基于多分类非线性SVM（+交叉验证法）的MNIST手写数据集训练（无框架）算法

程序流程

1.将数据进行预处理。
2.通过一对一方法将45类训练样本（(0,1),(0,2),…(1,2)…(2,3)）送入交叉验证法，训练算法为smo
3.得出45个模型，测试时在利用投票法判定

数据结构 '''*************************************************************** * @Fun_Name : judgeStruct: * @Function : 存放训练后的分类器参数 * @Parameter : * @Return : * @Creed : Talk is cheap , show me the code ***********************xieqinyu creates in 1:28 2020/5/8***''' class judgeStruct: def __init__(self): self.Alpha = [] self.label = [] self.B = 0 self.feature = [] '''*************************************************************** * @Fun_Name : class svmStruct * @Function : 数据结构 * @Parameter : * @Return : * @Creed : Talk is cheap , show me the code ***********************xieqinyu creates in 1:29 2020/5/8***''' class svmStruct: def __init__(self, dataMatIn, classLabels, C, toler, kTup): self.X = dataMatIn #数据矩阵 self.labelMat = classLabels #数据标签 self.C = C #松弛变量 self.tol = toler #容错率 self.m = np.shape(dataMatIn)[0] #数据矩阵行数 self.alphas = np.mat(np.zeros((self.m,1))) #根据矩阵行数初始化alpha参数为0 self.b = 0 #初始化b参数为0 self.eCache = np.mat(np.zeros((self.m,2))) #根据矩阵行数初始化虎误差缓存，第一列为是否有效的标志位，第二列为实际的误差E的值。 self.K = np.mat(np.zeros((self.m,self.m))) #初始化核K for i in range(self.m): #计算所有数据的核K self.K[:,i] = kernelTrans(self.X, self.X[i,:], kTup) 数据处理 样本数据由28 x 28 -> 1 x 784 '''*************************************************************** * @Fun_Name : def dealData(images,n): * @Function : 将60000*28*28 => 60000 * 784 * @Parameter : images 传入特征 n维数 * @Return : 6000 * 784 维度 * @Creed : Talk is cheap , show me the code ***********************xieqinyu creates in 16:30 2020/5/4***''' def dealData(images,n): feature = np.empty(shape=[n,784]) for i in range(n): feature[i] = images[i].reshape(1,-1) return feature 将每类数据各自分好 '''*************************************************************** * @Fun_Name : def classify_feature(feature,label,n): * @Function : 分类 * @Parameter : 将每一类的样本各自分好 * @Return : * @Creed : Talk is cheap , show me the code ***********************xieqinyu creates in 16:33 2020/5/4***''' zero_train_feature = np.empty(shape=[5923,784]) zero_train_label = np.empty(5923) one_train_feature = np.empty(shape=[6742,784]) one_train_label = np.empty(6742) two_train_feature = np.empty(shape=[5958,784]) two_train_label = np.empty(5958) three_train_feature = np.empty(shape=[6131,784]) three_train_label = np.empty(6131) four_train_feature = np.empty(shape=[5842,784]) four_train_label = np.empty(5842) five_train_feature = np.empty(shape=[5421,784]) five_train_label = np.empty(5421) six_train_feature = np.empty(shape=[5918,784]) six_train_label = np.empty(5918) seven_train_feature = np.empty(shape=[6265,784]) seven_train_label = np.empty(6265) eight_train_feature = np.empty(shape=[5851,784]) eight_train_label = np.empty(5851) nine_train_feature = np.empty(shape=[5949,784]) nine_train_label = np.empty(5949) list_train_feature = [zero_train_feature,one_train_feature,two_train_feature,three_train_feature,four_train_feature,\ five_train_feature,six_train_feature,seven_train_feature,eight_train_feature,nine_train_feature] list_train_label = [zero_train_label,one_train_label,two_train_label,three_train_label,four_train_label,\ five_train_label,six_train_label,seven_train_label,eight_train_label,nine_train_label] def classify_feature(feature,label,n): num = np.zeros(10,int) for i in range(n): k = int(label[i]) list_train_feature[k][num[k]] = feature[i] list_train_label[k][num[k]] = k num[k] += 1 任意选取其中两类，合并后将特征和样本按同一乱序打乱。取前X个X<=10000

这边 m是训练样本数，n的话可以用来训练好后自己测试下结果对不对，最后用不到的，调试时候用。

'''*************************************************************** * @Fun_Name : def disruptData(a,b,rand,m,n) * @Function : 打乱两类数据 * @Parameter : 比如 a=1 b=0 打乱 1,0,训练样本 因为每两种样本数量不太一致 不太方便 交叉检验，所以只取打乱后前10000个样本 * @Return : 第一个是特征 第二个是标签 * @Creed : Talk is cheap , show me the code ***********************xieqinyu creates in 21:40 2020/5/4***''' def disruptData(a,b,rand,m,n): np.random.seed(rand) new_train_feature = np.vstack((list_train_feature[a], list_train_feature[b])) np.random.shuffle(new_train_feature) np.random.seed(rand) new_train_label = np.hstack((list_train_label[a], list_train_label[b])) np.random.shuffle(new_train_label) new_test_feature = new_train_feature[-n:,:] new_test_label = new_train_label[-n:] new_train_feature = new_train_feature[0:m,:] new_train_label = new_train_label[0:m] for i in range(m): if (new_train_label[i] == a): new_train_label[i] = -1 else: new_train_label[i] = 1 for c in range(n): if (new_test_label[c] == a): new_test_label[c] = -1 else: new_test_label[c] = 1 return new_train_feature , new_train_label, new_test_feature,new_test_label 核函数

