這次作業，我也是照著別人看的，但是最后我發現會報錯，而且結果明顯不合理，找了好長，還會報錯

<ipython>:5: RuntimeWarning: invalid value encountered in log cost = (-1/m) * np.sum(np.log(A2)* Y + (1 - Y) * np.log(1 - A2)) <ipython>:5: RuntimeWarning: divide by zero encountered in log cost = (-1/m) * np.sum(np.log(A2)* Y + (1 - Y) * np.log(1 - A2))

其實原因就在于構建網絡的時候，第二個應該是sigmoid函數，博主寫成了tanh函數，導致計算成本為而且準確的比較低

主函數

#tetsCases提供一些函數來評估函數的正確性 #planar_utils提供了各種的功能 import numpy as np import matplotlib.pyplot as plt from testCases import * import sklearn import sklearn.datasets import sklearn.linear_model from planar_utils import plot_decision_boundary,sigmoid,load_planar_dataset,load_extra_datasetsnp.random.seed(1)X,Y=load_planar_dataset()shape_X=X.shape#[2,400] shape_Y=Y.shape#[1,400] m=Y.shape[1]#400'''' ##sklearn內置函數，可以簡單的進行邏輯回歸處理 ##內置函數不能畫圖，懶得解決了，不管怎么樣我們得到線性回歸的正確率不好 clf=sklearn.linear_model.LogisticRegressionCV() clf.fit(X.T,Y.T) LR_predictions=clf.predict(X.T) print ("邏輯回歸的準確性： %d " % float((np.dot(Y, LR_predictions) +np.dot(1 - Y,1 - LR_predictions)) / float(Y.size) * 100) +"% " + "(正確標記的數據點所占的百分比)") '''#定義神經網絡結構 def layer_sizes(X,Y):n_x=X.shape[0]#輸入層數量n_h=4#隱藏層數量n_y=Y.shape[0]#輸出層數量return (n_x,n_h,n_y)#初始化模型的參數 def initialize_parameters(n_x,n_h,n_y):np.random.seed(2)##保證你隨機輸入的數據和他們的一樣W1=np.random.randn(n_h,n_x)*0.01b1=np.zeros(shape=(n_h,1))W2=np.random.randn(n_y,n_h)*0.01b2=np.zeros(shape=(n_y,1))assert (W1.shape==(n_h,n_x))assert (b1.shape==(n_h,1))assert (W2.shape==(n_y,n_h))assert (b2.shape==(n_y,1))parameters={"W1":W1,"W2":W2,"b1":b1,"b2":b2}return parametersdef forward_propagation(X,parameters):W1=parameters["W1"]W2=parameters["W2"]b1=parameters["b1"]b2=parameters["b2"]##向前傳播Z1=np.dot(W1,X)+b1A1=np.tanh(Z1)Z2=np.dot(W2,A1)+b2##這里應該使用sigmoid函數，不然最后的成本為NaN，而且學習成本特別高，準確率也不太行A2=sigmoid(Z2)assert (A2.shape==(1,X.shape[1]))cache={"Z1":Z1,"A1":A1,"Z2":Z2,"A2":A2}return (A2,cache)##計算交叉熵損失 def compute_cost(A2,Y,parameters):m=Y.shape[1]W1=parameters["W1"]W2=parameters["W2"]logprobs=logprobs=np.multiply(np.log(A2),Y)+np.multiply((1-Y),np.log(1-A2))cost=-np.sum(logprobs)/mcost=float(np.squeeze(cost))assert (isinstance(cost,float))##isinstance判斷兩種類型是否想等、return costdef backward_propagation(parameters,cache,X,Y):m=X.shape[1]W1=parameters["W1"]W2=parameters["W2"]A1=cache["A1"]A2=cache["A2"]dZ2=A2-YdW2=(1/m)*np.dot(dZ2,A1.T)db2=(1/m)*np.sum(dZ2,axis=1,keepdims=True)dZ1=np.multiply(np.dot(W2.T,dZ2),1-np.power(A1,2))dW1=(1/m)*np.dot(dZ1,X.T)db1=(1/m)*np.sum(dZ1,axis=1,keepdims=True)grads={"dW1":dW1,"db1":db1,"dW2":dW2,"db2":db2}return grads##更新參數 ##parameters為w,b,,grads為dw，db def update_parameters(parameters,grads,learning_rates=1.2):W1,W2=parameters["W1"],parameters["W2"]b1,b2=parameters["b1"],parameters["b2"]dW1,dW2=grads["dW1"],grads["dW2"]db1,db2=grads["db1"],grads["db2"]W1=W1-learning_rates*dW1W2=W2-learning_rates*dW2b1=b1-learning_rates*db1b2=b2-learning_rates*db2parameters={"W1":W1,"b1":b1,"W2":W2,"b2":b2}return parameters##然后我們做一個main函數 def nn_model(X,Y,n_h,num_iterations,print_cost=False):np.random.seed(3)##該函數返回n_x,n_h,n_yn_x=layer_sizes(X,Y)[0]n_y=layer_sizes(X,Y)[2]parameters=initialize_parameters(n_x,n_h,n_y)W1=parameters["W1"]b1=parameters["b1"]W2=parameters["W2"]b2=parameters["b2"]for i in range(num_iterations):A2,cache=forward_propagation(X,parameters)cost=compute_cost(A2,Y,parameters)grads=backward_propagation(parameters,cache,X,Y)parameters=update_parameters(parameters,grads,learning_rates=0.4)if print_cost:if i%1000==0:print("第",i,"次循環，成本為："+str(cost))return parameters##預測結果 def predict (parameters,X):A2,cache=forward_propagation(X,parameters)predictions=np.round(A2)##去整return predictionsparameters = nn_model(X, Y, n_h = 4, num_iterations=10000, print_cost=True)#繪制邊界 plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y) plt.title("Decision Boundary for hidden layer size " + str(4)) plt.show()predictions = predict(parameters, X) print ('準確率: %d' % float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size) * 100) + '%')

