利用Pybrain庫進行神經網路函數擬合__函數

Pybrain是一個比較有名的Python神經網路程式庫，今天我用它做了一個實驗，參考了這篇部落格，感謝原作者，給出了具體的實現，代碼可以直接拷貝運行。
我們的問題主要如下：

首先我們給出構造產生這個題目要求的資料集的函數

def generate_data():    """generate original data of u and y"""    u = np.random.uniform(-1,1,200)    y=[]    former_y_value = 0    for i in np.arange(0,200):        y.append(former_y_value)        next_y_value = (29 / 40) * np.sin(            (16 * u[i] + 8 * former_y_value) / (3 + 4 * (u[i] ** 2) + 4 * (former_y_value ** 2))) \                       + (2 / 10) * u[i] + (2 / 10) * former_y_value        former_y_value = next_y_value    return u,y

這個題目的函數畫出來是這樣子的：

我們的例子，就是用前100個點訓練，後100個點作為預測。 構建Pybrain神經網路的基本步驟： 構建神經網路 構造資料集 訓練神經網路 結果可視化 驗證和分析 構造神經網路

構建神經網路的過程非常清晰，設定幾個層次，幾個節點，都簡單明了，看一次就會了。

import numpy as npimport matplotlib.pyplot as pltfrom pybrain.structure import *from pybrain.datasets import SupervisedDataSetfrom pybrain.supervised.trainers import BackpropTrainer# createa neural networkfnn = FeedForwardNetwork()# create three layers, input layer:2 input unit; hidden layer: 10 units; output layer: 1 outputinLayer = LinearLayer(2, name='inLayer')hiddenLayer0 = SigmoidLayer(10, name='hiddenLayer0')outLayer = LinearLayer(1, name='outLayer')# add three layers to the neural networkfnn.addInputModule(inLayer)fnn.addModule(hiddenLayer0)fnn.addOutputModule(outLayer)# link three layersin_to_hidden0 = FullConnection(inLayer,hiddenLayer0)hidden0_to_out = FullConnection(hiddenLayer0, outLayer)# add the links to neural networkfnn.addConnection(in_to_hidden0)fnn.addConnection(hidden0_to_out)# make neural network come into effectfnn.sortModules()

構建資料集

我們選擇2輸入1輸出，80%用於訓練，20%用於預測

# definite the dataset as two input , one outputDS = SupervisedDataSet(2,1)# add data element to the datasetfor i in np.arange(199):    DS.addSample([u[i],y[i]],[y[i+1]])# you can get your input/output this wayX = DS['input']Y = DS['target']# split the dataset into train dataset and test datasetdataTrain, dataTest = DS.splitWithProportion(0.8)xTrain, yTrain = dataTrain['input'],dataTrain['target']xTest, yTest = dataTest['input'], dataTest['target']

訓練神經網路

我們暫且讓他迭代1000次

# train the NN# we use BP Algorithm# verbose = True means print th total errortrainer = BackpropTrainer(fnn, dataTrain, verbose=True,learningrate=0.01)# set the epoch times to make the NN  fittrainer.trainUntilConvergence(maxEpochs=1000)

結果可視化

我們用matlibplot畫出來這個預測值和實際值

predict_resutl=[]for i in np.arange(len(xTest)):    predict_resutl.append(fnn.activate(xTest[i])[0])print(predict_resutl)plt.figure()plt.plot(np.arange(0,len(xTest)), predict_resutl, 'ro--', label='predict number')plt.plot(np.arange(0,len(xTest)), yTest, 'ko-', label='true number')plt.legend()plt.xlabel("x")plt.ylabel("y")plt.show()

我們拿這個題目來做一下預測，畫出來的圖形如下
分析

for mod in fnn.modules:  print ("Module:", mod.name)  if mod.paramdim > 0:    print ("--parameters:", mod.params)  for conn in fnn.connections[mod]:    print ("-connection to", conn.outmod.name)    if conn.paramdim > 0:       print ("- parameters", conn.params)  if hasattr(fnn, "recurrentConns"):    print ("Recurrent connections")    for conn in fnn.recurrentConns:       print ("-", conn.inmod.name, " to", conn.outmod.name)       if conn.paramdim > 0:          print ("- parameters", conn.params)

