分别用SVM、贝叶斯分类、二叉树、CNN实现手写数字识别

Author：南岛鹋
发布时间：June 14, 2022
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21606 words
Categories： python 机器学习 opencv

环境

opencv-python 4.5.5.62
scipy 1.81
scikit-learn 1.0.2
torch 1.11.0
数据集 http://yann.lecun.com/exdb/mnist/

成果体验

SVM

训练

from mlxtend.data import loadlocal_mnist
# 从本地加载数据集
train_img, train_label = loadlocal_mnist(
    images_path='D:\data\mnist\\train-images.idx3-ubyte',
    labels_path='D:\data\mnist\\train-labels.idx1-ubyte')
print("训练图片:",train_img,"训练数据格式:",train_img.shape)
print("训练标签",train_label,"训练标签格式:",train_label)

from skimage.feature import hog
import numpy as np
# 提取特征值
list_hog_ft = []
for feature in train_img:
    ft = hog(feature.reshape((28, 28)), orientations=9, pixels_per_cell=(14, 14), cells_per_block=(1, 1), visualize=False)
    list_hog_ft.append(ft)
hog_features = np.array(list_hog_ft, 'float64')

from sklearn import preprocessing
# 特征值归一化
pp = preprocessing.StandardScaler().fit(hog_features)
hog_features = pp.transform(hog_features)
print(hog_features.shape)

test_img, test_label = loadlocal_mnist(
    images_path='D:\data\mnist\\t10k-images.idx3-ubyte',
    labels_path='D:\data\mnist\\t10k-labels.idx1-ubyte')
print("训练图片:",test_img,"训练数据格式:",test_img.shape)
print("训练标签",test_label,"训练标签格式:",test_label)

list_hog_ft = []
for feature in test_img:
    ft = hog(feature.reshape((28, 28)), orientations=9, pixels_per_cell=(14, 14), cells_per_block=(1, 1), visualize=False)
    list_hog_ft.append(ft)
hog_features_test = np.array(list_hog_ft, 'float64')

pp = preprocessing.StandardScaler().fit(hog_features_test)
hog_features_test = pp.transform(hog_features_test)
print(hog_features_test.shape)

clf.score(hog_features_test, test_label)
# 保存模型
import joblib
# Save the classifier
joblib.dump((clf, pp), "D:\data\mnist\digits_cls1.pkl", compress=3)

预测

import cv2
import joblib
from skimage.feature import hog
import numpy as np

from number_dis.model import model_path

modelPath = model_path('SVM.pkl')


class SVM_Predict:
    def __init__(self):
        self.clf, self.pp = joblib.load(modelPath)

    def pre_nums(self, pic_path):
        img, im_th, rects = self.get_num_recs(pic_path)
        for rect in rects:
            # Draw the rectangles
            cv2.rectangle(img, (rect[0], rect[1]), (rect[0] + rect[2], rect[1] + rect[3]), (0, 255, 0), 3)
            # 使数字周围的矩形区域
            leng = int(rect[3] * 1.6)
            pt1 = int(rect[1] + rect[3] // 2 - leng // 2)
            pt2 = int(rect[0] + rect[2] // 2 - leng // 2)
            roi = im_th[pt1:pt1 + leng, pt2:pt2 + leng]
            # Resize the image
            roi = cv2.resize(roi, (28, 28), interpolation=cv2.INTER_AREA)
            roi = cv2.dilate(roi, (3, 3))

            # 计算HOG特征
            roi_hog_fd = hog(roi, orientations=9, pixels_per_cell=(14, 14), cells_per_block=(1, 1), visualize=False)
            roi_hog_fd = self.pp.transform(np.array([roi_hog_fd], 'float64'))
            # Pridict digit
            nbr = self.clf.predict(roi_hog_fd)
            cv2.putText(img, str(int(nbr[0])), (rect[0], rect[1]), cv2.FONT_HERSHEY_DUPLEX, 2, (0, 255, 255), 3)
        return img

    def get_num_recs(self, pic_path):
        img = cv2.imread(pic_path)
        # 灰度处理
        img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        # (5, 5)表示高斯矩阵的长与宽都是5，标准差取0
        img_gray = cv2.GaussianBlur(img_gray, (5, 5), 0)
        # 图像的阈值
        ret, im_th = cv2.threshold(img_gray, 120, 255, cv2.THRESH_BINARY_INV)
        # 寻找图像中的轮廓线
        ctrs, hier = cv2.findContours(im_th.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
        # 获取包含每个轮廓的矩形
        rects = [cv2.boundingRect(ctr) for ctr in ctrs]
        return img, im_th, rects


if __name__ == '__main__':
    img = SVM_Predict().pre_nums(model_path("demo.png"))
    cv2.imwrite(model_path("demopre.png"), img)

贝叶斯分类

训练

from PIL import Image
import numpy as np
import struct
import math
import matplotlib.pyplot as plt
from collections import Counter
from mlxtend.data import loadlocal_mnist


#二值化
def Binarization(images):
    for i in range(images.shape[0]):
        imageMean = images[i].mean()
        images[i] = np.array([0 if x < imageMean else 1 for x in images[i]])
    return images

#模型训练
def Bayes_train(train_x, train_y):    
    #先验概率P(0), P(1)....
    totalNum = train_x.shape[0]
    print(totalNum)
    classNum = Counter(train_y)
    print(classNum)
    prioriP = np.array([classNum[i]/totalNum for i in range(10)])
    print(prioriP,prioriP.shape)
    #后验概率
    posteriorNum = np.empty((10, train_x.shape[1]))
    print(posteriorNum,posteriorNum.shape)
    posteriorP = np.empty((10, train_x.shape[1]))
    print(posteriorP,posteriorP.shape)
    for i in range(10):
        posteriorNum[i] = train_x[np.where(train_y == i)].sum(axis = 0)  
        #拉普拉斯平滑      
        posteriorP[i] = (posteriorNum[i] + 1) / (classNum[i] + 2)  
    print(posteriorNum,posteriorNum.shape)
    print(posteriorP,posteriorP.shape)
    return prioriP, posteriorP



