用keras建立擬合網路解決迴歸問題Regression_機器學習

實現了正弦曲線的擬合，即regression問題。

建立的模型單輸入單輸出，兩個隱層分別為100、50個神經元。

在keras的官方文檔中，給的例子多是關於分類的。因此在測試regression時，遇到了一些問題。總結來說，應注意以下幾個方面：

1）訓練資料需是矩陣型，這裡的輸入和輸出是1000*1，即1000個樣本；每個樣本得到一個輸出；

注意：訓練資料的產生非常關鍵，首先需要檢查輸入資料和輸出資料的維度匹配；

2）對資料進行正常化，這裡用到的是零均值單位方差的規範方法。正常化方法對於各種訓練模型很有講究，具體參照另一篇筆記：http://blog.csdn.net/csmqq/article/details/51461696；

3）輸出層的啟用函數選擇很重要，該擬合的輸出有正負值，因此選擇tanh比較合適；

4）regression問題中，訓練函數compile中的誤差函數通常選擇mean_squared_error。

5）值得注意的是，在訓練時，可以將測試資料的輸入和輸出繪製出來，這樣可以協助調試參數。

6）keras中實現迴歸問題，返回的準確率為0。

# -*- coding: utf-8 -*-"""Created on Mon May 16 13:34:30 2016@author: Michelle"""from keras.models import Sequential    from keras.layers.core import Dense, Activation   from keras.optimizers import SGDfrom keras.layers.advanced_activations import LeakyReLUfrom sklearn import preprocessingfrom keras.utils.visualize_plots import figuresimport matplotlib.pyplot as pltimport numpy as np      #part1: train data  #generate 100 numbers from -2pi to 2pi    x_train = np.linspace(-2*np.pi, 2*np.pi, 1000)  #array: [1000,]  x_train = np.array(x_train).reshape((len(x_train), 1)) #reshape to matrix with [100,1]n=0.1*np.random.rand(len(x_train),1) #generate a matrix with size [len(x),1], value in (0,1),array: [1000,1]  y_train=np.sin(x_train)+n  #訓練資料集：零均值單位方差x_train = preprocessing.scale(x_train)scaler = preprocessing.StandardScaler().fit(x_train) y_train = scaler.transform(y_train)#part2: test data  x_test = np.linspace(-5,5,2000)  x_test = np.array(x_test).reshape((len(x_test), 1))y_test=np.sin(x_test)#零均值單位方差x_test = scaler.transform(x_test)#y_test = scaler.transform(y_test)##plot testing data#fig, ax = plt.subplots()#ax.plot(x_test, y_test,'g')#prediction datax_prd = np.linspace(-3,3,101)  x_prd = np.array(x_prd).reshape((len(x_prd), 1))x_prd = scaler.transform(x_prd)y_prd=np.sin(x_prd)#plot testing datafig, ax = plt.subplots()ax.plot(x_prd, y_prd,'r')#part3: create models, with 1hidden layers    model = Sequential()    model.add(Dense(100, init='uniform', input_dim=1))    #model.add(Activation(LeakyReLU(alpha=0.01))) model.add(Activation('relu'))model.add(Dense(50))    #model.add(Activation(LeakyReLU(alpha=0.1))) model.add(Activation('relu'))model.add(Dense(1))    #model.add(Activation(LeakyReLU(alpha=0.01))) model.add(Activation('tanh'))#sgd = SGD(lr=0.01, decay=1e-6, momentum=0.9, nesterov=True)model.compile(loss='mean_squared_error', optimizer="rmsprop", metrics=["accuracy"])#model.compile(loss='mean_squared_error', optimizer=sgd, metrics=["accuracy"])  #model.fit(x_train, y_train, nb_epoch=64, batch_size=20, verbose=0)   hist = model.fit(x_test, y_test, batch_size=10, nb_epoch=100, shuffle=True,verbose=0,validation_split=0.2)#print(hist.history)score = model.evaluate(x_test, y_test, batch_size=10)out = model.predict(x_prd, batch_size=1)#plot prediction dataax.plot(x_prd, out, 'k--', lw=4)ax.set_xlabel('Measured')ax.set_ylabel('Predicted')plt.show()figures(hist)

虛線是預測值，紅色是輸入值；

繪製誤差值隨著迭代次數的曲線函數是Visualize_plots.py，

1）將其放在C:\Anaconda2\Lib\site-packages\keras\utils下面。

2）在使用時，需要添加這句話：from keras.utils.visualize_plots import figures，然後在程式中直接調用函數figures(hist)。

垓函數的實現代碼為：

# -*- coding: utf-8 -*-"""Created on Sat May 21 22:26:24 2016@author: Shemmy"""def figures(history,figure_name="plots"):    """ method to visualize accuracies and loss vs epoch for training as well as testind data\n        Argumets: history     = an instance returned by model.fit method\n                  figure_name = a string representing file name to plots. By default it is set to "plots" \n       Usage: hist = model.fit(X,y)\n              figures(hist) """    from keras.callbacks import History    if isinstance(history,History):        import matplotlib.pyplot as plt        hist     = history.history         epoch    = history.epoch        acc      = hist['acc']        loss     = hist['loss']        val_loss = hist['val_loss']        val_acc  = hist['val_acc']        plt.figure(1)        plt.subplot(221)        plt.plot(epoch,acc)        plt.title("Training accuracy vs Epoch")        plt.xlabel("Epoch")        plt.ylabel("Accuracy")             plt.subplot(222)        plt.plot(epoch,loss)        plt.title("Training loss vs Epoch")        plt.xlabel("Epoch")        plt.ylabel("Loss")          plt.subplot(223)        plt.plot(epoch,val_acc)        plt.title("Validation Acc vs Epoch")        plt.xlabel("Epoch")        plt.ylabel("Validation Accuracy")          plt.subplot(224)        plt.plot(epoch,val_loss)        plt.title("Validation loss vs Epoch")        plt.xlabel("Epoch")        plt.ylabel("Validation Loss")          plt.tight_layout()        plt.savefig(figure_name)    else:        print "Input Argument is not an instance of class History"

討論keras中實現擬合迴歸問題的文章： https://github.com/fchollet/keras/issues/108