极限学习机的pytorch代码实现

极限学习机是一种单层前馈神经网络，其输入层和隐层之间的连接权重和偏置项是随机初始化的，随后通过随机梯度下降法训练输出层的权重和偏置项。

以下是使用PyTorch实现极限学习机的代码：

import torch
import torch.nn as nn
import numpy as np

class ELM(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(ELM, self).__init__()
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        self.weight_input = nn.Parameter(torch.Tensor(self.input_size, self.hidden_size))
        self.bias_hidden = nn.Parameter(torch.Tensor(self.hidden_size))
        self.weight_output = nn.Parameter(torch.Tensor(self.hidden_size, self.output_size))
        self.bias_output = nn.Parameter(torch.Tensor(self.output_size))
        self.reset_parameters()

    def reset_parameters(self):
        nn.init.normal_(self.weight_input, mean=0, std=1)
        nn.init.zeros_(self.bias_hidden)
        nn.init.normal_(self.weight_output, mean=0, std=0.1)
        nn.init.zeros_(self.bias_output)

    def forward(self, x):
        x = torch.mm(x, self.weight_input)
        x = x + self.bias_hidden.expand_as(x)
        x = torch.sigmoid(x)
        x = torch.mm(x, self.weight_output)
        x = x + self.bias_output.expand_as(x)
        return x

    def fit(self, x_train, y_train):
        x_train = torch.from_numpy(x_train).float()
        y_train = torch.from_numpy(y_train).float()
        H = torch.mm(x_train, self.weight_input)
        H = H + self.bias_hidden.expand_as(H)
        H = torch.sigmoid(H)
        H = H.detach().numpy()
        H = np.linalg.pinv(H)
        beta = np.dot(H, y_train.detach().numpy())
        self.weight_output = nn.Parameter(torch.from_numpy(beta).float().T)

    def predict(self, x_test):
        x_test = torch.from_numpy(x_test).float()
        y_pred = self.forward(x_test)
        y_pred = torch.max(y_pred, 1)[1]
        return y_pred.detach().numpy()

该代码实现了一个名为`ELM`的类，该类继承自`nn.Module`，并实现了`__init__`、`reset_parameters`、`forward`、`fit`和`predict`方法。

`__init__`方法初始化了模型的输入层、隐层和输出层的大小，并定义了模型的权重和偏置项。`reset_parameters`方法对权重和偏置项进行初始化。`forward`方法定义了模型的前向传播过程。`fit`方法用于训练模型，其中利用`np.linalg.pinv`计算矩阵的伪逆。`predict`方法用于对测试数据进行预测。

使用该类的方法类似于使用其他PyTorch模型。例如，以下代码演示了如何使用iris数据集训练和测试一个ELM模型：

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

data = load_iris()
x = data.data
y = data.target
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=42)

elm = ELM(input_size=4, hidden_size=100, output_size=3)
elm.fit(x_train, y_train)
y_pred = elm.predict(x_test)
accuracy = accuracy_score(y_test, y_pred)
print('Accuracy:', accuracy)