結合歸一化和正則化來優化網絡模型結構，觀察對比loss結果
搭建的神經網絡，使用olivettiface數據集進行訓練，結合歸一化和正則化來優化網絡模型結構，觀察對比loss結果
from sklearn.datasets import fetch_olivetti_faces #倒入數據集
olivetti_faces = fetch_olivetti_faces(data_home='./face_data', shuffle=True)
print(olivetti_faces.data.shape) #打印數據集的形狀
print(olivetti_faces.target.shape) #打印目標的形狀
print(olivetti_faces.images.shape) #打印圖像的形狀
(400, 4096)
(400,)
(400, 64, 64)
import matplotlib.pyplot as pltface = olivetti_faces.images[1] #選擇第二張人臉圖像
plt.imshow(face, cmap='gray') #顯示圖像 cmap='gray'表示灰度圖
plt.show()
olivetti_faces.data[1] #選擇第二張人臉圖像的扁平化數據
array([0.76859504, 0.75619835, 0.74380165, ..., 0.48347107, 0.6280992 ,0.6528926 ], shape=(4096,), dtype=float32)
import torch
import torch.nn as nn
images = torch.tensor(olivetti_faces.data) #將數據轉換為tensor
targets = torch.tensor(olivetti_faces.target) #將目標轉換為tensor
images.shape #打印圖像的形狀
torch.Size([400, 4096])
targets.shape #打印目標的形狀
torch.Size([400])
dataset = [(img,lbl) for img,lbl in zip(images, targets)] #將圖像和標簽組合成一個數據集
dataset[0] #打印數據集的第一個元素
(tensor([0.6694, 0.6364, 0.6488, ..., 0.0868, 0.0826, 0.0744]), tensor(13))
dataloader = torch.utils.data.DataLoader(dataset, batch_size=10, shuffle=True) #創建數據加載器，批量大小為10，打亂數據
# device = torch.device('mps' if torch.backends.mps.is_available() else 'cpu')
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')device
device(type='cpu')
使用Dropout正則化優化
# 多層神經網絡模型
model = nn.Sequential(nn.Linear(4096, 8192), # 輸入層，輸入特征數為4096nn.ReLU(), # ReLU激活函數nn.Dropout(), # Dropout正則化nn.Linear(8192, 16384), # 隱藏層，輸出特征數為16384nn.ReLU(),nn.Dropout(),nn.Linear(16384, 1024), # 隱藏層，輸出特征數為1024nn.ReLU(),nn.Dropout(),nn.Linear(1024, 40) # 輸出層，輸出特征數為40（對應40個類別）
).to(device) # 模型結構搬到GPU內存中
print(model) # 打印模型結構
Sequential((0): Linear(in_features=4096, out_features=8192, bias=True)(1): ReLU()(2): Dropout(p=0.5, inplace=False)(3): Linear(in_features=8192, out_features=16384, bias=True)(4): ReLU()(5): Dropout(p=0.5, inplace=False)(6): Linear(in_features=16384, out_features=1024, bias=True)(7): ReLU()(8): Dropout(p=0.5, inplace=False)(9): Linear(in_features=1024, out_features=40, bias=True)
)
criterion = nn.CrossEntropyLoss() # 損失函數為交叉熵損失
optimizer = torch.optim.Adam(model.parameters(), lr=1e-3) # 優化器為Adam，學習率為1e-3
# 訓練模型
loss_hist = [] # 用于記錄損失值
# 將模型設置為訓練模式
model.train()
for i in range(20): # 訓練20個epochfor img,lbl in dataloader:img,lbl = img.to(device), lbl.to(device) # 數據和模型在同一個設備端result = model(img)loss = criterion(result, lbl)loss.backward()optimizer.step()optimizer.zero_grad()loss_hist.append(loss.item()) # 記錄損失值print(f'epoch:{i+1} loss:{loss.item():.4f}') # 打印當前epoch和損失值
epoch:1 loss:3.7076