planar_utils.py函數 import matplotlib.pyplot as plt import numpy as np import sklearn import sklearn.datasets import sklearn.linear_model#繪制決策邊界 def plot_decision_boundary(model, X, y):# Set min and max values and give it some paddingx_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1h = 0.01# Generate a grid of points with distance h between themxx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))# Predict the function value for the whole gridZ = model(np.c_[xx.ravel(), yy.ravel()])Z = Z.reshape(xx.shape)# Plot the contour and training examplesplt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)plt.ylabel('x2')plt.xlabel('x1')plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral)def sigmoid(x):s = 1/(1+np.exp(-x))return s#加載平面數據集 def load_planar_dataset():np.random.seed(1)m = 400 # number of examples例子的數量N = int(m/2) # number of points per class，把數據分為兩類，每一類的點數D = 2 # dimensionality，維度X = np.zeros((m,D)) # data matrix where each row is a single example，行，X應該需要取轉置Y = np.zeros((m,1), dtype='uint8') # labels vector (0 for red, 1 for blue)a = 4 # maximum ray of the flowerfor j in range(2):ix = range(N*j,N*(j+1))t = np.linspace(j*3.12,(j+1)*3.12,N) + np.random.randn(N)*0.2 # thetar = a*np.sin(4*t) + np.random.randn(N)*0.2 # radiusX[ix] = np.c_[r*np.sin(t), r*np.cos(t)]Y[ix] = jX = X.TY = Y.Treturn X, Ydef load_extra_datasets():N = 200noisy_circles = sklearn.datasets.make_circles(n_samples=N, factor=.5, noise=.3)noisy_moons = sklearn.datasets.make_moons(n_samples=N, noise=.2)blobs = sklearn.datasets.make_blobs(n_samples=N, random_state=5, n_features=2, centers=6)gaussian_quantiles = sklearn.datasets.make_gaussian_quantiles(mean=None, cov=0.5, n_samples=N, n_features=2, n_classes=2, shuffle=True, random_state=None)no_structure = np.random.rand(N, 2), np.random.rand(N, 2)return noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure testCases.py函數 #-*- coding: UTF-8 -*- """ # WANGZHE12 """ import numpy as npdef layer_sizes_test_case():np.random.seed(1)X_assess = np.random.randn(5, 3)Y_assess = np.random.randn(2, 3)return X_assess, Y_assessdef initialize_parameters_test_case():n_x, n_h, n_y = 2, 4, 1return n_x, n_h, n_ydef forward_propagation_test_case():np.random.seed(1)X_assess = np.random.randn(2, 3)parameters = {'W1': np.array([[-0.00416758, -0.00056267],[-0.02136196, 0.01640271],[-0.01793436, -0.00841747],[ 0.00502881, -0.01245288]]),'W2': np.array([[-0.01057952, -0.00909008, 0.00551454, 0.02292208]]),'b1': np.array([[ 0.],[ 0.],[ 0.],[ 0.]]),'b2': np.array([[ 0.]])