简要阅读谷歌2017年的论文《MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications》,体会 Depthwise 卷积 和 Pointwise 卷积。同时,阅读代码:https://github.com/OUCTheoryGroup/colab_demo/blob/master/202003_models/MobileNetV1_CIFAR10.ipynb 把代码敲入 Colab 运行,观察并体会效果。
BatchNorm2d() :在使用pytorch的 nn.BatchNorm2d() 层的时候,经常地使用方式为在参数里面只加上待处理的数据的通道数(特征数量)。作用是根据统计的mean 和var来对数据进行标准化,并且这个mena和var在每个batch(计算一次cost需要输入的样本个数,当数据集比较大的时候,一次性将所有样本输入去计算一次cost存储会吃不消,因此会采用一次输入一定量的样本来进行训练。)中都会进行。
Depthwise 处理一个三通道的图像,使用3×3的卷积核,完全在二维平面上进行,卷积核的数量与输入的通道数相同,所以经过运算会生成3个feature map。卷积的参数为: 3 × 3 × 3 = 27,如下所示:
Pointwise 不同之处在于卷积核的尺寸为1×1×k,k为输入通道的数量。所以,这里的卷积运算会将上一层的feature map加权融合,有几个filter就有几个feature map,参数数量为:1 × 1 × 3 × 4 = 12,如下图所示:
因此,可以看出,同样得到4个feature map,使用Depthwise+Pointwise处理,参数数量可以大大降低。
import torch
import torch.nn as nn
import torch.nn.functional as F
import torchvision
import torchvision.transforms as transforms
import matplotlib.pyplot as plt
import numpy as np
import torch.optim as optim
class Block(nn.Module):
'''Depthwise conv + Pointwise conv'''
def __init__(self, in_planes, out_planes, stride=1):
super(Block, self).__init__()
# Depthwise 卷积,3*3 的卷积核,分为 in_planes,即各层单独进行卷积
self.conv1 = nn.Conv2d(in_planes, in_planes, kernel_size=3, stride=stride, padding=1, groups=in_planes, bias=False)
self.bn1 = nn.BatchNorm2d(in_planes)
# Pointwise 卷积,1*1 的卷积核
self.conv2 = nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=1, padding=0, bias=False)
self.bn2 = nn.BatchNorm2d(out_planes)
def forward(self, x):
out = F.relu(self.bn1(self.conv1(x)))
out = F.relu(self.bn2(self.conv2(out)))
return out
# 使用GPU训练,可以在菜单 "代码执行工具" -> "更改运行时类型" 里进行设置
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
transform_train = transforms.Compose([
transforms.RandomCrop(32, padding=4),
transforms.RandomHorizontalFlip(),
transforms.ToTensor(),
transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010))])
transform_test = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010))])
trainset = torchvision.datasets.CIFAR10(root='./data', train=True, download=True, transform=transform_train)
testset = torchvision.datasets.CIFAR10(root='./data', train=False, download=True, transform=transform_test)
trainloader = torch.utils.data.DataLoader(trainset, batch_size=128, shuffle=True, num_workers=2)
testloader = torch.utils.data.DataLoader(testset, batch_size=128, shuffle=False, num_workers=2)
32×32×3 ==>
32×32×32 ==> 32×32×64 ==> 16×16×128 ==> 16×16×128 ==>
8×8×256 ==> 8×8×256 ==> 4×4×512 ==> 4×4×512 ==>
2×2×1024 ==> 2×2×1024
接下来为均值 pooling ==> 1×1×1024
最后全连接到 10个输出节点
class MobileNetV1(nn.Module):
# (128,2) means conv planes=128, stride=2
cfg = [(64,1), (128,2), (128,1), (256,2), (256,1), (512,2), (512,1),
(1024,2), (1024,1)]
def __init__(self, num_classes=10):
super(MobileNetV1, self).__init__()
self.conv1 = nn.Conv2d(3, 32, kernel_size=3, stride=1, padding=1, bias=False)
self.bn1 = nn.BatchNorm2d(32)
self.layers = self._make_layers(in_planes=32)
self.linear = nn.Linear(1024, num_classes)
def _make_layers(self, in_planes):
layers = []
for x in self.cfg:
out_planes = x[0]
stride = x[1]
layers.append(Block(in_planes, out_planes, stride))
in_planes = out_planes