#模型预测
def Bayes_pret(test_x, test_y, prioriP, posteriorP):
    pret = np.empty(test_x.shape[0])
    for i in range(test_x.shape[0]):
        prob = np.empty(10)
        for j in range(10):
            temp = sum([math.log(1-posteriorP[j][x]) if test_x[i][x] == 0 else math.log(posteriorP[j][x]) for x in range(test_x.shape[1])])
            prob[j] = np.array(math.log(prioriP[j]) + temp)
        pret[i] = np.argmax(prob)
    return pret, (pret == test_y).sum()/ test_y.shape[0]


train_img, train_y = loadlocal_mnist(
images_path='D:\data\mnist\\train-images.idx3-ubyte',
labels_path='D:\data\mnist\\train-labels.idx1-ubyte')
train_x_data = train_img.reshape(60000, 28, 28)
#train_x_data = decode_idx3_ubyte('D:/data/mnist/train-images.idx3-ubyte')
# train_x = imageResize(train_x)
#train_y = deconde_idx1_ubyte('D:/data/mnist/train-labels.idx1-ubyte')
#print(train_y.shape)
train_x = np.resize(train_x_data, (train_x_data.shape[0], train_x_data.shape[1]*train_x_data.shape[2]))
train_x = Binarization(train_x)
print(train_x.shape)
test_img, test_y = loadlocal_mnist(
images_path='D:\data\mnist\\t10k-images.idx3-ubyte',
labels_path='D:\data\mnist\\t10k-labels.idx1-ubyte')
test_x_data = test_img.reshape(10000, 28, 28)
#test_x_data = decode_idx3_ubyte('D:/data/mnist/t10k-images.idx3-ubyte')
#print(test_x_data.shape)
# test_x = imageResize(test_x)
#test_y = deconde_idx1_ubyte('D:/data/mnist/t10k-labels.idx1-ubyte')
#print(test_y.shape)
test_x = np.resize(test_x_data, (test_x_data.shape[0], test_x_data.shape[1]*test_x_data.shape[2]))
test_x = Binarization(test_x)


prioriP, posteriorP = Bayes_train(train_x, train_y)
accuracy = Bayes_pret(test_x, test_y, prioriP, posteriorP)

# 保存模型
import joblib
# Save the classifier
joblib.dump((prioriP, posteriorP), "D:\data\mnist\digits_cls1.pkl", compress=3)

预测

import math

import cv2
import joblib
import numpy as np

from number_dis.model import model_path

modelPath = model_path('NB.pkl')


class NB_Predict:
    def __init__(self):
        self.prioriP, self.posteriorP = joblib.load(modelPath)

    def pre_nums(self, pic_path):
        img, im_th, rects = self.get_num_recs(pic_path)
        for rect in rects:
            # Draw the rectangles
            cv2.rectangle(img, (rect[0], rect[1]), (rect[0] + rect[2], rect[1] + rect[3]), (0, 255, 0), 3)
            # 使数字周围的矩形区域
            leng = int(rect[3] * 1.6)
            pt1 = int(rect[1] + rect[3] // 2 - leng // 2)
            pt2 = int(rect[0] + rect[2] // 2 - leng // 2)
            roi = im_th[pt1:pt1 + leng, pt2:pt2 + leng]
            # Resize the image
            roi = cv2.resize(roi, (28, 28), interpolation=cv2.INTER_AREA)
            #     print(roi,roi.shape)
            test_x = np.resize(roi, (1, 28 * 28))
            test_x = self.Binarization(test_x)
            nbr = self.Bayes_pret(test_x, self.prioriP, self.posteriorP)
            cv2.putText(img, str(int(nbr[0])), (rect[0], rect[1]), cv2.FONT_HERSHEY_DUPLEX, 2, (0, 255, 255), 3)
        return img

    def get_num_recs(self, pic_path):
        img = cv2.imread(pic_path)
        im_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        im_gray = cv2.GaussianBlur(im_gray, (5, 5), 0)
        ret, im_th = cv2.threshold(im_gray, 120, 255, cv2.THRESH_BINARY_INV)
        ctrs, hier = cv2.findContours(im_th.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
        rects = [cv2.boundingRect(ctr) for ctr in ctrs]
        return img, im_th, rects

    # 二值化
    def Binarization(self, images):
        for i in range(images.shape[0]):
            imageMean = images[i].mean()
            images[i] = np.array([0 if x < imageMean else 1 for x in images[i]])
        return images

    def Bayes_pret(self, test_x, prioriP, posteriorP):
        pret = np.empty(test_x.shape[0])
        for i in range(test_x.shape[0]):
            prob = np.empty(10)
            for j in range(10):
                temp = sum([math.log(1 - posteriorP[j][x]) if test_x[i][x] == 0 else math.log(posteriorP[j][x]) for x in
                            range(test_x.shape[1])])
                prob[j] = np.array(math.log(prioriP[j]) + temp)
            pret[i] = np.argmax(prob)
        return pret


if __name__ == '__main__':
    img = NB_Predict().pre_nums(model_path("demo.png"))
    cv2.imwrite(model_path("demopre.png"), img)

二叉树

训练

#二值化
def Binarization(images):
    for i in range(images.shape[0]):
        imageMean = images[i].mean()
        images[i] = np.array([0 if x < imageMean else 1 for x in images[i]])
    return images

from mlxtend.data import loadlocal_mnist

train_img, train_label = loadlocal_mnist(
    images_path='D:\data\mnist\\train-images.idx3-ubyte',
    labels_path='D:\data\mnist\\train-labels.idx1-ubyte')
print("训练图片:",train_img,"训练数据格式:",train_img.shape)
print("训练标签",train_label,"训练标签格式:",train_label.shape)

train_img = Binarization(train_img)

test_img, test_label = loadlocal_mnist(
    images_path='D:\data\mnist\\t10k-images.idx3-ubyte',
    labels_path='D:\data\mnist\\t10k-labels.idx1-ubyte')
print("训练图片:",test_img[0],"训练数据格式:",test_img.shape)
print("训练标签",test_label,"训练标签格式:",test_label.shape)

test_img = Binarization(test_img)

