalty=0.1)
optimized_model.fit(X, y)
predictions_opt = optimized_model.predict(X_test)
print("优化版预测结果:", predictions_opt)

R语言实现

# 模糊粗糙核回归
rough_kernel_regression <- function(train_x, train_y, test_x, kernel = "gaussian", 
                                    bandwidth = 1.0, roughness_penalty = 0.1) {
  # 核函数
  kernel_func <- function(x, y, bw) {
    dist <- sqrt(sum((x - y)^2))
    if (kernel == "gaussian") {
      return(exp(-dist^2 / (2 * bw^2)))
    } else if (kernel == "epanechnikov") {
      if (dist <= bw) {
        return(0.75 * (1 - (dist/bw)^2))
      }
      return(0)
    }
  }
  # 粗糙度惩罚
  roughness_pen <- function(x, y, penalty) {
    dist_pen <- sqrt(sum((x - y)^2))
    return(exp(-penalty * dist_pen^2))
  }
  # 预测函数
  predict_single <- function(x_test) {
    weights <- numeric(nrow(train_x))
    for (i in 1:nrow(train_x)) {
      kernel_val <- kernel_func(x_test, train_x[i,], bandwidth)
      roughness <- roughness_pen(x_test, train_x[i,], roughness_penalty)
      weights[i] <- kernel_val * roughness
    }
    # 归一化权重
    if (sum(weights) > 0) {
      weights <- weights / sum(weights)
    } else {
      weights <- rep(1/length(weights), length(weights))
    }
    # 预测
    return(sum(weights * train_y))
  }
  # 对所有测试点进行预测
  predictions <- apply(test_x, 1, predict_single)
  return(predictions)
}
# 使用示例
set.seed(42)
train_x <- matrix(runif(200), ncol=2) * 10
train_y <- sin(train_x[,1]) + cos(train_x[,2]) + rnorm(100, sd=0.1)
test_x <- matrix(c(5, 5, 3, 7), ncol=2, byrow=TRUE)
predictions <- rough_kernel_regression(train_x, train_y, test_x)
print(predictions)

MATLAB/Octave实现

function model = rough_kernel_regression_train(X, y, bandwidth, roughness_penalty)
    % 训练模糊粗糙核回归模型
    model.X = X;
    model.y = y;
    model.bandwidth = bandwidth;
    model.roughness_penalty = roughness_penalty;
end
function predictions = rough_kernel_regression_predict(model, X_test)
    % 预测
    n_train = size(model.X, 1);
    n_test = size(X_test, 1);
    predictions = zeros(n_test, 1);
    for i = 1:n_test
        weights = zeros(n_train, 1);
        for j = 1:n_train
            % 计算距离
            dist = norm(X_test(i,:) - model.X(j,:));
            % 高斯核
            kernel_val = exp(-dist^2 / (2 * model.bandwidth^2));
            % 粗糙度惩罚
            roughness = exp(-model.roughness_penalty * dist^2);
            % 组合权重
            weights(j) = kernel_val * roughness;
        end
        % 归一化
        if sum(weights) > 0
            weights = weights / sum(weights);
        else
            weights = ones(n_train, 1) / n_train;
        end
        % 预测
        predictions(i) = weights' * model.y;
    end
end
% 使用示例
X = rand(100, 2) * 10;
y = sin(X(:,1)) + cos(X(:,2)) + 0.1 * randn(100, 1);
model = rough_kernel_regression_train(X, y, 1.5, 0.1);
X_test = [5, 5; 3, 7];
predictions = rough_kernel_regression_predict(model, X_test);
disp('预测结果:');
disp(predictions);

关键参数说明

应用场景

• 数据平滑：处理噪声数据
• 缺失值填充：基于邻近点估计
• 趋势预测：时间序列分析
• 图像处理：去噪和边缘保持

根据你的具体应用场景和数据特征,可以选择合适的实现方式和参数设置。