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import numpy as np import matplotlib.pyplot as plt import sklearn import sklearn.datasets import sklearn.linear_model from planar_utils import plot_decision_boundary, sigmoid , load_planar_dataset %matplotlib inline np.random.seed(1)
X, Y = load_planar_dataset()#加载数据
plt.scatter(X[0, :], X[1, :], c = np.squeeze(Y), s = 40, cmap=plt.cm.Spectral)
[外链图片转存失败(img-BZ767nBS-1565067964715)()]
shape_X = X.shape shape_Y = Y.shape m = Y.shape[1] print(shape_X) print(shape_Y) print(m)
(2, 400) (1, 400) 400
def layer_size(X, Y): n_x = X.shape[0] n_h = 4 n_y = Y.shape[0] return (n_x, n_h, n_y)
def initialize_parametiers(n_x, n_h, n_y): np.random.seed(2) W1 = np.random.randn(n_h, n_x) * 0.01 b1 = np.zeros(shape=(n_h, 1)) W2 = np.random.randn(n_y, n_h) * 0.01 b2 = 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, "b1" : b1, "W2" : W2, "b2" : b2 } return parameters def forward_propagation(X, parameters): W1 = parameters["W1"] b1 = parameters["b1"] W2 = parameters["W2"] b2 = parameters["b2"] Z1 = np.dot(W1, X) + b1 A1 = np.tanh(Z1) Z2 = np.dot(W2, A1) + b2 A2 = sigmoid(Z2) assert(A2.shape == (1, X.shape[1])) cache = { "Z1" : Z1, "A1" : A1, "Z2" : Z2, "A2" : A2 } return (A2, cache) def compute_cost(A2, Y, parameters): m = Y.shape[1] W1 = parameters["W1"] W2 = parameters["W2"] logprobs = np.multiply(np.log(A2), Y) + np.multiply( np.log(1 - A2), (1 - Y)) cost = -np.sum(logprobs) / m cost = float(np.squeeze(cost)) assert(isinstance(cost, float)) return cost
def backward_propagation(parameters, chche, X, Y): m = X.shape[1] W1 = parameters["W1"] W2 = parameters["W2"] A1 = chche["A1"] A2 = chche["A2"] dZ2 = A2 - Y dW2 = (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 def update_parameters(parameters, grads, learning_rate=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_rate * dW1 b1 = b1 - learning_rate * db1 W2 = W2 - learning_rate * dW2 b2 = b2 - learning_rate * db2 parameters = { "W1" : W1, "b1" : b1, "W2" : W2, "b2" : b2 } return parameters def nn_model(X, Y, n_h, num_iterations, learning_rate=0.5, print_cost=False): np.random.seed(3) n_x, n_y = layer_size(X, Y)[0], layer_size(X, Y)[2] parameters = initialize_parametiers(n_x, n_h, n_y) W1, b1 = parameters["W1"], parameters["b1"] W2, b2 = parameters["W2"], 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_rate) if print_cost: if i % 1000 == 0: print("第%d次循环， 成本为：%s" % (i, str(cost))) return parameters def predict(parameters, X): A2, cache = forward_propagation(X, parameters) predictions = np.round(A2) return predictions
parameters = nn_model(X, Y, n_h = 4, num_iterations=10000, print_cost=True) #plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y) plot_decision_boundary(lambda x: predict(parameters, x.T), X, np.squeeze(Y)) plt.title("Decison Boundary for hidden layer size" + str(4)) predictions = predict(parameters, X) print ('准确率: %d' % float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size) * 100) + '%') 第0次循环， 成本为：0.6930480201239823 第1000次循环， 成本为：0.3098018601352803 第2000次循环， 成本为：0.2924326333792646 第3000次循环， 成本为：0.2833492852647412 第4000次循环， 成本为：0.27678077562979253 第5000次循环， 成本为：0.26347155088593144 第6000次循环， 成本为：0.24204413129940763 第7000次循环， 成本为：0.23552486626608762 第8000次循环， 成本为：0.23140964509854278 第9000次循环， 成本为：0.22846408048352365 准确率: 90%
[外链图片转存失败(img-yCZ2kkTe-1565067964716)()]
plt.figure(figsize=(16, 32)) hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 50] #隐藏层数量 for i, n_h in enumerate(hidden_layer_sizes): plt.subplot(5, 2, i + 1) plt.title('Hidden Layer of size %d' % n_h) parameters = nn_model(X, Y, n_h, num_iterations=5000) plot_decision_boundary(lambda x: predict(parameters, x.T), X, np.squeeze(Y)) predictions = predict(parameters, X) accuracy = float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size) * 100) print ("隐藏层的节点数量： {} ，准确率: {} %".format(n_h, accuracy)) 隐藏层的节点数量： 1 ，准确率: 67.25 % 隐藏层的节点数量： 2 ，准确率: 66.5 % 隐藏层的节点数量： 3 ，准确率: 89.25 % 隐藏层的节点数量： 4 ，准确率: 90.0 % 隐藏层的节点数量： 5 ，准确率: 89.75 % 隐藏层的节点数量： 20 ，准确率: 90.0 % 隐藏层的节点数量： 50 ，准确率: 89.75 %
[外链图片转存失败(img-SpoxUCuu-1565067964717)()]
import matplotlib.pyplot as plt import numpy as np import sklearn import sklearn.datasets import sklearn.linear_model def plot_decision_boundary(model, X, y): # Set min and max values and give it some padding x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1 y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1 h = 0.01 # Generate a grid of points with distance h between them xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) # Predict the function value for the whole grid Z = model(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) # Plot the contour and training examples plt.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 def load_planar_dataset(): np.random.seed(1) m = 400 # number of examples N = int(m/2) # number of points per class D = 2 # dimensionality X = np.zeros((m,D)) # data matrix where each row is a single example Y = np.zeros((m,1), dtype='uint8') # labels vector (0 for red, 1 for blue) a = 4 # maximum ray of the flower for 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 # theta r = a*np.sin(4*t) + np.random.randn(N)*0.2 # radius X[ix] = np.c_[r*np.sin(t), r*np.cos(t)] Y[ix] = j X = X.T Y = Y.T return X, Y def load_extra_datasets(): N = 200 noisy_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 请勿留言，本博文只做分享，由要咨询博主问题的请访问博主
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