# 建模和机器学习
from sklearn.tree import DecisionTreeClassifier
from sklearn.metrics import confusion_matrix,accuracy_score, classification_report
from sklearn.model_selection import train_test_split

dtModel = DecisionTreeClassifier()  # 建立模型
dtModel.fit(train_img,train_label)
prediction = dtModel.predict(test_img)
acc = accuracy_score(test_label,prediction)  
print(f"Sum Axis-1 as Classification accuracy: {acc* 100}")

prediction = dtModel.predict([test_img[0]])

预测

import cv2
import joblib
import numpy as np

from number_dis.model import model_path

modelPath = model_path('DecisionTree.pkl')


class Tree_Predict:
    def __init__(self):
        self.model = joblib.load(modelPath)

    def pre_nums(self, pic_path):
        img, im_th, rects = self.get_num_recs(pic_path)
        for rect in rects:
            # Draw the rectangles
            cv2.rectangle(img, (rect[0], rect[1]), (rect[0] + rect[2], rect[1] + rect[3]), (0, 255, 0), 3)
            # 使数字周围的矩形区域
            leng = int(rect[3] * 1.6)
            pt1 = int(rect[1] + rect[3] // 2 - leng // 2)
            pt2 = int(rect[0] + rect[2] // 2 - leng // 2)
            roi = im_th[pt1:pt1 + leng, pt2:pt2 + leng]
            roi = cv2.resize(roi, (28, 28), interpolation=cv2.INTER_AREA)
            test_x = np.resize(roi, (1, 28 * 28))
            test_x = self.Binarization(test_x)
            result = self.model.predict(test_x)
            cv2.putText(img, str(int(result[0])), (rect[0], rect[1]), cv2.FONT_HERSHEY_DUPLEX, 2, (0, 255, 255), 3)
        return img

    def get_num_recs(self, pic_path):
        img = cv2.imread(pic_path)
        # 灰度处理
        img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        # (5, 5)表示高斯矩阵的长与宽都是5，标准差取0
        img_gray = cv2.GaussianBlur(img_gray, (5, 5), 0)
        # 图像的阈值
        ret, im_th = cv2.threshold(img_gray, 120, 255, cv2.THRESH_BINARY_INV)
        # 寻找图像中的轮廓线
        ctrs, hier = cv2.findContours(im_th.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
        # 获取包含每个轮廓的矩形
        rects = [cv2.boundingRect(ctr) for ctr in ctrs]
        return img, im_th, rects

    # 二值化
    def Binarization(self, images):
        for i in range(images.shape[0]):
            imageMean = images[i].mean()
            images[i] = np.array([0 if x < imageMean else 1 for x in images[i]])
        return images

CNN

训练用的GPU，预测用的CPU

训练

import torch
import torch.nn as nn
import matplotlib.pyplot as plt
from torch.utils.data import DataLoader
from torchvision import datasets, transforms

# 检测是否有GPU
device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')

EPOCH = 10
BATCH_SIZE = 128
LR = 1E-3

# 读取数据集，transforms.ToTensor()将PIL格式的图像以及numpy转化为tensor格式
train_file = datasets.MNIST(
    root='D:\data\mnist\data',
    train=True,
    transform=transforms.ToTensor(),
    download=True
)
test_file = datasets.MNIST(
    root='D:\data\mnist\data',
    train=False,
    transform=transforms.ToTensor()
)

# shuffle = True:是否打乱数据
train_loader = DataLoader(
    dataset=train_file,
    batch_size=BATCH_SIZE,
    shuffle=True
)
test_loader = DataLoader(
    dataset=test_file,
    batch_size=BATCH_SIZE,
    shuffle=False
)

class CNN(nn.Module):
    def __init__(self):
        super(CNN, self).__init__()
        self.conv = nn.Sequential(
            # 参数1：输入通道数，黑白为1，彩色为3
            # 参数2：输出通道数，生成32个特征图
            # 参数3：卷积窗口 5*5
            # 参数4： 步长1
            # 参数5： 补两圈0，(3*3补充一圈0)
            nn.Conv2d(1, 32, 5, 1, 2),
            # 小于0为0，大于0不变
            nn.ReLU(),
            # 最大池化的窗口大小
            nn.MaxPool2d(2),
            # [BATCH_SIZE, 32, 14, 14]
            nn.Conv2d(32, 64, 5, 1, 2),
            # [BATCH_SIZE, 64, 14, 14]
            nn.ReLU(),
            nn.MaxPool2d(2)
            # [BATCH_SIZE, 64, 7, 7]
        )
        self.fc = nn.Linear(64 * 7 * 7, 10)

    def forward(self, x):
        x = self.conv(x)
        x = x.view(x.size(0), -1)
        y = self.fc(x)
        return y
    
model = CNN().to(device)
# 优化器
optim = torch.optim.Adam(model.parameters(), LR)
# 损失函数
lossf = nn.CrossEntropyLoss()

import time
from torch.utils.tensorboard import SummaryWriter
writer = SummaryWriter('D:\data\mnist\logs')
#%% 定义计算整个训练集或测试集loss及acc的函数
def calc(data_loader):
    loss = 0
    total = 0
    correct = 0
    with torch.no_grad():
        for data, targets in data_loader:
            data = data.to(device)
            targets = targets.to(device)
            output = model(data)
            loss += lossf(output, targets)
            correct += (output.argmax(1) == targets).sum()
            total += data.size(0)
    loss = loss.item()/len(data_loader)
    acc = correct.item()/total
    return loss, acc
#%% 训练过程打印函数
def show():
    # 定义全局变量
    if epoch == 0:
        global model_saved_list
        global temp
        temp = 0
    # 打印训练的EPOCH和STEP信息
    header_list = [
        f'EPOCH: {epoch+1:0>{len(str(EPOCH))}}/{EPOCH}',
        f'STEP: {step+1:0>{len(str(len(train_loader)))}}/{len(train_loader)}'
    ]
    header_show = ' '.join(header_list)
    print(header_show, end=' ')
    # 打印训练的LOSS和ACC信息
    loss, acc = calc(train_loader)
    writer.add_scalar('loss', loss, epoch+1)
    writer.add_scalar('acc', acc, epoch+1)
    train_list = [
        f'LOSS: {loss:.4f}',
        f'ACC: {acc:.4f}'
    ]
    train_show = ' '.join(train_list)
    print(train_show, end=' ')
    # 打印测试的LOSS和ACC信息
    val_loss, val_acc = calc(test_loader)
    writer.add_scalar('val_loss', val_loss, epoch+1)
    writer.add_scalar('val_acc', val_acc, epoch+1)
    test_list = [
        f'VAL-LOSS: {val_loss:.4f}',
        f'VAL-ACC: {val_acc:.4f}'
    ]
    test_show = ' '.join(test_list)
    print(test_show, end=' ')
    # 保存最佳模型
    if val_acc > temp:
        model_saved_list = header_list+train_list+test_list
        torch.save(model.state_dict(), 'model.pt')
        temp = val_acc
#%% 训练模型
for epoch in range(EPOCH):
    start_time = time.time()
    for step, (data, targets) in enumerate(train_loader):
#         梯度信息置零
        optim.zero_grad()
        data = data.to(device)
        targets = targets.to(device)
        output = model(data)
        loss = lossf(output, targets)
        acc = (output.argmax(1) == targets).sum().item()/BATCH_SIZE
        loss.backward()
        optim.step()
        print(
            f'EPOCH: {epoch+1:0>{len(str(EPOCH))}}/{EPOCH}',
            f'STEP: {step+1:0>{len(str(len(train_loader)))}}/{len(train_loader)}',
            f'LOSS: {loss.item():.4f}',
            f'ACC: {acc:.4f}',
            end='\r'
        )
    show()
    end_time = time.time()
    print(f'TOTAL-TIME: {round(end_time-start_time)}')