return nn.Sequential(*layers)
def forward(self, x):
out = F.relu(self.bn1(self.conv1(x)))
out = self.layers(out)
out = F.avg_pool2d(out, 2)
out = out.view(out.size(0), -1)
out = self.linear(out)
return out
# 网络放到GPU上
net = MobileNetV1().to(device)
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(net.parameters(), lr=0.001)
for epoch in range(10): # 重复多轮训练
for i, (inputs, labels) in enumerate(trainloader):
inputs = inputs.to(device)
labels = labels.to(device)
# 优化器梯度归零
optimizer.zero_grad()
# 正向传播 + 反向传播 + 优化
outputs = net(inputs)
loss = criterion(outputs, labels)
loss.backward()
optimizer.step()
# 输出统计信息
if i % 100 == 0:
print('Epoch: %d Minibatch: %5d loss: %.3f' %(epoch + 1, i + 1, loss.item()))
print('Finished Training')
correct = 0
total = 0
for data in testloader:
images, labels = data
images, labels = images.to(device), labels.to(device)
outputs = net(images)
_, predicted = torch.max(outputs.data, 1)
total += labels.size(0)
correct += (predicted == labels).sum().item()
print('Accuracy of the network on the 10000 test images: %.2f %%' % (
100 * correct / total))
简要阅读谷歌在CVPR2018上的论文《MobileNetV2: Inverted Residuals and Linear Bottlenecks》,体会第二个版本的改进。阅读代码:https://github.com/OUCTheoryGroup/colab_demo/blob/master/202003_models/MobileNetV2_CIFAR10.ipynb 把代码敲入 Colab 运行,观察并体会效果。
MobileNet V2 的主要改动一:设计了Inverted residual block
ResNet中的bottleneck,先用1x1卷积把通道数由256降到64,然后进行3x3卷积,不然中间3x3卷积计算量太大。所以bottleneck是两边宽中间窄(也是名字的由来)。
现在我们中间的3x3卷积可以变成Depthwise,计算量很少了,所以通道可以多一些。所以MobileNet V2 先用1x1卷积提升通道数,然后用Depthwise 3x3的卷积,再使用1x1的卷积降维。作者称之为Inverted residual block,中间宽两边窄。
MobileNet V2 的主要改动二:去掉输出部分的ReLU6
在 MobileNet V1 里面使用 ReLU6,ReLU6 就是普通的ReLU但是限制最大输出值为 6,这是为了在移动端设备 float16/int8 的低精度的时候,也能有很好的数值分辨率。Depthwise输出比较浅,应用ReLU会带来信息损失,所以在最后把ReLU去掉了(注意下图中标红的部分没有ReLU)。
import torch
import torch.nn as nn
import torch.nn.functional as F
import torchvision
import torchvision.transforms as transforms
import matplotlib.pyplot as plt
import numpy as np
import torch.optim as optim
class Block(nn.Module):
'''expand + depthwise + pointwise'''
def __init__(self, in_planes, out_planes, expansion, stride):
super(Block, self).__init__()
self.stride = stride
# 通过 expansion 增大 feature map 的数量
planes = expansion * in_planes
self.conv1 = nn.Conv2d(in_planes, planes, kernel_size=1, stride=1, padding=0, bias=False)
self.bn1 = nn.BatchNorm2d(planes)
self.conv2 = nn.Conv2d(planes, planes, kernel_size=3, stride=stride, padding=1, groups=planes, bias=False)
self.bn2 = nn.BatchNorm2d(planes)
self.conv3 = nn.Conv2d(planes, out_planes, kernel_size=1, stride=1, padding=0, bias=False)
self.bn3 = nn.BatchNorm2d(out_planes)
# 步长为 1 时,如果 in 和 out 的 feature map 通道不同,用一个卷积改变通道数
if stride == 1 and in_planes != out_planes:
self.shortcut = nn.Sequential(
nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=1, padding=0, bias=False),
nn.BatchNorm2d(out_planes))
# 步长为 1 时,如果 in 和 out 的 feature map 通道相同,直接返回输入
if stride == 1 and in_planes == out_planes:
self.shortcut = nn.Sequential()
def forward(self, x):
out = F.relu(self.bn1(self.conv1(x)))
out = F.relu(self.bn2(self.conv2(out)))
out = self.bn3(self.conv3(out))
# 步长为1,加 shortcut 操作
if self.stride == 1:
return out + self.shortcut(x)
# 步长为2,直接输出
else:
return out
注意,因为 CIFAR10 是 32*32,因此,网络有一定修改。
class MobileNetV2(nn.Module):
# (expansion, out_planes, num_blocks, stride)
cfg = [(1, 16, 1, 1),
(6, 24, 2, 1),
(6, 32, 3, 2),
(6, 64, 4, 2),
(6, 96, 3, 1),
(6, 160, 3, 2),
(6, 320, 1, 1)]
def __init__(self, num_classes=10):
super(MobileNetV2, self).__init__()
self.conv1 = nn.Conv2d(3, 32, kernel_size=3, stride=1, padding=1, bias=False)
self.bn1 = nn.BatchNorm2d(32)
self.layers = self._make_layers(in_planes=32)
self.conv2 = nn.Conv2d(320, 1280, kernel_size=1, stride=1, padding=0, bias=False)
self.bn2 = nn.BatchNorm2d(1280)
self.linear = nn.Linear(1280, num_classes)
def _make_layers(self, in_planes):
layers = []
for expansion, out_planes, num_blocks, stride in self.cfg:
strides = [stride] + [1]*(num_blocks-1)
for stride in strides:
layers.append(Block(in_planes, out_planes, expansion, stride))
in_planes = out_planes
return nn.Sequential(*layers)
def forward(self, x):
out = F.relu(self.bn1(self.conv1(x)))
out = self.layers(out)
out = F.relu(self.bn2(self.conv2(out)))
out = F.avg_pool2d(out, 4)
out = out.view(out.size(0), -1)
out = self.linear(out)
return out
# 使用GPU训练,可以在菜单 "代码执行工具" -> "更改运行时类型" 里进行设置
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
transform_train = transforms.Compose([
transforms.RandomCrop(32, padding=4),
transforms.RandomHorizontalFlip(),
transforms.ToTensor(),
transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010))])
transform_test = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010))])
trainset = torchvision.datasets.CIFAR10(root='./data', train=True, download=True, transform=transform_train)
testset = torchvision.datasets.CIFAR10(root='./data', train=False, download=True, transform=transform_test)
trainloader = torch.utils.data.DataLoader(trainset, batch_size=128, shuffle=True, num_workers=2)
testloader = torch.utils.data.DataLoader(testset, batch_size=128, shuffle=False, num_workers=2)
# 网络放到GPU上
net = MobileNetV2().to(device)
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(net.parameters(), lr=0.001)
for epoch in range(10): # 重复多轮训练
for i, (inputs, labels) in enumerate(trainloader):
inputs = inputs.to(device)
labels = labels.to(device)
# 优化器梯度归零
optimizer.zero_grad()
# 正向传播 + 反向传播 + 优化
outputs = net(inputs)
loss = criterion(outputs, labels)
loss.backward()
optimizer.step()
# 输出统计信息
if i % 100 == 0:
print('Epoch: %d Minibatch: %5d loss: %.3f' %(epoch + 1, i + 1, loss.item()))
print('Finished Training')
correct = 0
total = 0
for data in testloader:
images, labels = data
images, labels = images.to(device), labels.to(device)
outputs = net(images)
_, predicted = torch.max(outputs.data, 1)
total += labels.size(0)
correct += (predicted == labels).sum().item()
print('Accuracy of the network on the 10000 test images: %.2f %%' % (
100 * correct / total))
阅读论文《HybridSN: Exploring 3-D–2-DCNN Feature Hierarchy for Hyperspectral Image Classification》,思考3D卷积和2D卷积的区别。阅读代码:https://github.com/OUCTheoryGroup/colab_demo/blob/master/202003_models/HybridSN_GRSL2020.ipynb 把代码敲入 Colab 运行,网络部分需要自己完成。训练网络,然后多测试几次,会发现每次分类的结果都不一样,请思考为什么?同时,思考问题,如果想要进一步提升高光谱图像的分类性能,可以如何改进?
