Python code cs231n Softmax linear classifier, non-linear classifier comparison example (with Python drawing display results)

1 #examples of linear and nonlinear classifiers in cs231n (Softmax)2 #Note that the calculation of the inverse propagation3 4 #-*-coding:utf-8-*-5 ImportNumPy as NP6 ImportMatplotlib.pyplot as Plt7N = 100#Number of points per class8D = 2#dimensionality9K = 3#Number of classesTenX = Np.zeros ((n*k,d))#data Matrix (each row = Single example) Oney = Np.zeros (n*k, dtype='uint8')#Class Labels A  forJinchxrange (K): -IX = Range (n*j,n* (j+1)) -R = Np.linspace (0.0,1,n)#radius thet = Np.linspace (j*4, (j+1) *4,n) + NP.RANDOM.RANDN (N) *0.2#Theta -X[ix] = Np.c_[r*np.sin (t), r*Np.cos (t)] -Y[ix] =J - #lets visualize the data: +Plt.xlim ([-1, 1]) -Plt.ylim ([-1, 1]) +Plt.scatter (x[:, 0], x[:, 1], c=y, s=40, cmap=plt.cm.Spectral) A plt.show () at  -  -  - #Initialize parameters randomly - #linear classifier -W = 0.01 *Np.random.randn (d,k) inb = Np.zeros ((1, K)) -  to #some hyperparameters +Step_size = 1e-0 -Reg = 1e-3#regularization Strength the  * #gradient descent Loop $Num_examples =X.shape[0]Panax Notoginseng  forIinchXrange (200): -    the   #evaluate class scores, [N x K] +Scores = Np.dot (X, W) +b A    the   #compute the class probabilities +Exp_scores =Np.exp (scores) -probs = Exp_scores/np.sum (Exp_scores, Axis=1, Keepdims=true)#[N x K] $    $   #compute the Loss:average cross-entropy loss and regularization -Corect_logprobs =-Np.log (Probs[range (num_examples), y]) -Data_loss = Np.sum (corect_logprobs)/Num_examples theReg_loss = 0.5*reg*np.sum (w*W) -Loss = Data_loss +Reg_lossWuyi   ifI% 10 = =0: the     Print "Iteration%d:loss%f"%(i, loss) -    Wu   #compute the gradient on scores -Dscores =probs AboutDscores[range (Num_examples), y]-= 1 $Dscores/=Num_examples -    -   #backpropate the gradient to the parameters (W,b) -DW =Np.dot (x.t, Dscores) Adb = Np.sum (Dscores, axis=0, keepdims=True) +    theDW + = Reg*w#regularization Gradient -    $   #perform a parameter update theW + =-step_size *DW theb + =-step_size *DB the    the   #evaluate training set accuracy -Scores = Np.dot (X, W) +b inPredicted_class = Np.argmax (scores, Axis=1) the Print 'Training accuracy:%.2f'% (Np.mean (Predicted_class = =y)) the  About #plot the resulting classifier theH = 0.02 theX_min, X_max = x[:, 0].min ()-1, x[:, 0].max () + 1 theY_min, Y_max = x[:, 1].min ()-1, x[:, 1].max () + 1 +xx, yy =Np.meshgrid (Np.arange (X_min, X_max, h), - Np.arange (Y_min, Y_max, h)) theZ = Np.dot (Np.c_[xx.ravel (), Yy.ravel ()], W) +bBayiz = Np.argmax (z, Axis=1) theZ =Z.reshape (Xx.shape) theFig =plt.figure () -Plt.contourf (xx, yy, Z, Cmap=plt.cm.spectral, alpha=0.8) -Plt.scatter (x[:, 0], x[:, 1], c=y, s=40, cmap=plt.cm.Spectral) the Plt.xlim (Xx.min (), Xx.max ()) the Plt.ylim (Yy.min (), Yy.max ()) the  the ## Initialize parameters randomly - #non-linear classifier with a hidden layer using Relu theH = 100#size of hidden layer theW = 0.01 *Np.random.randn (d,h) theb = Np.zeros ((1, h))94W2 = 0.01 *Np.random.randn (h,k) theB2 = Np.zeros ((1, K)) the  the #some hyperparameters98Step_size = 1e-0 AboutReg = 1e-3#regularization Strength - 101 #gradient descent Loop102Num_examples =X.shape[0]103  forIinchXrange (10000):104    the   #evaluate class scores, [N x K]106Hidden_layer = Np.maximum (0, Np.dot (X, W) + b)#Note, ReLU activation107Scores = Np.dot (Hidden_layer, W2) +B2108   109   #compute the class probabilities theExp_scores =Np.exp (scores)111probs = Exp_scores/np.sum (Exp_scores, Axis=1, Keepdims=true)#[N x K] the   113   #compute the Loss:average cross-entropy loss and regularization theCorect_logprobs =-Np.log (Probs[range (num_examples), y]) theData_loss = Np.sum (corect_logprobs)/Num_examples theReg_loss = 0.5*reg*np.sum (w*w) + 0.5*reg*np.sum (w2*W2)117Loss = Data_loss +Reg_loss118   ifI% 1000 = =0:119     Print "Iteration%d:loss%f"%(i, loss) -   121   #compute the gradient on scores122Dscores =probs123Dscores[range (Num_examples), y]-= 1124Dscores/=Num_examples the   126   #backpropate The gradient to the parameters127   #First backprop into parameters W2 and B2 -DW2 =Np.dot (Hidden_layer. T, Dscores)129DB2 = Np.sum (Dscores, axis=0, keepdims=True) the   #next backprop into hidden layer131Dhidden =Np.dot (Dscores, w2.t) the   #Backprop the ReLU non-linearity133Dhidden[hidden_layer <= 0] =0134   #finally into W,b135DW =Np.dot (x.t, Dhidden)136db = Np.sum (Dhidden, axis=0, keepdims=True)137   138   #Add regularization gradient contribution139DW2 + = Reg *W2 $DW + = Reg *W141   142   #perform a parameter update143W + =-step_size *DW144b + =-step_size *DB145W2 + =-step_size *dW2146B2 + =-step_size *DB2147 #evaluate training set accuracy148Hidden_layer = Np.maximum (0, Np.dot (X, W) +b)149Scores = Np.dot (Hidden_layer, W2) +B2 MaxPredicted_class = Np.argmax (scores, Axis=1)151 Print 'Training accuracy:%.2f'% (Np.mean (Predicted_class = =y)) the #plot the resulting classifier153H = 0.02154X_min, X_max = x[:, 0].min ()-1, x[:, 0].max () + 1155Y_min, Y_max = x[:, 1].min ()-1, x[:, 1].max () + 1156xx, yy =Np.meshgrid (Np.arange (X_min, X_max, h),157 Np.arange (Y_min, Y_max, h))158Z = Np.dot (np.maximum (0, Np.dot (Np.c_[xx.ravel (), Yy.ravel ()], W) + b), W2) +B2159z = Np.argmax (z, Axis=1) theZ =Z.reshape (Xx.shape)161Fig =plt.figure ()162Plt.contourf (xx, yy, Z, Cmap=plt.cm.spectral, alpha=0.8)163Plt.scatter (x[:, 0], x[:, 1], c=y, s=40, cmap=plt.cm.Spectral)164 Plt.xlim (Xx.min (), Xx.max ())165Plt.ylim (Yy.min (), Yy.max ())

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Python code cs231n softmax linear classifier, non-linear classifier comparison example (with Python drawing display results)