预测

import base64

import cv2
import torch
import torch.nn as nn
import numpy as np
from torchvision import transforms

from service.v3.number_dis.model import model_path

# 检测是否有GPU
device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')
modelPath = model_path('CNN.pt')


class CNN(nn.Module):
    def __init__(self):
        super(CNN, self).__init__()
        self.conv = nn.Sequential(
            # 参数1：输入通道数，黑白为1，彩色为3
            # 参数2：输出通道数，生成32个特征图
            # 参数3：卷积窗口 5*5
            # 参数4： 步长1
            # 参数5： 补两圈0，(3*3补充一圈0)
            nn.Conv2d(1, 32, 5, 1, 2),
            # 小于0为0，大于0不变
            nn.ReLU(),
            # 最大池化的窗口大小
            nn.MaxPool2d(2),
            # [BATCH_SIZE, 32, 14, 14]
            nn.Conv2d(32, 64, 5, 1, 2),
            # [BATCH_SIZE, 64, 14, 14]
            nn.ReLU(),
            nn.MaxPool2d(2)
            # [BATCH_SIZE, 64, 7, 7]
        )
        self.fc = nn.Linear(64 * 7 * 7, 10)

    def forward(self, x):
        x = self.conv(x)
        x = x.view(x.size(0), -1)
        y = self.fc(x)
        return y


class CNN_Predict:
    def __init__(self):
        self.model = CNN()
        self.model.load_state_dict(torch.load(modelPath, map_location=torch.device(device)))
        # 评估模式
        self.model.eval()

    def transform_pic(self, img):
        my_transforms = transforms.Compose([
            transforms.ToPILImage(),
            transforms.Resize(28),
            transforms.Grayscale(),
            transforms.ToTensor()
        ])
        return my_transforms(img)

    def pre_nums(self, pic_path):
        img, im_th, rects = self.get_num_recs(pic_path)
        for rect in rects:
            cv2.rectangle(img, (rect[0], rect[1]), (rect[0] + rect[2], rect[1] + rect[3]), (0, 255, 0), 3)
            leng = int(rect[3] * 1.6)
            pt1 = int(rect[1] + rect[3] // 2 - leng // 2)
            pt2 = int(rect[0] + rect[2] // 2 - leng // 2)
            roi = im_th[pt1:pt1 + leng, pt2:pt2 + leng]
            roi = cv2.resize(roi, (28, 28), interpolation=cv2.INTER_AREA)
            with torch.no_grad():
                data = self.transform_pic(roi)
                data_pre = data.to(device)
                data_pre = data_pre.unsqueeze(0)
                result = self.model(data_pre).argmax(1).item()
            cv2.putText(img, str(int(result)), (rect[0], rect[1]), cv2.FONT_HERSHEY_DUPLEX, 2, (0, 255, 255), 3)
        return img

    def pre_num(self, pic_path):
        pic_path = pic_path.split("base64,")[1]
        image_data = base64.b64decode(pic_path)
        image_array = np.frombuffer(image_data, np.uint8)
        img = cv2.imdecode(image_array, cv2.IMREAD_COLOR)
        im_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        im_gray = cv2.GaussianBlur(im_gray, (5, 5), 0)
        ret, im_th = cv2.threshold(im_gray, 120, 255, cv2.THRESH_BINARY_INV)
        with torch.no_grad():
            data = self.transform_pic(im_th)
            data_pre = data.to(device)
            data_pre = data_pre.unsqueeze(0)
            result = self.model(data_pre).argmax(1).item()
        return result

    def get_num_recs(self, pic_path):
        img = cv2.imread(pic_path)
        im_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        im_gray = cv2.GaussianBlur(im_gray, (5, 5), 0)
        ret, im_th = cv2.threshold(im_gray, 120, 255, cv2.THRESH_BINARY_INV)
        ctrs, hier = cv2.findContours(im_th.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
        rects = [cv2.boundingRect(ctr) for ctr in ctrs]
        return img, im_th, rects


if __name__ == '__main__':
    img = CNN_Predict().pre_nums(model_path("demo.png"))
    cv2.imwrite(model_path("demopre.jpg"), img)

参考

https://blog.csdn.net/qq_44977889/article/details/119353366
https://blog.csdn.net/qwe900/article/details/110189207
https://www.freesion.com/article/2957960288/
https://blog.csdn.net/QRDSHU/article/details/123832876
https://blog.csdn.net/m0_37306360/article/details/79311501
https://blog.csdn.net/qq_42951560/article/details/109565625

