今年华为杯研究生数学建模的C题第四问用到了lstm，这里配合代码简要地讲一下。

数据类型

磁通密度是一个时序数据，包含了一个周期内的磁通密度变化，我们需要对它进行降维，但PCA是不合适的，因为PCA主要关注数据的方差，无法有效捕捉周期性数据的重要特征，而磁通密度是周期性变化的。

在自然语言处理领域中，LSTM可以捕获序列内部元素之间的关联性，并且其隐藏层可以包含前序序列的信息。最后一层的隐藏层就包含了整个序列的信息，所以我们可以将最后一层的隐藏层作为降维后的向量。

我们选择LSTM对1024 维的磁通密度进行降维，具体做法是：训练时对一个周期进行切片，使用LSTM预测切片的下一时刻的磁通密度；降维时使用整个周期，获取最后一 层的hidden state作为该样本的磁通密度特征。

代码

1.数据处理

import pandas as pd
import torch as pt
import os
os.chdir('/home/burger/math/')df1 = pd.read_excel('./data/附件一（训练集）.xlsx', sheet_name='材料1')
df2 = pd.read_excel('./data/附件一（训练集）.xlsx', sheet_name='材料2')
df3 = pd.read_excel('./data/附件一（训练集）.xlsx', sheet_name='材料3')
df4 = pd.read_excel('./data/附件一（训练集）.xlsx', sheet_name='材料4')collom_name = [i for i in range(1,1024)]
B1 = df1[['0（磁通密度B，T）']+collom_name]
B2 = df2[['0（磁通密度，T）']+collom_name]
B3 = df3[['0（磁通密度B，T）']+collom_name]
B4 = df4[['0（磁通密度B，T）']+collom_name]
print(B1.head())B1_t = pt.tensor(B1.values)
B2_t = pt.tensor(B2.values)
B3_t = pt.tensor(B3.values)
B4_t = pt.tensor(B4.values)
B = pt.cat((B1_t, B2_t, B3_t, B4_t), 0)
print(B.shape)def create_dataset(data, time_step=64):  x, y = [], []  for i in range(0, data.shape[1] - time_step, 32):  a = data[:, i:(i + time_step)]  x.append(a)  y.append(data[:, i + time_step])  return pt.concat(x).float(), pt.concat(y).float()X, Y = create_dataset(B)
print(X.shape, Y.shape)
X, Y = X.unsqueeze(-1), Y.unsqueeze(-1)
print(X.shape, Y.shape)

 2.模型定义

import torch.nn as nn 
import torch.optim as optim
from torch.utils.data import DataLoader, TensorDataset
from tqdm import tqdm# LSTM模型定义
class LSTMModel(nn.Module):def __init__(self, input_size, hidden_size, output_size, num_layers=1):super(LSTMModel, self).__init__()self.lstm = nn.LSTM(input_size, hidden_size, num_layers, batch_first=True)self.fc = nn.Linear(hidden_size, output_size)def forward(self, x):lstm_out, _ = self.lstm(x)out = self.fc(lstm_out[:, -1, :])  # 只取最后一个时间步的输出return outdef embedding(self, x):_, hid_cell = self.lstm(x)return hid_cell[0]

3.训练

input_size = 1
hidden_size = 1
output_size = 1
num_layers = 1
num_epochs = 5
batch_size = 2048
gpu = 6
train_dataset = TensorDataset(X.to(gpu), Y.to(gpu))
train_loader = DataLoader(dataset=train_dataset, batch_size=batch_size, shuffle=True)model = LSTMModel(input_size, hidden_size, output_size, num_layers).to(gpu)
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)def train(model, dataloader, criterion, optimizer, num_epochs):model.train()for epoch in range(num_epochs):for inputs, labels in tqdm(dataloader, unit='batch'):optimizer.zero_grad()outputs = model(inputs)loss = criterion(outputs, labels)loss.backward()optimizer.step()print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')
train(model, train_loader, criterion, optimizer, num_epochs)

4.降维

df_san = pd.read_excel('./data/附件三（测试集）.xlsx')
B_san = df_san[['0（磁通密度B，T）']+collom_name]
B_san_t = pt.tensor(B_san.values)
B_san_t = B_san_t.unsqueeze(-1).float().to(gpu)
print(B_san_t.shape)emb_dataset = TensorDataset(B_san_t)
emb_loader = DataLoader(dataset=emb_dataset, batch_size=400, shuffle=False)def embedding(model, dataloader):model.eval()embeddings = []for inputs in tqdm(dataloader, unit='batch'):outputs = model.embedding(inputs[0])embeddings.append(outputs)return pt.cat(embeddings).cpu().detach().numpy()embeddings = embedding(model, emb_loader)
print(embeddings.shape)
embeddings = embeddings.reshape(-1)
print(embeddings.shape)embeddings_df = pd.DataFrame({'磁通密度编码': embeddings,
})
embeddings_df.to_excel('./data/磁通密度编码1.xlsx', index=False)

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