卷积神经网络 回归问题

卷积神经网络（Convolutional Neural Network，CNN）是一种前馈神经网络，通常用于处理具有类似网格结构的数据，例如图像。CNN在图像和语音识别、推荐系统、自然语言处理等领域都有广泛应用。回归问题是指预测一个连续值的问题，例如预测股票价格或者房价等。卷积神经网络也可以用于回归问题，其输出层可以是一个或多个神经元，每个神经元输出一个连续值。下面是两个实现卷积神经网络回归问题的例子：

1. Pytorch实现卷积神经网络回归问题

import torch
import torch.nn as nn

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(3, 6, 5)
        self.pool = nn.MaxPool2d(2, 2)
        self.conv2 = nn.Conv2d(6, 16, 5)
        self.fc1 = nn.Linear(16 * 5 * 5, 120)
        self.fc2 = nn.Linear(120, 84)
        self.fc3 = nn.Linear(84, 1)

    def forward(self, x):
        x = self.pool(torch.relu(self.conv1(x)))
        x = self.pool(torch.relu(self.conv2(x)))
        x = x.view(-1, 16 * 5 * 5)
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = self.fc3(x)
        return x

net = Net()
criterion = nn.MSELoss()
optimizer = torch.optim.SGD(net.parameters(), lr=0.001, momentum=0.9)
# 训练代码省略

2. MATLAB实现CNN卷积神经网络多输入回归预测

% 加载数据
load('data.mat');
x = data(:, 1:7)';
y = data(:, 8)';

% 构建网络
layers = [
    imageInputLayer([7 1 1])
    convolution2dLayer([3 1], 16)
    reluLayer
    maxPooling2dLayer([2 1], 'Stride', 2)
    convolution2dLayer([3 1], 32)
    reluLayer
    maxPooling2dLayer([2 1], 'Stride', 2)
    fullyConnectedLayer(64)
    reluLayer
    fullyConnectedLayer(1)
    regressionLayer];

% 训练网络
options = trainingOptions('adam', ...
    'MaxEpochs', 100, ...
    'MiniBatchSize', 64, ...
    'ValidationData', {x, y}, ...
    'ValidationFrequency', 10, ...
    'Verbose', false);
net = trainNetwork(x, y, layers, options);

% 预测
x_test = [1 2 3 4 5 6 7]';
y_pred = predict(net, x_test);
disp(y_pred);