Last modification：June 14, 2022

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One comment

Niba
July 25, 2022

温柔帅气的大哥哥

Reply

分别用SVM、贝叶斯分类、二叉树、CNN实现手写数字识别

南岛鹋 • 2022 年 06 月 14 日

<h1>环境</h1><blockquote>opencv-python 4.5.5.62<br>scipy 1.81<br>scikit-learn 1.0.2<br>torch 1.11.0<br>数据集 <span class="external-link"><a class="no-external-link" href="http://yann.lecun.com/exdb/mnist/" target="_blank"><i data-feather="external-link"></i>http://yann.lecun.com/exdb/mnist/</a></span></blockquote><h1>成果体验</h1><p><div class='photos'><figure class="image-thumb" itemprop="associatedMedia" itemscope="" itemtype="http://schema.org/ImageObject">
          <img src="https://www.ndmiao.cn/usr/uploads/2022/06/1805708290.png" alt="" title="" style="">
          <figcaption itemprop="caption description"></figcaption>
      </figure><figure class="image-thumb" itemprop="associatedMedia" itemscope="" itemtype="http://schema.org/ImageObject">
          <img src="https://www.ndmiao.cn/usr/uploads/2022/06/10838800.png" alt="" title="" style="">
          <figcaption itemprop="caption description"></figcaption>
      </figure><figure class="image-thumb" itemprop="associatedMedia" itemscope="" itemtype="http://schema.org/ImageObject">
          <img src="https://www.ndmiao.cn/usr/uploads/2022/06/262938429.jpg" alt="" title="" style="">
          <figcaption itemprop="caption description"></figcaption>
      </figure></div></p><h1>SVM</h1><h2>训练</h2><pre><code>from mlxtend.data import loadlocal_mnist
# 从本地加载数据集
train_img, train_label = loadlocal_mnist(
    images_path='D:\data\mnist\\train-images.idx3-ubyte',
    labels_path='D:\data\mnist\\train-labels.idx1-ubyte')
print(&quot;训练图片:&quot;,train_img,&quot;训练数据格式:&quot;,train_img.shape)
print(&quot;训练标签&quot;,train_label,&quot;训练标签格式:&quot;,train_label)

from skimage.feature import hog
import numpy as np
# 提取特征值
list_hog_ft = []
for feature in train_img:
    ft = hog(feature.reshape((28, 28)), orientations=9, pixels_per_cell=(14, 14), cells_per_block=(1, 1), visualize=False)
    list_hog_ft.append(ft)
hog_features = np.array(list_hog_ft, 'float64')

from sklearn import preprocessing
# 特征值归一化
pp = preprocessing.StandardScaler().fit(hog_features)
hog_features = pp.transform(hog_features)
print(hog_features.shape)

test_img, test_label = loadlocal_mnist(
    images_path='D:\data\mnist\\t10k-images.idx3-ubyte',
    labels_path='D:\data\mnist\\t10k-labels.idx1-ubyte')
print(&quot;训练图片:&quot;,test_img,&quot;训练数据格式:&quot;,test_img.shape)
print(&quot;训练标签&quot;,test_label,&quot;训练标签格式:&quot;,test_label)

list_hog_ft = []
for feature in test_img:
    ft = hog(feature.reshape((28, 28)), orientations=9, pixels_per_cell=(14, 14), cells_per_block=(1, 1), visualize=False)
    list_hog_ft.append(ft)
hog_features_test = np.array(list_hog_ft, 'float64')

pp = preprocessing.StandardScaler().fit(hog_features_test)
hog_features_test = pp.transform(hog_features_test)
print(hog_features_test.shape)

clf.score(hog_features_test, test_label)
# 保存模型
import joblib
# Save the classifier
joblib.dump((clf, pp), &quot;D:\data\mnist\digits_cls1.pkl&quot;, compress=3)</code></pre><h2>预测</h2><pre><code>import cv2
import joblib
from skimage.feature import hog
import numpy as np

from number_dis.model import model_path

modelPath = model_path('SVM.pkl')

class SVM_Predict:
    def __init__(self):
        self.clf, self.pp = joblib.load(modelPath)

# 计算HOG特征
            roi_hog_fd = hog(roi, orientations=9, pixels_per_cell=(14, 14), cells_per_block=(1, 1), visualize=False)
            roi_hog_fd = self.pp.transform(np.array([roi_hog_fd], 'float64'))
            # Pridict digit
            nbr = self.clf.predict(roi_hog_fd)
            cv2.putText(img, str(int(nbr[0])), (rect[0], rect[1]), cv2.FONT_HERSHEY_DUPLEX, 2, (0, 255, 255), 3)
        return img

def get_num_recs(self, pic_path):
        img = cv2.imread(pic_path)
        # 灰度处理
        img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        # (5, 5)表示高斯矩阵的长与宽都是5，标准差取0
        img_gray = cv2.GaussianBlur(img_gray, (5, 5), 0)
        # 图像的阈值
        ret, im_th = cv2.threshold(img_gray, 120, 255, cv2.THRESH_BINARY_INV)
        # 寻找图像中的轮廓线
        ctrs, hier = cv2.findContours(im_th.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
        # 获取包含每个轮廓的矩形
        rects = [cv2.boundingRect(ctr) for ctr in ctrs]
        return img, im_th, rects

if __name__ == '__main__':
    img = SVM_Predict().pre_nums(model_path(&quot;demo.png&quot;))
    cv2.imwrite(model_path(&quot;demopre.png&quot;), img)</code></pre><h1>贝叶斯分类</h1><h2>训练</h2><pre><code>from PIL import Image
import numpy as np
import struct
import math
import matplotlib.pyplot as plt
from collections import Counter
from mlxtend.data import loadlocal_mnist

#二值化
def Binarization(images):
    for i in range(images.shape[0]):
        imageMean = images[i].mean()
        images[i] = np.array([0 if x &lt; imageMean else 1 for x in images[i]])
    return images

#模型训练
def Bayes_train(train_x, train_y):    
    #先验概率P(0), P(1)....
    totalNum = train_x.shape[0]
    print(totalNum)
    classNum = Counter(train_y)
    print(classNum)
    prioriP = np.array([classNum[i]/totalNum for i in range(10)])
    print(prioriP,prioriP.shape)
    #后验概率
    posteriorNum = np.empty((10, train_x.shape[1]))
    print(posteriorNum,posteriorNum.shape)
    posteriorP = np.empty((10, train_x.shape[1]))
    print(posteriorP,posteriorP.shape)
    for i in range(10):
        posteriorNum[i] = train_x[np.where(train_y == i)].sum(axis = 0)  
        #拉普拉斯平滑      
        posteriorP[i] = (posteriorNum[i] + 1) / (classNum[i] + 2)  
    print(posteriorNum,posteriorNum.shape)
    print(posteriorP,posteriorP.shape)
    return prioriP, posteriorP