这篇论文构建了一个 混合网络 解决高光谱图像分类问题,首先用 3D卷积,然后使用 2D卷积。
三维卷积部分:
接下来要进行二维卷积,因此把前面的 32*18 reshape 一下,得到 (576, 19, 19)
二维卷积:(576, 19, 19) 64个 3x3 的卷积核,得到 (64, 17, 17)
接下来是一个 flatten 操作,变为 18496 维的向量,
接下来依次为256,128节点的全连接层,都使用比例为0.4的 Dropout,
最后输出为 16 个节点,是最终的分类类别数。
! wget http://www.ehu.eus/ccwintco/uploads/6/67/Indian_pines_corrected.mat
! wget http://www.ehu.eus/ccwintco/uploads/c/c4/Indian_pines_gt.mat
! pip install spectral
import numpy as np
import matplotlib.pyplot as plt
import scipy.io as sio
from sklearn.decomposition import PCA
from sklearn.model_selection import train_test_split
from sklearn.metrics import confusion_matrix, accuracy_score, classification_report, cohen_kappa_score
import spectral
import torch
import torchvision
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
class_num = 16
class HybridSN(nn.Module):
''' your code here '''
# 随机输入,测试网络结构是否通
# x = torch.randn(1, 1, 30, 25, 25)
# net = HybridSN()
# y = net(x)
# print(y.shape)
首先对高光谱数据实施PCA降维;然后创建 keras 方便处理的数据格式;然后随机抽取 10% 数据做为训练集,剩余的做为测试集。
首先定义基本函数:
# 对高光谱数据 X 应用 PCA 变换
def applyPCA(X, numComponents):
newX = np.reshape(X, (-1, X.shape[2]))
pca = PCA(n_components=numComponents, whiten=True)
newX = pca.fit_transform(newX)
newX = np.reshape(newX, (X.shape[0], X.shape[1], numComponents))
return newX
# 对单个像素周围提取 patch 时,边缘像素就无法取了,因此,给这部分像素进行 padding 操作
def padWithZeros(X, margin=2):
newX = np.zeros((X.shape[0] + 2 * margin, X.shape[1] + 2* margin, X.shape[2]))
x_offset = margin
y_offset = margin
newX[x_offset:X.shape[0] + x_offset, y_offset:X.shape[1] + y_offset, :] = X
return newX
# 在每个像素周围提取 patch ,然后创建成符合 keras 处理的格式
def createImageCubes(X, y, windowSize=5, removeZeroLabels = True):
# 给 X 做 padding
margin = int((windowSize - 1) / 2)
zeroPaddedX = padWithZeros(X, margin=margin)
# split patches
patchesData = np.zeros((X.shape[0] * X.shape[1], windowSize, windowSize, X.shape[2]))
patchesLabels = np.zeros((X.shape[0] * X.shape[1]))
patchIndex = 0
for r in range(margin, zeroPaddedX.shape[0] - margin):
for c in range(margin, zeroPaddedX.shape[1] - margin):
patch = zeroPaddedX[r - margin:r + margin + 1, c - margin:c + margin + 1]
patchesData[patchIndex, :, :, :] = patch
patchesLabels[patchIndex] = y[r-margin, c-margin]
patchIndex = patchIndex + 1
if removeZeroLabels:
patchesData = patchesData[patchesLabels>0,:,:,:]
patchesLabels = patchesLabels[patchesLabels>0]
patchesLabels -= 1
return patchesData, patchesLabels
def splitTrainTestSet(X, y, testRatio, randomState=345):
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=testRatio, random_state=randomState, stratify=y)
return X_train, X_test, y_train, y_test
# 地物类别
class_num = 16
X = sio.loadmat('Indian_pines_corrected.mat')['indian_pines_corrected']
y = sio.loadmat('Indian_pines_gt.mat')['indian_pines_gt']
# 用于测试样本的比例
test_ratio = 0.90
# 每个像素周围提取 patch 的尺寸
patch_size = 25
# 使用 PCA 降维,得到主成分的数量
pca_components = 30
print('Hyperspectral data shape: ', X.shape)
print('Label shape: ', y.shape)
print('\n... ... PCA tranformation ... ...')