epoch:1 loss:12.3654
epoch:1 loss:13.7588
epoch:1 loss:6.2780
epoch:1 loss:4.3650
epoch:1 loss:3.9659
epoch:1 loss:3.9149
epoch:1 loss:3.8406
epoch:1 loss:3.8485
epoch:1 loss:3.8279
epoch:1 loss:3.8980
epoch:1 loss:3.8377
epoch:1 loss:3.7295
epoch:1 loss:3.7737
epoch:1 loss:3.7615
epoch:1 loss:3.7997
epoch:1 loss:3.7737
epoch:1 loss:3.7385
epoch:1 loss:3.7080
epoch:1 loss:3.6875
epoch:1 loss:3.7611
epoch:1 loss:3.6810
epoch:1 loss:3.5438
epoch:1 loss:3.7640
epoch:1 loss:3.9102
epoch:1 loss:4.2676
epoch:1 loss:3.8784
epoch:1 loss:3.8589
epoch:1 loss:3.6792
。。。。。。
epoch:20 loss:3.6929
epoch:20 loss:3.6839
epoch:20 loss:3.6866
epoch:20 loss:3.6917
epoch:20 loss:3.6881
epoch:20 loss:3.6903
epoch:20 loss:3.6893
epoch:20 loss:3.6838
epoch:20 loss:3.6909
epoch:20 loss:3.6903
epoch:20 loss:3.6869
epoch:20 loss:3.6871
epoch:20 loss:3.6939
epoch:20 loss:3.6909
epoch:20 loss:3.6971
epoch:20 loss:3.6935
epoch:20 loss:3.6875
epoch:20 loss:3.6901
epoch:20 loss:3.6864
epoch:20 loss:3.6891
epoch:20 loss:3.6912
epoch:20 loss:3.6913
epoch:20 loss:3.6845
epoch:20 loss:3.6889
epoch:20 loss:3.6898
epoch:20 loss:3.6811
epoch:20 loss:3.6926
epoch:20 loss:3.6888
epoch:20 loss:3.6993
epoch:20 loss:3.6898
epoch:20 loss:3.6947
epoch:20 loss:3.6931
epoch:20 loss:3.6951
epoch:20 loss:3.6901
epoch:20 loss:3.6877
epoch:20 loss:3.6880
epoch:20 loss:3.6926
epoch:20 loss:3.6864
epoch:20 loss:3.6910
epoch:20 loss:3.6951
plt.plot(range(len(loss_hist)), loss_hist) # 繪制損失值曲線
plt.show()
使用BatchNorm1d歸一化優化
# 多層神經網絡模型
model2 = nn.Sequential(nn.Linear(4096, 8192),nn.BatchNorm1d(8192),nn.ReLU(),nn.Dropout(),nn.Linear(8192, 16384),nn.BatchNorm1d(16384), # 批歸一化nn.ReLU(),nn.Dropout(),nn.Linear(16384, 1024),nn.BatchNorm1d(1024),nn.ReLU(),nn.Dropout(),nn.Linear(1024, 40)
).to(device) # 模型結構搬到GPU內存中
print(model2)
Sequential((0): Linear(in_features=4096, out_features=8192, bias=True)(1): BatchNorm1d(8192, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)(2): ReLU()(3): Dropout(p=0.5, inplace=False)(4): Linear(in_features=8192, out_features=16384, bias=True)(5): BatchNorm1d(16384, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)(6): ReLU()(7): Dropout(p=0.5, inplace=False)(8): Linear(in_features=16384, out_features=1024, bias=True)(9): BatchNorm1d(1024, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)(10): ReLU()(11): Dropout(p=0.5, inplace=False)(12): Linear(in_features=1024, out_features=40, bias=True)
)
criterion2 = nn.CrossEntropyLoss() # 損失函數為交叉熵損失
optimizer2 = torch.optim.Adam(model2.parameters(), lr=1e-3) # 優化器為Adam，學習率為1e-3
loss_hist2 = []
model2.train()