#模型预测
def Bayes_pret(test_x, test_y, prioriP, posteriorP):
    pret = np.empty(test_x.shape[0])
    for i in range(test_x.shape[0]):
        prob = np.empty(10)
        for j in range(10):
            temp = sum([math.log(1-posteriorP[j][x]) if test_x[i][x] == 0 else math.log(posteriorP[j][x]) for x in range(test_x.shape[1])])
            prob[j] = np.array(math.log(prioriP[j]) + temp)
        pret[i] = np.argmax(prob)
    return pret, (pret == test_y).sum()/ test_y.shape[0]

train_img, train_y = loadlocal_mnist(
images_path='D:\data\mnist\\train-images.idx3-ubyte',
labels_path='D:\data\mnist\\train-labels.idx1-ubyte')
train_x_data = train_img.reshape(60000, 28, 28)
#train_x_data = decode_idx3_ubyte('D:/data/mnist/train-images.idx3-ubyte')
# train_x = imageResize(train_x)
#train_y = deconde_idx1_ubyte('D:/data/mnist/train-labels.idx1-ubyte')
#print(train_y.shape)
train_x = np.resize(train_x_data, (train_x_data.shape[0], train_x_data.shape[1]*train_x_data.shape[2]))
train_x = Binarization(train_x)
print(train_x.shape)
test_img, test_y = loadlocal_mnist(
images_path='D:\data\mnist\\t10k-images.idx3-ubyte',
labels_path='D:\data\mnist\\t10k-labels.idx1-ubyte')
test_x_data = test_img.reshape(10000, 28, 28)
#test_x_data = decode_idx3_ubyte('D:/data/mnist/t10k-images.idx3-ubyte')
#print(test_x_data.shape)
# test_x = imageResize(test_x)
#test_y = deconde_idx1_ubyte('D:/data/mnist/t10k-labels.idx1-ubyte')
#print(test_y.shape)
test_x = np.resize(test_x_data, (test_x_data.shape[0], test_x_data.shape[1]*test_x_data.shape[2]))
test_x = Binarization(test_x)

prioriP, posteriorP = Bayes_train(train_x, train_y)
accuracy = Bayes_pret(test_x, test_y, prioriP, posteriorP)

# 保存模型
import joblib
# Save the classifier
joblib.dump((prioriP, posteriorP), &quot;D:\data\mnist\digits_cls1.pkl&quot;, compress=3)</code></pre><h2>预测</h2><pre><code>import math

import cv2
import joblib
import numpy as np

from number_dis.model import model_path

modelPath = model_path('NB.pkl')

class NB_Predict:
    def __init__(self):
        self.prioriP, self.posteriorP = joblib.load(modelPath)

def pre_nums(self, pic_path):
        img, im_th, rects = self.get_num_recs(pic_path)
        for rect in rects:
            # Draw the rectangles
            cv2.rectangle(img, (rect[0], rect[1]), (rect[0] + rect[2], rect[1] + rect[3]), (0, 255, 0), 3)
            # 使数字周围的矩形区域
            leng = int(rect[3] * 1.6)
            pt1 = int(rect[1] + rect[3] // 2 - leng // 2)
            pt2 = int(rect[0] + rect[2] // 2 - leng // 2)
            roi = im_th[pt1:pt1 + leng, pt2:pt2 + leng]
            # Resize the image
            roi = cv2.resize(roi, (28, 28), interpolation=cv2.INTER_AREA)
            #     print(roi,roi.shape)
            test_x = np.resize(roi, (1, 28 * 28))
            test_x = self.Binarization(test_x)
            nbr = self.Bayes_pret(test_x, self.prioriP, self.posteriorP)
            cv2.putText(img, str(int(nbr[0])), (rect[0], rect[1]), cv2.FONT_HERSHEY_DUPLEX, 2, (0, 255, 255), 3)
        return img

def get_num_recs(self, pic_path):
        img = cv2.imread(pic_path)
        im_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        im_gray = cv2.GaussianBlur(im_gray, (5, 5), 0)
        ret, im_th = cv2.threshold(im_gray, 120, 255, cv2.THRESH_BINARY_INV)
        ctrs, hier = cv2.findContours(im_th.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
        rects = [cv2.boundingRect(ctr) for ctr in ctrs]
        return img, im_th, rects

def Bayes_pret(self, test_x, prioriP, posteriorP):
        pret = np.empty(test_x.shape[0])
        for i in range(test_x.shape[0]):
            prob = np.empty(10)
            for j in range(10):
                temp = sum([math.log(1 - posteriorP[j][x]) if test_x[i][x] == 0 else math.log(posteriorP[j][x]) for x in
                            range(test_x.shape[1])])
                prob[j] = np.array(math.log(prioriP[j]) + temp)
            pret[i] = np.argmax(prob)
        return pret

if __name__ == '__main__':
    img = NB_Predict().pre_nums(model_path(&quot;demo.png&quot;))
    cv2.imwrite(model_path(&quot;demopre.png&quot;), img)</code></pre><h1>二叉树</h1><h2>训练</h2><pre><code>#二值化
def Binarization(images):
    for i in range(images.shape[0]):
        imageMean = images[i].mean()
        images[i] = np.array([0 if x &lt; imageMean else 1 for x in images[i]])
    return images

from mlxtend.data import loadlocal_mnist

train_img, train_label = loadlocal_mnist(
    images_path='D:\data\mnist\\train-images.idx3-ubyte',
    labels_path='D:\data\mnist\\train-labels.idx1-ubyte')
print(&quot;训练图片:&quot;,train_img,&quot;训练数据格式:&quot;,train_img.shape)
print(&quot;训练标签&quot;,train_label,&quot;训练标签格式:&quot;,train_label.shape)

train_img = Binarization(train_img)

test_img, test_label = loadlocal_mnist(
    images_path='D:\data\mnist\\t10k-images.idx3-ubyte',
    labels_path='D:\data\mnist\\t10k-labels.idx1-ubyte')
print(&quot;训练图片:&quot;,test_img[0],&quot;训练数据格式:&quot;,test_img.shape)
print(&quot;训练标签&quot;,test_label,&quot;训练标签格式:&quot;,test_label.shape)

test_img = Binarization(test_img)

