实现深度神经网络只需60行代码
0 1 准备数据集
采用的数据集是sklearn中的breast cancer数据集，30维特征，569个样本。训练前进行MinMax标准化缩放至[0,1]区间。按照75/25比例划分成训练集和验证集。
# 获取数据集
import numpy as npimport pandas as pdfrom sklearn import datasetsfrom sklearn import preprocessingfrom sklearn.model_selection import train_test_splitbreast = datasets.load_breast_cancer()scaler = preprocessing.MinMaxScaler()data = scaler.fit_transform(breast['data'])target = breast['target']X_train,X_test,y_train,y_test = train_test_split(data,target)
0 2 模型结构图
0 3 正反传播公式
0 4 NN实现代码
import numpy as np
import pandas as pd#定义激活函数ReLu = lambda z:np.maximum(0.0,z)d_ReLu = lambda z:np.where(z<0,0,1)LeakyReLu = lambda z:np.maximum(0.01*z,z)d_LeakyReLu = lambda z:np.where(z<0,0.01,1)Sigmoid = lambda z:1/(1+np.exp(-z))d_Sigmoid = lambda z: Sigmoid(z)*(1-Sigmoid(z)) #d_Sigmoid = a(1-a)Tanh = np.tanhd_Tanh = lambda z:1 - Tanh(z)**2#d_Tanh = 1 - a**2classNNClassifier(object):def__init__(self,n = [np.nan,5,5,1],alpha = 0.1,ITERNUM = 50000, gfunc = 'ReLu'): self.n = n #各层节点数 self.gfunc = gfunc #隐藏层激活函数 self.alpha,self.ITERNUM = alpha,ITERNUM self.dfJ = pd.DataFrame(data = np.zeros((ITERNUM,1)),columns = ['J']) self.W,self.b = np.nan,np.nan# 确定各层激活函数 self.g = [eval(self.gfunc) for i in range(len(n))]; self.g[-1] = Sigmoid;self.g[0] = np.nan# 确定隐藏层激活函数的导数 self.d_gfunc = eval('d_' + self.gfunc)deffit(self,X_train,y_train): X,Y = X_train.T,y_train.reshape(1,-1) m = X.shape[1] #样本个数 n = self.n; n[0] = X.shape[0] # 各层节点数量# 节点值和参数初始化 A = [np.zeros((ni,m)) for ni in n];A[0] = X #各层节点输出值初始化 Z = [np.zeros((ni,m)) for ni in n];Z[0] = np.nan #各层节点中间值初始化 W = [np.nan] + [np.random.randn(n[i],n[i-1]) * 0.01for i in range(1,len(n))] #各层系数参数 b = [np.zeros((ni,1)) for ni in n];b[0] = np.nan #n各层偏置参数# 导数初始化 dA = [np.zeros(Ai.shape) for Ai in A] dZ = [np.zeros(Ai.shape) for Ai in A] dW = [np.zeros(Wi.shape) if isinstance(Wi,np.ndarray) else np.nan for Wi in W] db = [np.zeros(bi.shape) if isinstance(bi,np.ndarray) else np.nan for bi in b] for k in range(self.ITERNUM):# ---------正向传播 ----------for i in range(1,len(n)): Z[i] = np.dot(W[i],A[i-1]) + b[i] A[i] = self.g[i](Z[i]) J = (1/m) * np.sum(- Y*np.log(A[len(n)-1]) -(1-Y)*np.log(1-A[len(n)-1])) self.dfJ.loc[k]['J']= J# ----------反向传播 --------- hmax = len(n) - 1 dA[hmax] = 1/m*(-Y/A[hmax] + (1-Y)/(1-A[hmax])) dZ[hmax] = 1/m*(A[hmax]-Y) dW[hmax] = np.dot(dZ[hmax],A[hmax-1].T) db[hmax] = np.dot(dZ[hmax],np.ones((m,1)))for i in range(len(n)-2,0,-1): dA[i] = np.dot(W[i+1].T,dZ[i+1]) dZ[i] = dA[i]* self.d_gfunc(Z[i]) dW[i] = np.dot(dZ[i],A[i-1].T) db[i] = np.dot(dZ[i],np.ones((m,1)))#-----------梯度下降 ---------for i in range(1,len(n)): W[i] = W[i] - self.alpha*dW[i] b[i] = b[i] - self.alpha*db[i]# 显示进度if (k+1)%1000 == 0: print('progress rate：{}/{}'.format(k+1,self.ITERNUM),end = 'r') self.W,self.b = W,bdefpredict_prob(self,X_test):# ---------正向传播 ---------- W,b = self.W,self.b Ai = X_test.Tfor i in range(1,len(self.n)): Zi = np.dot(W[i],Ai) + b[i] Ai = self.g[i](Zi)return(Ai.reshape(-1))defpredict(self,X_test): Y_prob = self.predict_prob(X_test) Y_test = Y_prob.copy() Y_test[Y_prob>=0.5] = 1 Y_test[Y_prob< 0.5] = 0return(Y_test)