本例使用高斯核（也可使用线性核）

'''*************************************************************** * @Fun_Name : def kernelTrans(X, A, kTup): * @Function : 和函数选择 这边选gass * @Parameter : X 整个训练样本 A一个训练样本 kTup核参数 * @Return : * @Creed : Talk is cheap , show me the code ***********************xieqinyu creates in 1:27 2020/5/8***''' def kernelTrans(X, A, kTup): m,n = np.shape(X) K = np.mat(np.zeros((m,1))) if kTup[0] == 'lin': K = X * A.T #线性核函数,只进行内积。 elif kTup[0] == 'rbf': #高斯核函数,根据高斯核函数公式进行计算 for j in range(m): deltaRow = X[j,:] - A K[j] = deltaRow*deltaRow.T K = np.exp(K/(-1*kTup[1]**2)) #计算高斯核K return K #返回计算的核K K折交叉验证法

每次训练样本分十份，九份训练，一份验证。交叉验证10次
选取正确率最高的一次作为本次最优模型

'''*************************************************************** * @Fun_Name : def crossValidation(train_feature,train_label,k1 =100): * @Function : 交叉验证加训练 * @Parameter : k1为高斯参数 * @Return : * @Creed : Talk is cheap , show me the code ***********************xieqinyu creates in 1:20 2020/5/8***''' def crossValidation(train_feature,train_label,k1 =100): m,n = np.shape(train_feature) accuracy = np.zeros(10) B = np.zeros(10) label = [] Alphas = [] feature =[] x = int(m/10) for i in range(10): #交叉验证法 分成10份 0-999，1000-1999 .. #验证集 featureMatrix_verify = train_feature[i*x:(i+1)*x,:] labelMatrix_verify = train_label[i*x:(i+1)*x] #训练集 featureMatrix_train = np.vstack((train_feature[0:i*x,:],train_feature[(i+1)*x:int(m),:])) labelMatrix_train = np.hstack((train_label[0:i*x],train_label[(i+1)*x:int(m)])) print("第%d/10次交叉验证：" %(i+1)) b, alphas = smoP(featureMatrix_train, labelMatrix_train, 0.1, 0.0001, 10, ('rbf', k1)) # 根据训练集计算b和alphas datMat = np.mat(train_feature); labelMat = np.mat(train_label).transpose() svInd = np.nonzero(alphas.A > 0)[0] # 获得支持向量 sVs = datMat[svInd] # 支持向量的特征样本 labelSV = labelMat[svInd]; # 支持向量的标签样本 print("支持向量个数:%d" % np.shape(sVs)[0]) rightCount = 0 datMat = np.mat(featureMatrix_verify); labelMat = np.mat(labelMatrix_verify).transpose() m, n = np.shape(datMat) for j in range(m): kernelEval = kernelTrans(sVs, datMat[j, :], ('rbf', k1)) # 计算各个点的核 predict = kernelEval.T * np.multiply(labelSV, alphas[svInd]) + b # 根据支持向量的点，计算超平面，返回预测结果 if np.sign(predict) == labelMatrix_verify[j]: rightCount += 1 # 返回数组中各元素的正负符号，用1和-1表示，并统计错误个数 accuracy[i] = (float(rightCount) / m)*100 # print(alphas[svInd]) print("验证集正确率: %.2f%%" % (accuracy[i])) feature.append(sVs) label.append(labelSV) B[i] = b Alphas.append(alphas[svInd]) best = np.argmax(accuracy) return feature[best], label[best],B[best],Alphas[best] SMO

参考
https://blog.csdn.net/c406495762/article/details/78158354

测试 if __name__ == '__main__': # 加载数据库 train_images = decode.load_train_images() train_labels = decode.load_train_labels() test_images = decode.load_test_images() test_labels = decode.load_test_labels() # # f = dealData(train_images,60000) classify_feature(f,train_labels,60000) judge = [[judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], [judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct(), judgeStruct()], ] # 开始训练 for i in range(10): for j in range(i+1,10): print("第%d,%d次训练"%(i,j)) new_train_feature, new_train_label ,new_test_feature,new_test_label= disruptData(i, j, 16,1000,100) #i 是-1 judge[i][j].feature,judge[i][j].label,judge[i][j].B ,judge[i][j].Alpha = crossValidation(new_train_feature,new_train_label) # 开始验证 f = dealData(test_images, 10000) f =f[0:20,] accuracy = 0 m,n = np.shape(f) vote = np.zeros(10) for k in range(m): # print(test_labels[k]) for i in range(10): for j in range(i+1,10): kernelEval = kernelTrans(judge[i][j].feature, f[k, :], ('rbf', 100)) # 计算各个点的核 predict = kernelEval.T * np.multiply(judge[i][j].label, judge[i][j].Alpha) + judge[i][j].B # 根据支持向 if(predict0): vote[j] += 1 if(vote.argmax() == test_labels[k]): accuracy += 1 vote = np.zeros(10) print(accuracy/m) 效果

这边训练了一千个，测试100个（程序忘记改了），100个有点少了，如果测试1000+准确率还得上升。但是训练时长有点长，程序就没改了。

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训练 数据集 数据 多分类 分类 交叉验证法 交叉验证 交叉 mnist svm 算法 框架