woa-lssvm回归预测

WOA-LSSVM是一种基于鲸鱼优化算法（Whale Optimization Algorithm, WOA）和局部支持向量机（Least Squares Support Vector Machine, LSSVM）的回归预测方法。

实现步骤如下：

1. 数据预处理：将数据集分为训练集和测试集。

2. 参数设置：设置WOA-LSSVM模型的参数，包括种群大小、最大迭代次数、收敛精度等。

3. WOA算法：使用WOA算法对LSSVM模型进行优化，得到最优的支持向量和相应的系数。

4. 模型训练：使用优化后的LSSVM模型对训练集进行训练，得到模型。

5. 模型预测：使用训练好的模型对测试集进行预测，得到预测结果。

6. 模型评估：使用评价指标（如均方误差、平均绝对误差等）评估模型的预测效果。

代码实现可以参考以下步骤：

1.导入必要的库和数据集

import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error, mean_absolute_error
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_boston

data = load_boston()
X = data.data
y = data.target

2.数据标准化

scaler = StandardScaler()
X = scaler.fit_transform(X)

3.数据集划分

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

4.模型训练和预测

class WOA_LSSVM:
    def __init__(self, population_size=10, max_iter=100, C=1.0, sigma=1.0, a=2.0):
        self.population_size = population_size  # 种群大小
        self.max_iter = max_iter  # 最大迭代次数
        self.C = C  # 正则化参数
        self.sigma = sigma  # 高斯核参数
        self.a = a  # 参数a
        self.X_train = None
        self.y_train = None
        self.alpha = None
        self.b = None

    def woa(self, fitness_func):
        # 初始化鲸鱼位置和速度
        positions = np.random.uniform(low=-1, high=1, size=(self.population_size, self.alpha.shape[0]))
        velocities = np.zeros_like(positions)
        best_position = None
        best_fitness = np.inf
        for i in range(self.max_iter):
            # 计算适应度值并更新最优位置
            fitness = fitness_func(positions)
            if np.min(fitness) < best_fitness:
                best_fitness = np.min(fitness)
                best_position = positions[np.argmin(fitness)]
            a = 2 - i * ((2) / self.max_iter)  # 更新参数a
            # 更新速度和位置
            for j in range(self.population_size):
                r1, r2 = np.random.uniform(size=2)
                A = 2 * a * r1 - a
                C = 2 * r2
                D = np.abs(C * best_position - positions[j])
                velocities[j] = velocities[j] * self.a + A * D
                positions[j] = positions[j] + velocities[j]
                # 边界处理
                positions[j] = np.clip(positions[j], -1, 1)

        return best_position, best_fitness

    def fit(self, X, y):
        self.X_train = X
        self.y_train = y
        # 计算核矩阵
        K = np.exp(-((X[:, np.newaxis] - X) ** 2).sum(axis=2) / (2 * self.sigma ** 2))
        # 构建优化问题的矩阵形式
        H = np.dot(K, K.T) + np.eye(X.shape[0]) / self.C
        f = -y
        A = y.reshape(1, -1)
        b = np.array([0.0])
        # 使用WOA算法优化问题
        self.alpha, _ = self.woa(lambda x: np.array([np.dot(np.dot(x, H), x.T) / 2 + np.dot(f, x.T)]))
        # 计算b
        support_vector_indices = np.where(self.alpha > 1e-5)[0]
        self.b = np.mean(y[support_vector_indices] - np.dot(K[support_vector_indices], self.alpha * y))

    def predict(self, X):
        # 计算核矩阵
        K = np.exp(-((X[:, np.newaxis] - self.X_train) ** 2).sum(axis=2) / (2 * self.sigma ** 2))
        return np.dot(K, self.alpha * self.y_train) + self.b

model = WOA_LSSVM(population_size=20, max_iter=100, C=1.0, sigma=1.0, a=2.0)
model.fit(X_train, y_train)
y_pred = model.predict(X_test)

5.模型评估

mse = mean_squared_error(y_test, y_pred)
mae = mean_absolute_error(y_test, y_pred)
print("MSE:", mse)
print("MAE:", mae)

6.可视化结果

plt.scatter(y_test, y_pred)
plt.plot([0, 50], [0, 50], '--k')
plt.xlabel('True Values')
plt.ylabel('Predictions')
plt.show()

这样就可以使用WOA-LSSVM进行回归预测了。