0 5 单隐层神经网络
设置1个隐藏层，隐藏层节点数为5，隐藏层使用Sigmoid激活函数。
# 采用Sigmoid激活函数
NN = NNClassifier(n = [np.nan,5,1],alpha = 0.02, ITERNUM = 200000, gfunc = 'Sigmoid')NN.fit(X_train,y_train)# 绘制目标函数迭代曲线%matplotlib inlineNN.dfJ.plot(figsize = (12,8))# 测试在验证集的auc得分from sklearn.metrics import roc_auc_scoreY_prob = NN.predict_prob(X_test)
roc_auc_score(list(y_test),list(Y_prob))
隐藏层使用Tanh激活函数。
# 采用 Tanh激活函数
NN = NNClassifier(n = [np.nan,5,1],alpha = 0.02, ITERNUM = 200000, gfunc = 'Tanh')NN.fit(X_train,y_train)# 绘制目标函数迭代曲线%matplotlib inlineNN.dfJ.plot(figsize = (12,8))# 测试在验证集的auc得分from sklearn.metrics import roc_auc_scoreY_prob = NN.predict_prob(X_test)roc_auc_score(list(y_test),list(Y_prob))
隐藏层使用ReLu激活函数。
# 采用 ReLu激活函数
NN = NNClassifier(n = [np.nan,5,1],alpha = 0.02, ITERNUM = 200000, gfunc = 'ReLu')NN.fit(X_train,y_train)# 绘制目标函数迭代曲线%matplotlib inlineNN.dfJ.plot(figsize = (12,8))# 测试在验证集的auc得分from sklearn.metrics import roc_auc_scoreY_prob = NN.predict_prob(X_test)roc_auc_score(list(y_test),list(Y_prob))
隐藏层使用LeakyReLu激活函数。
# 采用 LeakyReLu激活函数
NN = NNClassifier(n = [np.nan,5,1],alpha = 0.02, ITERNUM = 200000, gfunc = 'LeakyReLu')NN.fit(X_train,y_train)# 绘制目标函数迭代曲线%matplotlib inlineNN.dfJ.plot(figsize = (12,8))# 测试在验证集的auc得分from sklearn.metrics import roc_auc_scoreY_prob = NN.predict_prob(X_test)roc_auc_score(list(y_test),list(Y_prob))
以上试验似乎表明，在当前的数据集上，隐藏层采用ReLu激活函数是一个最好的选择，AUC最高得分为0.99958。
0 6 双隐层神经网络
设置2个隐藏层，隐藏层节点数都为5，隐藏层都使用ReLu激活函数。
# 设置两个隐藏层，采用ReLu激活函数
NN = NNClassifier(n = [np.nan,5,5,1],alpha = 0.02, ITERNUM = 200000, gfunc = 'ReLu')NN.fit(X_train,y_train)# 绘制目标函数迭代曲线%matplotlib inlineNN.dfJ.plot(figsize = (12,8))# 测试在验证集的auc得分from sklearn.metrics import roc_auc_scoreY_prob = NN.predict_prob(X_test)roc_auc_score(list(y_test),list(Y_prob))
AUC得分0.99874比采用单隐藏层的最优得分0.99958有所降低，可能是模型复杂度过高，我们尝试减少隐藏层节点的个数至3以降低模型复杂度。
# 双隐藏层，隐藏层节点数为3
NN = NNClassifier(n = [np.nan,3,3,1],alpha = 0.02, ITERNUM = 200000, gfunc = 'ReLu')NN.fit(X_train,y_train)# 绘制目标函数迭代曲线%matplotlib inlineNN.dfJ.plot(figsize = (12,8))# 测试在验证集的auc得分from sklearn.metrics import roc_auc_scoreY_prob = NN.predict_prob(X_test)roc_auc_score(list(y_test),list(Y_prob))
AUC得分0.99979，又有所提高。
和sklearn中自带的神经网络分类器进行对比。
# 和sklearn中的模型对比
from sklearn.neural_network import MLPClassifier# 第一隐藏层神经元个数为3，第二隐藏层神经元个数为3MLPClf = MLPClassifier(hidden_layer_sizes=(3,3),max_iter=200000,activation='relu')MLPClf.fit(X_train,y_train)# 绘制目标函数迭代曲线dfJ = pd.DataFrame(data = np.array(MLPClf.loss_curve_),columns = ['J'])dfJ.plot(figsize = (12,8))# 测试在验证集的auc得分from sklearn.metrics import roc_auc_scoreY_prob = MLPClf.predict_proba(X_test)[:,1]roc_auc_score(list(y_test),list(Y_prob))
以上试验表明，针对当前数据数据集，选择ReLu激活函数，采用双隐藏层，每个隐藏层节点数设置为3是一个不错的选择，AUC得分为0.99979。该得分高于采用CV交叉验证优化超参数后的逻辑回归模型的0.99897的AUC得分。
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如有侵权，请联系 cloudcommunity@tencent.com 删除。