Example of a Python neural network

#http://python.jobbole.com/82758/#import NumPy as NP#### sigmoid function#def nonlin (x, deriv=false):#if (Deriv = = True):#return x * (1-x)#return 1/(1 + np.exp (-X))#### Input DataSet#X = Np.array ([[0, 0, 1],#[0, 1, 1],#[1, 0, 1],#[1, 1, 1]])### Output DataSet#y = np.array ([[0, 0, 1, 1]]). T### Seed Random numbers to make calculation## deterministic (just a good practice)#np.random.seed (1)### Initialize weights randomly with mean 0#syn0 = 2 * Np.random.random ((3, 1))-1##For ITER in range (10000):## Forward Propagation#l0 = X#L1 = Nonlin (Np.dot (L0, syn0))### How much did we miss?#l1_error = Y-l1### Multiply how much we missed by the## slope of the sigmoid at the values in L1#L1_delta = l1_error * Nonlin (L1, True)### Update Weights#Syn0 + = Np.dot (l0. T, L1_delta) #反向传播, w = w + f (y) * L1_delta#print ("Output after Training:")#print (L1)ImportNumPy as NPdefNonlin (x, deriv=False):if(Deriv = =True):returnX * (1-x)return1/(1 + np.exp (-x)) X= Np.array ([[0, 0, 1], [0,1, 1],              [1, 0, 1],              [1, 1, 1]]) y=Np.array ([[0], [1],              [1], [0]]) np.random.seed (1)#randomly initialize our weights with mean 0Syn0 = 2 * Np.random.random ((3, 4))-1syn1= 2 * Np.random.random ((4, 1))-1 forJinchRange (60000):    #Feed forward through layers 0, 1, and 2L0 =X L1=Nonlin (Np.dot (L0, syn0)) L2=Nonlin (Np.dot (L1, syn1))#How much did we miss the target value?L2_error = y-L2if(j% 10000) = =0:Print("Error:"+Str (Np.mean (Np.abs (l2_error) ))#direction is the target value?    #were we really sure? If so, don ' t change too much.L2_delta = L2_error * Nonlin (L2, deriv=True)#How much do each L1 value contribute to the L2 error (according to the weights)?L1_error =L2_delta.dot (syn1. T)#direction is the target L1?    #were we really sure? If so, don ' t change too much.L1_delta = L1_error * Nonlin (L1, deriv=True) syn1+=L1. T.dot (L2_delta) syn0+=L0. T.dot (L1_delta)Print("Output after Training:")Print(L2)

#1.#on the nonlinear transformation equation (non-linear#Transformation#function)##sigmoid function (S#curve) used as a activation#function:##1.1#Hyperbolic function (tanh)##1.2#logical functions (Logistic#function)###2.#implementation of a simple neural network algorithmImportNumPy as NPdeftanh (x):returnNp.tanh (x)defTanh_deriv (x):return1.0-np.tanh (x) *Np.tanh (x)defLogistic (x):return1/(1 + np.exp (-x))deflogistic_derivative (x):returnLogistic (x) * (1-Logistic (x))classneuralnetwork:def __init__(self, layers, activation='Tanh'):        """:p Aram Layers:a list containing the number of units in each layer. Should is at least the values:p Aram activation:the activation function to be used. Can be "logistic" or "Tanh""""        ifActivation = ='Logistic': Self.activation=Logistic Self.activation_deriv=logistic_derivativeelifActivation = ='Tanh': Self.activation=Tanh Self.activation_deriv=Tanh_deriv self.weights= []         forIinchRange (1, Len (layers)-1):            #Layers[i-1] The number of nodes for the previous input layer is +1 plus a bias point,            #Layers[i] The number of output nodes for the current layer is +1 plus a bias point,Self.weights.append ((2 * np.random.random ((layers[i-1] + 1, layers[i] + 1))-1) * 0.25) Self.weights.append (2 * Np.random.random ((Layers[i] + 1, layers[i + 1]))-1) * 0.25)    defFit (self, X, y, learning_rate=0.2, epochs=10000): X= np.atleast_2d (X)#determine if the input training set is two-dimensionaltemp = Np.ones ([x.shape[0], x.shape[1] + 1]) temp[:, 0:-1] = X#adding the bias unit to the input layerX =Temp y=Np.array (y) forKinchRange (epochs): I=Np.random.randint (x.shape[0]) a=[X[i]]#Len (self.weights) is the number of output nodes, each output node corresponds to a set of weights is a row in weight self.weights[l]             forLinchRange (len (self.weights)):#going forward network, for each layer                #Computer The node value for each layer (o_i) using activation function                #A[l] is the characteristic value of the input data                Print(A[l])Print(Self.weights[l]) a.append (Self.activation (Np.dot (A[l], self.weights[l] )) error= Y[i]-a[-1]#computer The error at the top layerDeltas = [ERROR * SELF.ACTIVATION_DERIV (a[-1])]#for output layer, ERR calculation (delta is updated error)            #Staring backprobagation             forLinchRange (Len (a)-2, 0,-1):#we need to begin at the second-last layer                #Compute The updated error (I,e, deltas) for each node going from top layer to input layerDeltas.append (Deltas[-1].dot (self.weights[l). T) *Self.activation_deriv (A[l]) deltas.reverse () forIinchRange (len (self.weights)): Layer=np.atleast_2d (a[i]) Delta=np.atleast_2d (Deltas[i]) self.weights[i]+ = Learning_rate *layer. T.dot (Delta)defPredict (self, x): x=np.array (x) Temp= Np.ones (X.shape[0] + 1) Temp[0:-1] =x a=Temp forLinchRange (0, Len (self.weights)): a=self.activation (Np.dot (A, self.weights[l]))returnaPrint("Simple Nonlinear relational data set test (XOR)")#1. Simple nonlinear relational data set test (XOR):##x:y#0 0 0#0 1 1#1 0 1#1 1 0#From neuralnetwork import neuralnetworkImportNumPy as Npnn= Neuralnetwork ([2,2,1],'Tanh') X= Np.array ([[0, 0], [0, 1], [1, 0], [1, 1]]) y= Np.array ([0, 1, 1, 0]) Nn.fit (X, y) forIinch[[0, 0], [0, 1], [1, 0], []]:    Print(i, nn.predict (i))Print("\ n-Handwritten digit recognition")#2. Handwritten digit recognition:##each picture 8x8#identification number: 0,1,2,3,4,5,6,7,8,9ImportNumPy as NP fromSklearn.datasetsImportload_digits fromSklearn.metricsImportConfusion_matrix, Classification_report fromSklearn.preprocessingImportLabelbinarizer#From neuralnetwork import neuralnetwork fromSklearn.cross_validationImporttrain_test_splitdigits=load_digits () X=Digits.datay=Digits.targetx-= X.min ()#normalize the values to bring them into the range 0-1X/=X.max () nn= Neuralnetwork ([64,100,10],'Logistic') X_train, X_test, Y_train, Y_test=Train_test_split (X, y) labels_train=Labelbinarizer (). Fit_transform (y_train) labels_test=Labelbinarizer (). Fit_transform (y_test)Print("Start Fitting") Nn.fit (X_train,labels_train,epochs=3000) Predictions= [] forIinchRange (x_test.shape[0]): o=nn.predict (X_test[i]) predictions.append (Np.argmax (o) )Print(Confusion_matrix (y_test,predictions))Print(Classification_report (y_test,predictions))

Example of a Python neural network