# 建模和机器学习
from sklearn.tree import DecisionTreeClassifier
from sklearn.metrics import confusion_matrix,accuracy_score, classification_report
from sklearn.model_selection import train_test_split

dtModel = DecisionTreeClassifier()  # 建立模型
dtModel.fit(train_img,train_label)
prediction = dtModel.predict(test_img)
acc = accuracy_score(test_label,prediction)  
print(f&quot;Sum Axis-1 as Classification accuracy: {acc* 100}&quot;)

prediction = dtModel.predict([test_img[0]])</code></pre><h2>预测</h2><pre><code>import cv2
import joblib
import numpy as np

from number_dis.model import model_path

modelPath = model_path('DecisionTree.pkl')

class Tree_Predict:
    def __init__(self):
        self.model = joblib.load(modelPath)

def pre_nums(self, pic_path):
        img, im_th, rects = self.get_num_recs(pic_path)
        for rect in rects:
            # Draw the rectangles
            cv2.rectangle(img, (rect[0], rect[1]), (rect[0] + rect[2], rect[1] + rect[3]), (0, 255, 0), 3)
            # 使数字周围的矩形区域
            leng = int(rect[3] * 1.6)
            pt1 = int(rect[1] + rect[3] // 2 - leng // 2)
            pt2 = int(rect[0] + rect[2] // 2 - leng // 2)
            roi = im_th[pt1:pt1 + leng, pt2:pt2 + leng]
            roi = cv2.resize(roi, (28, 28), interpolation=cv2.INTER_AREA)
            test_x = np.resize(roi, (1, 28 * 28))
            test_x = self.Binarization(test_x)
            result = self.model.predict(test_x)
            cv2.putText(img, str(int(result[0])), (rect[0], rect[1]), cv2.FONT_HERSHEY_DUPLEX, 2, (0, 255, 255), 3)
        return img

# 二值化
    def Binarization(self, images):
        for i in range(images.shape[0]):
            imageMean = images[i].mean()
            images[i] = np.array([0 if x &lt; imageMean else 1 for x in images[i]])
        return images</code></pre><h1>CNN</h1><blockquote>训练用的GPU，预测用的CPU</blockquote><h2>训练</h2><pre><code>import torch
import torch.nn as nn
import matplotlib.pyplot as plt
from torch.utils.data import DataLoader
from torchvision import datasets, transforms

# 检测是否有GPU
device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')

EPOCH = 10
BATCH_SIZE = 128
LR = 1E-3

# 读取数据集，transforms.ToTensor()将PIL格式的图像以及numpy转化为tensor格式
train_file = datasets.MNIST(
    root='D:\data\mnist\data',
    train=True,
    transform=transforms.ToTensor(),
    download=True
)
test_file = datasets.MNIST(
    root='D:\data\mnist\data',
    train=False,
    transform=transforms.ToTensor()
)

# shuffle = True:是否打乱数据
train_loader = DataLoader(
    dataset=train_file,
    batch_size=BATCH_SIZE,
    shuffle=True
)
test_loader = DataLoader(
    dataset=test_file,
    batch_size=BATCH_SIZE,
    shuffle=False
)

class CNN(nn.Module):
    def __init__(self):
        super(CNN, self).__init__()
        self.conv = nn.Sequential(
            # 参数1：输入通道数，黑白为1，彩色为3
            # 参数2：输出通道数，生成32个特征图
            # 参数3：卷积窗口 5*5
            # 参数4： 步长1
            # 参数5： 补两圈0，(3*3补充一圈0)
            nn.Conv2d(1, 32, 5, 1, 2),
            # 小于0为0，大于0不变
            nn.ReLU(),
            # 最大池化的窗口大小
            nn.MaxPool2d(2),
            # [BATCH_SIZE, 32, 14, 14]
            nn.Conv2d(32, 64, 5, 1, 2),
            # [BATCH_SIZE, 64, 14, 14]
            nn.ReLU(),
            nn.MaxPool2d(2)
            # [BATCH_SIZE, 64, 7, 7]
        )
        self.fc = nn.Linear(64 * 7 * 7, 10)

def forward(self, x):
        x = self.conv(x)
        x = x.view(x.size(0), -1)
        y = self.fc(x)
        return y
    
model = CNN().to(device)
# 优化器
optim = torch.optim.Adam(model.parameters(), LR)
# 损失函数
lossf = nn.CrossEntropyLoss()

import time
from torch.utils.tensorboard import SummaryWriter
writer = SummaryWriter('D:\data\mnist\logs')
#%% 定义计算整个训练集或测试集loss及acc的函数
def calc(data_loader):
    loss = 0
    total = 0
    correct = 0
    with torch.no_grad():
        for data, targets in data_loader:
            data = data.to(device)
            targets = targets.to(device)
            output = model(data)
            loss += lossf(output, targets)
            correct += (output.argmax(1) == targets).sum()
            total += data.size(0)
    loss = loss.item()/len(data_loader)
    acc = correct.item()/total
    return loss, acc
#%% 训练过程打印函数
def show():
    # 定义全局变量
    if epoch == 0:
        global model_saved_list
        global temp
        temp = 0
    # 打印训练的EPOCH和STEP信息
    header_list = [
        f'EPOCH: {epoch+1:0&gt;{len(str(EPOCH))}}/{EPOCH}',
        f'STEP: {step+1:0&gt;{len(str(len(train_loader)))}}/{len(train_loader)}'
    ]
    header_show = ' '.join(header_list)
    print(header_show, end=' ')
    # 打印训练的LOSS和ACC信息
    loss, acc = calc(train_loader)
    writer.add_scalar('loss', loss, epoch+1)
    writer.add_scalar('acc', acc, epoch+1)
    train_list = [
        f'LOSS: {loss:.4f}',
        f'ACC: {acc:.4f}'
    ]
    train_show = ' '.join(train_list)
    print(train_show, end=' ')
    # 打印测试的LOSS和ACC信息
    val_loss, val_acc = calc(test_loader)
    writer.add_scalar('val_loss', val_loss, epoch+1)
    writer.add_scalar('val_acc', val_acc, epoch+1)
    test_list = [
        f'VAL-LOSS: {val_loss:.4f}',
        f'VAL-ACC: {val_acc:.4f}'
    ]
    test_show = ' '.join(test_list)
    print(test_show, end=' ')
    # 保存最佳模型
    if val_acc &gt; temp:
        model_saved_list = header_list+train_list+test_list
        torch.save(model.state_dict(), 'model.pt')
        temp = val_acc
#%% 训练模型
for epoch in range(EPOCH):
    start_time = time.time()
    for step, (data, targets) in enumerate(train_loader):
#         梯度信息置零
        optim.zero_grad()
        data = data.to(device)
        targets = targets.to(device)
        output = model(data)
        loss = lossf(output, targets)
        acc = (output.argmax(1) == targets).sum().item()/BATCH_SIZE
        loss.backward()
        optim.step()
        print(
            f'EPOCH: {epoch+1:0&gt;{len(str(EPOCH))}}/{EPOCH}',
            f'STEP: {step+1:0&gt;{len(str(len(train_loader)))}}/{len(train_loader)}',
            f'LOSS: {loss.item():.4f}',
            f'ACC: {acc:.4f}',
            end='\r'
        )
    show()
    end_time = time.time()
    print(f'TOTAL-TIME: {round(end_time-start_time)}')</code></pre><h2>预测</h2><pre><code>import base64