for i in range(20):for img,lbl in dataloader:img,lbl = img.to(device), lbl.to(device) # 數據和模型在同一個設備端result = model2(img)loss = criterion2(result, lbl)loss.backward()optimizer2.step()optimizer2.zero_grad()loss_hist2.append(loss.item())print(f'epoch:{i+1} loss:{loss.item():.4f}')
epoch:1 loss:3.5798
epoch:1 loss:3.2452
epoch:1 loss:3.5353
epoch:1 loss:4.1675
epoch:1 loss:4.0728
epoch:1 loss:3.4937
epoch:1 loss:3.9814
epoch:1 loss:3.6151
epoch:1 loss:3.5217
epoch:1 loss:3.1017
epoch:1 loss:3.4522
epoch:1 loss:4.8181
epoch:1 loss:4.0231
epoch:1 loss:4.3008
epoch:1 loss:3.3741
epoch:1 loss:3.9258
epoch:1 loss:3.6895
epoch:1 loss:4.0020
epoch:1 loss:3.1241
epoch:1 loss:2.9453
epoch:1 loss:3.3162
epoch:1 loss:4.3189
epoch:1 loss:3.4162
epoch:1 loss:4.3958
epoch:1 loss:3.1572
epoch:1 loss:3.2535
epoch:1 loss:3.4887
epoch:1 loss:3.4771
epoch:1 loss:3.5689
epoch:1 loss:2.5994
epoch:1 loss:2.7629
epoch:1 loss:2.9798
epoch:1 loss:2.7517
epoch:1 loss:2.7871
epoch:1 loss:2.6800
epoch:1 loss:2.9784
epoch:1 loss:3.4050
epoch:1 loss:2.6510
epoch:1 loss:3.5258
epoch:1 loss:4.0064
epoch:2 loss:2.8011
epoch:2 loss:2.5357
epoch:2 loss:2.6513
epoch:2 loss:2.5815
epoch:2 loss:2.0862
epoch:2 loss:2.9170
epoch:2 loss:2.5202。。。。。。
epoch:20 loss:0.0768
epoch:20 loss:0.0592
epoch:20 loss:0.4393
epoch:20 loss:0.2460
epoch:20 loss:0.1196
epoch:20 loss:0.0596
epoch:20 loss:0.0088
epoch:20 loss:0.1478
epoch:20 loss:0.0671
epoch:20 loss:0.1121
epoch:20 loss:0.1161
epoch:20 loss:0.0191
epoch:20 loss:0.1365
epoch:20 loss:0.0635
epoch:20 loss:0.0404
epoch:20 loss:0.0673
epoch:20 loss:0.0122
epoch:20 loss:0.6775
epoch:20 loss:0.0122
epoch:20 loss:0.0137
epoch:20 loss:0.0415
epoch:20 loss:0.1397
epoch:20 loss:0.0244
epoch:20 loss:0.2535
epoch:20 loss:0.3182
epoch:20 loss:0.2677
epoch:20 loss:0.0028
epoch:20 loss:0.0185
epoch:20 loss:0.1291
epoch:20 loss:0.0514
epoch:20 loss:0.0539
epoch:20 loss:0.0254
epoch:20 loss:0.0723
epoch:20 loss:0.4357
epoch:20 loss:0.1185
epoch:20 loss:0.0806
epoch:20 loss:0.7051
epoch:20 loss:0.0060
epoch:20 loss:0.0527
epoch:20 loss:0.0121
plt.plot(range(len(loss_hist2)), loss_hist2)
plt.show()
本實驗主要內容和結論總結如下：
-
數據集
使用了sklearn.datasets中的Olivetti人臉數據集，包含400張人臉圖片，每張圖片為64x64像素，分為40類。 -
數據處理
- 圖像數據被扁平化為4096維向量。
- 使用PyTorch的
DataLoader進行批量加載。
-
模型設計與優化
- 基礎模型：多層全連接神經網絡，使用ReLU激活和Dropout正則化。
- 優化模型：在基礎模型的每一層后增加了
BatchNorm1d批歸一化層，進一步提升訓練穩定性和收斂速度。
-
訓練過程
- 均采用交叉熵損失函數和Adam優化器，訓練20個epoch。
- 記錄并可視化loss變化曲線。
結果對比與觀察
- Dropout正則化：有效緩解過擬合，loss曲線整體下降，但可能波動較大。
- BatchNorm歸一化+Dropout：loss下降更快更平滑，模型收斂速度提升，訓練更穩定。
結論
- 結合歸一化（BatchNorm）和正則化（Dropout）可以顯著提升神經網絡的訓練效果和泛化能力。
- 歸一化有助于加速收斂，正則化有助于防止過擬合，兩者結合效果更佳。
