吴恩达神经网络与深度学习——神经网络基础习题2

神经网络思维的逻辑回归判断图像上是否有猫图像预处理问题叙述包可视化数据集尺寸reshape标准化数据集 总结 学习算法的一般结构构建我们算法的各个部分sigmoid函数初始化参数前向传播和反向传播梯度下降法预测 将所有函数合并到模型中例子迭代次数对代价函数的影响测试自己的图像

神经网络思维的逻辑回归

1.初始化参数 2.计算代价函数及其导数 3.使用梯度下降

判断图像上是否有猫

图像预处理

问题叙述

你得到了一个数据集(“data.h5”)，包含: -标记为cat ( y = 1 )或非cat ( y = 0 )的m个训练集 -标记为cat或非cat的m个测试集 -图像大小为(num_px,num_px,3)，其中3代表3个通道( RGB )。 你将建立一个简单的图像识别算法，可以正确地将图片分类为猫或非猫。

包

numpy h5py matplotlib PIL scipy # %load lr_utils.py import numpy as np import h5py def load_dataset(): train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r") train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r") test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels classes = np.array(test_dataset["list_classes"][:]) # the list of classes train_set_y_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0])) test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0])) return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes

可视化

index = 25 example = train_set_x_orig[index] plt.imshow(train_set_x_orig[index]) print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode("utf-8") + "' picture.")

数据集尺寸

### START CODE HERE ### (≈ 3 lines of code) m_train = train_set_x_orig.shape[0] m_test = test_set_x_orig.shape[0] num_px = train_set_x_orig.shape[2] ### END CODE HERE ### print("m_train:"+str(m_train)) print("m_test:"+str(m_test)) print("num_px:"+str(num_px))

reshape

# Reshape the training and test examples ### START CODE HERE ### (≈ 2 lines of code) train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0],-1).T test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0],-1).T ### END CODE HERE ### print ("train_set_x_flatten shape: " + str(train_set_x_flatten.shape)) print ("train_set_y shape: " + str(train_set_y.shape)) print ("test_set_x_flatten shape: " + str(test_set_x_flatten.shape)) print ("test_set_y shape: " + str(test_set_y.shape)) print ("sanity check after reshaping: " + str(train_set_x_flatten[0:5,0]))

标准化数据集

train_set_x = train_set_x_flatten/255. test_set_x = test_set_x_flatten/255.

总结

图像预处理步骤： 1.找出训练集及测试集个数及图像尺寸( m _ train，m _ test，num _ px，...) ) 2.resgape数据集，使每个图像成为一个大小为( num _ px * num _ px * 3，1 )的向量 3.“标准化”数据

学习算法的一般结构

-初始化模型的参数 -通过最小化成本来学习模型的参数 -使用学习到的参数进行预测(在测试集上) -分析结果并得出结论

构建我们算法的各个部分

sigmoid函数

# GRADED FUNCTION: sigmoid def sigmoid(z): """ Compute the sigmoid of z Arguments: z -- A scalar or numpy array of any size. Return: s -- sigmoid(z) """ ### START CODE HERE ### (≈ 1 line of code) s = 1 / ( 1 + np.exp(-z)) ### END CODE HERE ### return s

初始化参数

def initialize_with_zeros(dim): """ This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0. Argument: dim -- size of the w vector we want (or number of parameters in this case) Returns: w -- initialized vector of shape (dim, 1) b -- initialized scalar (corresponds to the bias) """ ### START CODE HERE ### (≈ 1 line of code) w = np.zeros(shape=(dim,1),dtype=np.float32) b = 0 ### END CODE HERE ### assert(w.shape == (dim, 1)) assert(isinstance(b, float) or isinstance(b, int)) return w, b dim = 2 w, b = initialize_with_zeros(dim) print ("w = " + str(w)) print ("b = " + str(b))

前向传播和反向传播

# GRADED FUNCTION: propagate def propagate(w, b, X, Y): """ Implement the cost function and its gradient for the propagation explained above Arguments: w -- weights, a numpy array of size (num_px * num_px * 3, 1) b -- bias, a scalar X -- data of size (num_px * num_px * 3, number of examples) Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples) Return: cost -- negative log-likelihood cost for logistic regression dw -- gradient of the loss with respect to w, thus same shape as w db -- gradient of the loss with respect to b, thus same shape as b Tips: - Write your code step by step for the propagation. np.log(), np.dot() """ m = X.shape[1] # FORWARD PROPAGATION (FROM X TO COST) ### START CODE HERE ### (≈ 2 lines of code) yhat = sigmoid(np.dot(w.T,X)+b) cost =-1/m*np.sum(Y*np.log(yhat)+(1-Y)*np.log(1-yhat),axis = 1) ### END CODE HERE ### # BACKWARD PROPAGATION (TO FIND GRAD) ### START CODE HERE ### (≈ 2 lines of code) dZ = yhat -Y dw = 1/m*np.dot(X,dZ.T) db = 1/m*np.sum(dZ,axis = 1 ,keepdims = True) ### END CODE HERE ### assert(dw.shape == w.shape) assert(db.dtype == float) cost = np.squeeze(cost) assert(cost.shape == ()) grads = {"dw": dw, "db": db} return grads, cost w, b, X, Y = np.array([[1],[2]]), 2, np.array([[1,2],[3,4]]), np.array([[1,0]]) grads, cost = propagate(w, b, X, Y) print ("dw = " + str(grads["dw"])) print ("db = " + str(grads["db"])) print ("cost = " + str(cost))