X_pca = applyPCA(X, numComponents=pca_components)
print('Data shape after PCA: ', X_pca.shape)
print('\n... ... create data cubes ... ...')
X_pca, y = createImageCubes(X_pca, y, windowSize=patch_size)
print('Data cube X shape: ', X_pca.shape)
print('Data cube y shape: ', y.shape)
print('\n... ... create train & test data ... ...')
Xtrain, Xtest, ytrain, ytest = splitTrainTestSet(X_pca, y, test_ratio)
print('Xtrain shape: ', Xtrain.shape)
print('Xtest shape: ', Xtest.shape)
# 改变 Xtrain, Ytrain 的形状,以符合 keras 的要求
Xtrain = Xtrain.reshape(-1, patch_size, patch_size, pca_components, 1)
Xtest = Xtest.reshape(-1, patch_size, patch_size, pca_components, 1)
print('before transpose: Xtrain shape: ', Xtrain.shape)
print('before transpose: Xtest shape: ', Xtest.shape)
# 为了适应 pytorch 结构,数据要做 transpose
Xtrain = Xtrain.transpose(0, 4, 3, 1, 2)
Xtest = Xtest.transpose(0, 4, 3, 1, 2)
print('after transpose: Xtrain shape: ', Xtrain.shape)
print('after transpose: Xtest shape: ', Xtest.shape)
""" Training dataset"""
class TrainDS(torch.utils.data.Dataset):
def __init__(self):
self.len = Xtrain.shape[0]
self.x_data = torch.FloatTensor(Xtrain)
self.y_data = torch.LongTensor(ytrain)
def __getitem__(self, index):
# 根据索引返回数据和对应的标签
return self.x_data[index], self.y_data[index]
def __len__(self):
# 返回文件数据的数目
return self.len
""" Testing dataset"""
class TestDS(torch.utils.data.Dataset):
def __init__(self):
self.len = Xtest.shape[0]
self.x_data = torch.FloatTensor(Xtest)
self.y_data = torch.LongTensor(ytest)
def __getitem__(self, index):
# 根据索引返回数据和对应的标签
return self.x_data[index], self.y_data[index]
def __len__(self):
# 返回文件数据的数目
return self.len
# 创建 trainloader 和 testloader
trainset = TrainDS()
testset = TestDS()
train_loader = torch.utils.data.DataLoader(dataset=trainset, batch_size=128, shuffle=True, num_workers=2)
test_loader = torch.utils.data.DataLoader(dataset=testset, batch_size=128, shuffle=False, num_workers=2)
# 使用GPU训练,可以在菜单 "代码执行工具" -> "更改运行时类型" 里进行设置
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
# 网络放到GPU上
net = HybridSN().to(device)
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(net.parameters(), lr=0.001)
# 开始训练
total_loss = 0
for epoch in range(100):
for i, (inputs, labels) in enumerate(train_loader):
inputs = inputs.to(device)
labels = labels.to(device)
# 优化器梯度归零
optimizer.zero_grad()
# 正向传播 + 反向传播 + 优化
outputs = net(inputs)
loss = criterion(outputs, labels)
loss.backward()
optimizer.step()
total_loss += loss.item()
print('[Epoch: %d] [loss avg: %.4f] [current loss: %.4f]' %(epoch + 1, total_loss/(epoch+1), loss.item()))
print('Finished Training')
count = 0
# 模型测试
for inputs, _ in test_loader:
inputs = inputs.to(device)
outputs = net(inputs)
outputs = np.argmax(outputs.detach().cpu().numpy(), axis=1)
if count == 0:
y_pred_test = outputs
count = 1
else:
y_pred_test = np.concatenate( (y_pred_test, outputs) )
# 生成分类报告
classification = classification_report(ytest, y_pred_test, digits=4)
print(classification)
下面是用于计算各个类准确率,显示结果的备用函数,以供参考
from operator import truediv
def AA_andEachClassAccuracy(confusion_matrix):
counter = confusion_matrix.shape[0]
