过拟合与正则化
正则化计算方法
#Tensorflow代码
loss(w) = tf.contrib.layers.l1_regularizer(REGULARIZER)(w)
#Tensorflow代码 loss(w) = tf.contrib.layers.l2_regularizer(REGULARIZER)(w)
tf.add_to_collection('losses', tf.contrib.layers.l2_regularizer(regularizer)(w) loss = cem + tf.add_n(tf.get_collection('losses'))
matplotlib可视化工具模块使用方法:
例子:
#coding:utf-8 import tensorflow as tf import numpy as np import matplotlib.pyplot as plt BATCH_SIZE = 30 SEED = 2333 #基于Seed参数随机数 rdm = np.random.RandomState(SEED) #随机数返回300行2列的矩阵 表示300组坐标点(x,y) X = rdm.randn(300,2) #从X中取一行,若其x^2+y^2<2 则Y=1 反之Y=0 #作为标签的正确答案 Y_ = [int(x0*x0 + x1*x1 <2) for(x0,x1) in X] #遍历Y中元素,1赋值红色,0赋值蓝色 Y_c = [['red' if y else 'blue'] for y in Y_] #对数据集X和标签Y进行shape整理,第一个元素为-1表示,随第二个参数计算得到 #第二个元素表示多少列,把X整理为n行2列,把Y整理为n行1列 X = np.vstack(X).reshape(-1,2) Y_ = np.vstack(Y_).reshape(-1,1) print (X) print (Y_) print (Y_c) #用plt.scatter 画出数据集X各行中0列元素和1列元素 #用各行Y_c的值表示颜色 plt.scatter(X[:,0], X[:,1],c=np.squeeze(Y_c)) plt.show() #定义神经网络的输入、参数和输出,定义前向传播过程 def get_weight(shape, regularizer): w = tf.Variable(tf.random_normal(shape), dtype=tf.float32) tf.add_to_collection('losses', tf.contrib.layers.l2_regularizer(regularizer)(w)) return w def get_biase(shape): b = tf.Variable(tf.constant(0.01,shape=shape)) return b x = tf.placeholder(tf.float32, shape=(None, 2)) y_ = tf.placeholder(tf.float32, shape=(None, 1)) w1 = get_weight([2,11], 0.01) b1 = get_biase([11]) y1 = tf.nn.relu(tf.matmul(x, w1)+b1) w2 = get_weight([11,1], 0.01) b2 = get_biase([1]) y = tf.matmul(y1, w2)+b2 #定义损失函数 loss_mse = tf.reduce_mean(tf.square(y-y_)) loss_total = loss_mse + tf.add_n(tf.get_collection('losses')) #定义反向传播函数:含正则化 train_step = tf.train.AdamOptimizer(0.0001).minimize(loss_total) with tf.Session() as sess: init_op = tf.global_variables_initializer() sess.run(init_op) STEPS = 40000 for i in range(STEPS): start = (i*BATCH_SIZE) % 300 end = start + BATCH_SIZE sess.run(train_step, feed_dict={x:X[start:end], y_:Y_[start:end]}) if i % 2000 == 0: loss_mse_v = sess.run(loss_mse, feed_dict={x:X, y_:Y_}) print("经过%d步后,loss:%f" %(i, loss_mse_v)) #xx在-3到3之间以步长为0.01, yy在-3到3之间以步长为0.01,生成二维网格坐标点 xx, yy = np.mgrid[-3:3:.01, -3:3:.01] #讲xx,yy拉直,并合并成一个2列矩阵,得到一个网格坐标点的集合 grid = np.c_[xx.ravel(), yy.ravel()] #将网格坐标点喂入神经网络,probs为输出 probs = sess.run(y, feed_dict={x:grid}) #probs的shape调整为xx的样子 probs = probs.reshape(xx.shape) print ("w1:\n",sess.run(w1)) print ("b1:\n",sess.run(b1)) print ("w2:\n",sess.run(w2)) print ("b2:\n",sess.run(b2)) plt.scatter(X[:,0], X[:,1], c=np.squeeze(Y_c)) plt.contour(xx, yy, probs, levels=[.5]) plt.show()