梯度下降法

# GRADED FUNCTION: optimize def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False): """ This function optimizes w and b by running a gradient descent algorithm Arguments: w -- weights, a numpy array of size (num_px * num_px * 3, 1) b -- bias, a scalar X -- data of shape (num_px * num_px * 3, number of examples) Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples) num_iterations -- number of iterations of the optimization loop learning_rate -- learning rate of the gradient descent update rule print_cost -- True to print the loss every 100 steps Returns: params -- dictionary containing the weights w and bias b grads -- dictionary containing the gradients of the weights and bias with respect to the cost function costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve. Tips: You basically need to write down two steps and iterate through them: 1) Calculate the cost and the gradient for the current parameters. Use propagate(). 2) Update the parameters using gradient descent rule for w and b. """ costs = [] for i in range(num_iterations): # Cost and gradient calculation (≈ 1-4 lines of code) ### START CODE HERE ### grads, cost = propagate(w=w, b=b, X=X, Y=Y) ### END CODE HERE ### # Retrieve derivatives from grads dw = grads["dw"] db = grads["db"] # update rule (≈ 2 lines of code) ### START CODE HERE ### w = w - learning_rate*dw b = b - learning_rate*db ### END CODE HERE ### # Record the costs if i % 100 == 0: costs.append(cost) # Print the cost every 100 training examples if print_cost and i % 100 == 0: print ("Cost after iteration %i: %f" %(i, cost)) params = {"w": w, "b": b} grads = {"dw": dw, "db": db} return params, grads, costs params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False) print ("w = " + str(params["w"])) print ("b = " + str(params["b"])) print ("dw = " + str(grads["dw"])) print ("db = " + str(grads["db"]))

预测

# GRADED FUNCTION: predict def predict(w, b, X): ''' Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b) Arguments: w -- weights, a numpy array of size (num_px * num_px * 3, 1) b -- bias, a scalar X -- data of size (num_px * num_px * 3, number of examples) Returns: Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X ''' m = X.shape[1] Y_prediction = np.zeros((1,m)) w = w.reshape(X.shape[0], 1) # Compute vector "A" predicting the probabilities of a cat being present in the picture ### START CODE HERE ### (≈ 1 line of code) A = sigmoid(np.dot(w.T,X)+b) ### END CODE HERE ### [print(x) for x in A] for i in range(A.shape[1]): # Convert probabilities A[0,i] to actual predictions p[0,i] ### START CODE HERE ### (≈ 4 lines of code) if A[0, i] >= 0.5: Y_prediction[0, i] = 1 else: Y_prediction[0, i] = 0 ### END CODE HERE ### assert(Y_prediction.shape == (1, m)) return Y_prediction print ("predictions = " + str(predict(w, b, X)))

将所有函数合并到模型中

# GRADED FUNCTION: model def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False): """ Builds the logistic regression model by calling the function you've implemented previously Arguments: X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train) Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train) X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test) Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test) num_iterations -- hyperparameter representing the number of iterations to optimize the parameters learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize() print_cost -- Set to true to print the cost every 100 iterations Returns: d -- dictionary containing information about the model. """ ### START CODE HERE ### # initialize parameters with zeros (≈ 1 line of code) w, b = initialize_with_zeros(X_train.shape[0]) # Gradient descent (≈ 1 line of code) parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost) # Retrieve parameters w and b from dictionary "parameters" w = parameters["w"] b = parameters["b"] # Predict test/train set examples (≈ 2 lines of code) Y_prediction_test = predict(w, b, X_test) Y_prediction_train = predict(w, b, X_train) ### END CODE HERE ### # Print train/test Errors print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100)) print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100)) d = {"costs": costs, "Y_prediction_test": Y_prediction_test, "Y_prediction_train" : Y_prediction_train, "w" : w, "b" : b, "learning_rate" : learning_rate, "num_iterations": num_iterations} return d d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)

例子

# Example of a picture that was wrongly classified. index = 1 plt.imshow(test_set_x[:,index].reshape((num_px, num_px, 3))) print ("y = " + str(test_set_y[0,index]) + ", you predicted that it is a \"" + classes[int(d["Y_prediction_test"][0,index])].decode("utf-8") + "\" picture.")

迭代次数对代价函数的影响

# Plot learning curve (with costs) costs = np.squeeze(d['costs']) plt.plot(costs) plt.ylabel('cost') plt.xlabel('iterations (per hundreds)') plt.title("Learning rate =" + str(d["learning_rate"])) plt.show()

测试自己的图像

## START CODE HERE ## (PUT YOUR IMAGE NAME) my_image = "my_image.jpg" # change this to the name of your image file ## END CODE HERE ## # We preprocess the image to fit your algorithm. fname = "images/" + my_image image = np.array(plt.imread(fname)) my_image = skimage.transform.resize(image, output_shape=(num_px,num_px)).reshape((1, num_px*num_px*3)).T my_predicted_image = predict(d["w"], d["b"], my_image) plt.imshow(image) print("y = " + str(np.squeeze(my_predicted_image)) + ", your algorithm predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") + "\" picture.")