import cv2
import torch
import torch.nn as nn
import numpy as np
from torchvision import transforms

from service.v3.number_dis.model import model_path

# 检测是否有GPU
device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')
modelPath = model_path('CNN.pt')

def forward(self, x):
        x = self.conv(x)
        x = x.view(x.size(0), -1)
        y = self.fc(x)
        return y

class CNN_Predict:
    def __init__(self):
        self.model = CNN()
        self.model.load_state_dict(torch.load(modelPath, map_location=torch.device(device)))
        # 评估模式
        self.model.eval()

def transform_pic(self, img):
        my_transforms = transforms.Compose([
            transforms.ToPILImage(),
            transforms.Resize(28),
            transforms.Grayscale(),
            transforms.ToTensor()
        ])
        return my_transforms(img)

def pre_nums(self, pic_path):
        img, im_th, rects = self.get_num_recs(pic_path)
        for rect in rects:
            cv2.rectangle(img, (rect[0], rect[1]), (rect[0] + rect[2], rect[1] + rect[3]), (0, 255, 0), 3)
            leng = int(rect[3] * 1.6)
            pt1 = int(rect[1] + rect[3] // 2 - leng // 2)
            pt2 = int(rect[0] + rect[2] // 2 - leng // 2)
            roi = im_th[pt1:pt1 + leng, pt2:pt2 + leng]
            roi = cv2.resize(roi, (28, 28), interpolation=cv2.INTER_AREA)
            with torch.no_grad():
                data = self.transform_pic(roi)
                data_pre = data.to(device)
                data_pre = data_pre.unsqueeze(0)
                result = self.model(data_pre).argmax(1).item()
            cv2.putText(img, str(int(result)), (rect[0], rect[1]), cv2.FONT_HERSHEY_DUPLEX, 2, (0, 255, 255), 3)
        return img

def pre_num(self, pic_path):
        pic_path = pic_path.split(&quot;base64,&quot;)[1]
        image_data = base64.b64decode(pic_path)
        image_array = np.frombuffer(image_data, np.uint8)
        img = cv2.imdecode(image_array, cv2.IMREAD_COLOR)
        im_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        im_gray = cv2.GaussianBlur(im_gray, (5, 5), 0)
        ret, im_th = cv2.threshold(im_gray, 120, 255, cv2.THRESH_BINARY_INV)
        with torch.no_grad():
            data = self.transform_pic(im_th)
            data_pre = data.to(device)
            data_pre = data_pre.unsqueeze(0)
            result = self.model(data_pre).argmax(1).item()
        return result

if __name__ == '__main__':
    img = CNN_Predict().pre_nums(model_path(&quot;demo.png&quot;))
    cv2.imwrite(model_path(&quot;demopre.jpg&quot;), img)</code></pre><h1>参考</h1><p><span class="external-link"><a class="no-external-link" href="https://blog.csdn.net/qq_44977889/article/details/119353366" target="_blank"><i data-feather="external-link"></i>https://blog.csdn.net/qq_44977889/article/details/119353366</a></span><br><span class="external-link"><a class="no-external-link" href="https://blog.csdn.net/qwe900/article/details/110189207" target="_blank"><i data-feather="external-link"></i>https://blog.csdn.net/qwe900/article/details/110189207</a></span><br><span class="external-link"><a class="no-external-link" href="https://www.freesion.com/article/2957960288/" target="_blank"><i data-feather="external-link"></i>https://www.freesion.com/article/2957960288/</a></span><br><span class="external-link"><a class="no-external-link" href="https://blog.csdn.net/QRDSHU/article/details/123832876" target="_blank"><i data-feather="external-link"></i>https://blog.csdn.net/QRDSHU/article/details/123832876</a></span><br><span class="external-link"><a class="no-external-link" href="https://blog.csdn.net/m0_37306360/article/details/79311501" target="_blank"><i data-feather="external-link"></i>https://blog.csdn.net/m0_37306360/article/details/79311501</a></span><br><span class="external-link"><a class="no-external-link" href="https://blog.csdn.net/qq_42951560/article/details/109565625" target="_blank"><i data-feather="external-link"></i>https://blog.csdn.net/qq_42951560/article/details/109565625</a></span></p>

分别用SVM、贝叶斯分类、二叉树、CNN实现手写数字识别

环境

成果体验

SVM

训练

预测

贝叶斯分类

训练

预测

二叉树

训练

预测

CNN

训练

预测

参考

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分别用SVM、贝叶斯分类、二叉树、CNN实现手写数字识别

环境

成果体验

SVM

训练

预测

贝叶斯分类

训练

预测

二叉树

训练

预测

CNN

训练

预测

参考

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分别用SVM、贝叶斯分类、二叉树、CNN实现手写数字识别

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