它可以列印出來神經網路的具體資訊，結果如下：

Module: hiddenLayer0-connection to outLayer- parameters [-0.48485978  1.94439991 -1.1686299  -1.01764515 -1.04221    -0.78088745  0.27321985 -1.76426041  2.0747614   1.98425053]Module: inLayer-connection to hiddenLayer0- parameters [ 1.48125364 -0.97942827  4.7258546   2.08059918 -1.96960441 -0.03098871  0.52430318  1.64983933  0.43738152  1.95122015  0.81952423 -0.24019787 -0.86026329  0.63505556  0.53870484  0.94078527  1.42263437  1.87720358 -1.12582038  0.70344489]Module: outLayer

完整的代碼

最後，我把完整的代碼貼出來，注意，你要先安裝pybrain才行

import numpy as npimport matplotlib.pyplot as pltfrom pybrain.structure import *from pybrain.datasets import SupervisedDataSetfrom pybrain.supervised.trainers import BackpropTrainerdef generate_data():    """generate original data of u and y"""    u = np.random.uniform(-1,1,200)    y=[]    former_y_value = 0    for i in np.arange(0,200):        y.append(former_y_value)        next_y_value = (29 / 40) * np.sin(            (16 * u[i] + 8 * former_y_value) / (3 + 4 * (u[i] ** 2) + 4 * (former_y_value ** 2))) \                       + (2 / 10) * u[i] + (2 / 10) * former_y_value        former_y_value = next_y_value    return u,y# obtain the original datau,y = generate_data()# createa neural networkfnn = FeedForwardNetwork()# create three layers, input layer:2 input unit; hidden layer: 10 units; output layer: 1 outputinLayer = LinearLayer(2, name='inLayer')hiddenLayer0 = SigmoidLayer(10, name='hiddenLayer0')outLayer = LinearLayer(1, name='outLayer')# add three layers to the neural networkfnn.addInputModule(inLayer)fnn.addModule(hiddenLayer0)fnn.addOutputModule(outLayer)# link three layersin_to_hidden0 = FullConnection(inLayer,hiddenLayer0)hidden0_to_out = FullConnection(hiddenLayer0, outLayer)# add the links to neural networkfnn.addConnection(in_to_hidden0)fnn.addConnection(hidden0_to_out)# make neural network come into effectfnn.sortModules()# definite the dataset as two input , one outputDS = SupervisedDataSet(2,1)# add data element to the datasetfor i in np.arange(199):    DS.addSample([u[i],y[i]],[y[i+1]])# you can get your input/output this wayX = DS['input']Y = DS['target']# split the dataset into train dataset and test datasetdataTrain, dataTest = DS.splitWithProportion(0.8)xTrain, yTrain = dataTrain['input'],dataTrain['target']xTest, yTest = dataTest['input'], dataTest['target']# train the NN# we use BP Algorithm# verbose = True means print th total errortrainer = BackpropTrainer(fnn, dataTrain, verbose=True,learningrate=0.01)# set the epoch times to make the NN  fittrainer.trainUntilConvergence(maxEpochs=1000)# prediction = fnn.activate(xTest[1])# print("the prediction number is :",prediction," the real number is:  ",yTest[1])predict_resutl=[]for i in np.arange(len(xTest)):    predict_resutl.append(fnn.activate(xTest[i])[0])print(predict_resutl)plt.figure()plt.plot(np.arange(0,len(xTest)), predict_resutl, 'ro--', label='predict number')plt.plot(np.arange(0,len(xTest)), yTest, 'ko-', label='true number')plt.legend()plt.xlabel("x")plt.ylabel("y")plt.show()for mod in fnn.modules:  print ("Module:", mod.name)  if mod.paramdim > 0:    print ("--parameters:", mod.params)  for conn in fnn.connections[mod]:    print ("-connection to", conn.outmod.name)    if conn.paramdim > 0:       print ("- parameters", conn.params)  if hasattr(fnn, "recurrentConns"):    print ("Recurrent connections")    for conn in fnn.recurrentConns:       print ("-", conn.inmod.name, " to", conn.outmod.name)       if conn.paramdim > 0:          print ("- parameters", conn.params)

文章引用：
[1]用Pybrain庫進行神經網路擬合