}return X_assess, parametersdef compute_cost_test_case():np.random.seed(1)Y_assess = np.random.randn(1, 3)parameters = {'W1': np.array([[-0.00416758, -0.00056267],[-0.02136196, 0.01640271],[-0.01793436, -0.00841747],[ 0.00502881, -0.01245288]]),'W2': np.array([[-0.01057952, -0.00909008, 0.00551454, 0.02292208]]),'b1': np.array([[ 0.],[ 0.],[ 0.],[ 0.]]),'b2': np.array([[ 0.]])}a2 = (np.array([[ 0.5002307 , 0.49985831, 0.50023963]]))return a2, Y_assess, parametersdef backward_propagation_test_case():np.random.seed(1)X_assess = np.random.randn(2, 3)Y_assess = np.random.randn(1, 3)parameters = {'W1': np.array([[-0.00416758, -0.00056267],[-0.02136196, 0.01640271],[-0.01793436, -0.00841747],[ 0.00502881, -0.01245288]]),'W2': np.array([[-0.01057952, -0.00909008, 0.00551454, 0.02292208]]),'b1': np.array([[ 0.],[ 0.],[ 0.],[ 0.]]),'b2': np.array([[ 0.]])}cache = {'A1': np.array([[-0.00616578, 0.0020626 , 0.00349619],[-0.05225116, 0.02725659, -0.02646251],[-0.02009721, 0.0036869 , 0.02883756],[ 0.02152675, -0.01385234, 0.02599885]]),'A2': np.array([[ 0.5002307 , 0.49985831, 0.50023963]]),'Z1': np.array([[-0.00616586, 0.0020626 , 0.0034962 ],[-0.05229879, 0.02726335, -0.02646869],[-0.02009991, 0.00368692, 0.02884556],[ 0.02153007, -0.01385322, 0.02600471]]),'Z2': np.array([[ 0.00092281, -0.00056678, 0.00095853]])}return parameters, cache, X_assess, Y_assessdef update_parameters_test_case():parameters = {'W1': np.array([[-0.00615039, 0.0169021 ],[-0.02311792, 0.03137121],[-0.0169217 , -0.01752545],[ 0.00935436, -0.05018221]]),'W2': np.array([[-0.0104319 , -0.04019007, 0.01607211, 0.04440255]]),'b1': np.array([[ -8.97523455e-07],[ 8.15562092e-06],[ 6.04810633e-07],[ -2.54560700e-06]]),'b2': np.array([[ 9.14954378e-05]])}grads = {'dW1': np.array([[ 0.00023322, -0.00205423],[ 0.00082222, -0.00700776],[-0.00031831, 0.0028636 ],[-0.00092857, 0.00809933]]),'dW2': np.array([[ -1.75740039e-05, 3.70231337e-03, -1.25683095e-03,-2.55715317e-03]]),'db1': np.array([[ 1.05570087e-07],[ -3.81814487e-06],[ -1.90155145e-07],[ 5.46467802e-07]]),'db2': np.array([[ -1.08923140e-05]])}return parameters, gradsdef nn_model_test_case():np.random.seed(1)X_assess = np.random.randn(2, 3)Y_assess = np.random.randn(1, 3)return X_assess, Y_assessdef predict_test_case():np.random.seed(1)X_assess = np.random.randn(2, 3)parameters = {'W1': np.array([[-0.00615039, 0.0169021 ],[-0.02311792, 0.03137121],[-0.0169217 , -0.01752545],[ 0.00935436, -0.05018221]]),'W2': np.array([[-0.0104319 , -0.04019007, 0.01607211, 0.04440255]]),'b1': np.array([[ -8.97523455e-07],[ 8.15562092e-06],[ 6.04810633e-07],[ -2.54560700e-06]]),'b2': np.array([[ 9.14954378e-05]])}return parameters, X_assess

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