list_diag = np.diag(confusion_matrix)
list_raw_sum = np.sum(confusion_matrix, axis=1)
each_acc = np.nan_to_num(truediv(list_diag, list_raw_sum))
average_acc = np.mean(each_acc)
return each_acc, average_acc
def reports (test_loader, y_test, name):
count = 0
# 模型测试
for inputs, _ in test_loader:
inputs = inputs.to(device)
outputs = net(inputs)
outputs = np.argmax(outputs.detach().cpu().numpy(), axis=1)
if count == 0:
y_pred = outputs
count = 1
else:
y_pred = np.concatenate( (y_pred, outputs) )
if name == 'IP':
target_names = ['Alfalfa', 'Corn-notill', 'Corn-mintill', 'Corn'
,'Grass-pasture', 'Grass-trees', 'Grass-pasture-mowed',
'Hay-windrowed', 'Oats', 'Soybean-notill', 'Soybean-mintill',
'Soybean-clean', 'Wheat', 'Woods', 'Buildings-Grass-Trees-Drives',
'Stone-Steel-Towers']
elif name == 'SA':
target_names = ['Brocoli_green_weeds_1','Brocoli_green_weeds_2','Fallow','Fallow_rough_plow','Fallow_smooth',
'Stubble','Celery','Grapes_untrained','Soil_vinyard_develop','Corn_senesced_green_weeds',
'Lettuce_romaine_4wk','Lettuce_romaine_5wk','Lettuce_romaine_6wk','Lettuce_romaine_7wk',
'Vinyard_untrained','Vinyard_vertical_trellis']
elif name == 'PU':
target_names = ['Asphalt','Meadows','Gravel','Trees', 'Painted metal sheets','Bare Soil','Bitumen',
'Self-Blocking Bricks','Shadows']
classification = classification_report(y_test, y_pred, target_names=target_names)
oa = accuracy_score(y_test, y_pred)
confusion = confusion_matrix(y_test, y_pred)
each_acc, aa = AA_andEachClassAccuracy(confusion)
kappa = cohen_kappa_score(y_test, y_pred)
return classification, confusion, oa*100, each_acc*100, aa*100, kappa*100
检测结果写在文件里:
classification, confusion, oa, each_acc, aa, kappa = reports(test_loader, ytest, 'IP')
classification = str(classification)
confusion = str(confusion)
file_name = "classification_report.txt"
with open(file_name, 'w') as x_file:
x_file.write('\n')
x_file.write('{} Kappa accuracy (%)'.format(kappa))
x_file.write('\n')
x_file.write('{} Overall accuracy (%)'.format(oa))
x_file.write('\n')
x_file.write('{} Average accuracy (%)'.format(aa))
x_file.write('\n')
x_file.write('\n')
x_file.write('{}'.format(classification))
x_file.write('\n')
x_file.write('{}'.format(confusion))
下面代码用于显示分类结果:
# load the original image
X = sio.loadmat('Indian_pines_corrected.mat')['indian_pines_corrected']
y = sio.loadmat('Indian_pines_gt.mat')['indian_pines_gt']
height = y.shape[0]
width = y.shape[1]
X = applyPCA(X, numComponents= pca_components)
X = padWithZeros(X, patch_size//2)
# 逐像素预测类别
outputs = np.zeros((height,width))
for i in range(height):
for j in range(width):
if int(y[i,j]) == 0:
continue
else :
image_patch = X[i:i+patch_size, j:j+patch_size, :]
image_patch = image_patch.reshape(1,image_patch.shape[0],image_patch.shape[1], image_patch.shape[2], 1)
X_test_image = torch.FloatTensor(image_patch.transpose(0, 4, 3, 1, 2)).to(device)
prediction = net(X_test_image)
prediction = np.argmax(prediction.detach().cpu().numpy(), axis=1)
outputs[i][j] = prediction+1
if i % 20 == 0:
print('... ... row ', i, ' handling ... ...')
predict_image = spectral.imshow(classes = outputs.astype(int),figsize =(5,5))