코세라) 신경망 및 딥러닝 - 얕은 신경망 - Planar data classification with one hidden layer (2)

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

# GRADED FUNCTION: compute_cost

def compute_cost(A2, Y):
    """
    Computes the cross-entropy cost given in equation (13)
    
    Arguments:
    A2 -- The sigmoid output of the second activation, of shape (1, number of examples)
    Y -- "true" labels vector of shape (1, number of examples)

    Returns:
    cost -- cross-entropy cost given equation (13)
    
    """
    
    m = Y.shape[1] # number of examples

    # Compute the cross-entropy cost
    # (≈ 2 lines of code)
    # logprobs = ...
    # cost = ...
    # YOUR CODE STARTS HERE
    logprobs = np.multiply(np.log(A2), Y) + np.multiply(np.log(1-A2), 1-Y)
    cost = - 1 * np.sum(logprobs) / m
    # YOUR CODE ENDS HERE
    
    cost = float(np.squeeze(cost))  # makes sure cost is the dimension we expect. 
                                    # E.g., turns [[17]] into 17 
    
    return cost

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59

# GRADED FUNCTION: backward_propagation

def backward_propagation(parameters, cache, X, Y):
    """
    Implement the backward propagation using the instructions above.
    
    Arguments:
    parameters -- python dictionary containing our parameters 
    cache -- a dictionary containing "Z1", "A1", "Z2" and "A2".
    X -- input data of shape (2, number of examples)
    Y -- "true" labels vector of shape (1, number of examples)
    
    Returns:
    grads -- python dictionary containing your gradients with respect to different parameters
    """
    m = X.shape[1]
    
    # First, retrieve W1 and W2 from the dictionary "parameters".
    #(≈ 2 lines of code)
    # W1 = ...
    # W2 = ...
    # YOUR CODE STARTS HERE
    W1 = parameters["W1"]
    W2 = parameters["W2"]
    # YOUR CODE ENDS HERE
        
    # Retrieve also A1 and A2 from dictionary "cache".
    #(≈ 2 lines of code)
    # A1 = ...
    # A2 = ...
    # YOUR CODE STARTS HERE
    A1 = cache["A1"]
    A2 = cache["A2"]
    # YOUR CODE ENDS HERE
    
    # Backward propagation: calculate dW1, db1, dW2, db2. 
    #(≈ 6 lines of code, corresponding to 6 equations on slide above)
    # dZ2 = ...
    # dW2 = ...
    # db2 = ...
    # dZ1 = ...
    # dW1 = ...
    # db1 = ...
    # YOUR CODE STARTS HERE
    dZ2 = A2 - Y
    dW2 = np.dot(dZ2, A1.T) / m
    db2 = np.sum(dZ2, axis=1, keepdims = True) / m
    
    dZ1 = np.dot(W2.T, dZ2) * (1 - np.power(A1, 2))
    dW1 = np.dot(dZ1, X.T) / m
    db1 = np.sum(dZ1, axis=1, keepdims = True) / m
    # YOUR CODE ENDS HERE
    
    grads = {"dW1": dW1,
             "db1": db1,
             "dW2": dW2,
             "db2": db2}
    
    return grads

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59

# GRADED FUNCTION: update_parameters

def update_parameters(parameters, grads, learning_rate = 1.2):
    """
    Updates parameters using the gradient descent update rule given above
    
    Arguments:
    parameters -- python dictionary containing your parameters 
    grads -- python dictionary containing your gradients 
    
    Returns:
    parameters -- python dictionary containing your updated parameters 
    """
    # Retrieve a copy of each parameter from the dictionary "parameters". Use copy.deepcopy(...) for W1 and W2
    #(≈ 4 lines of code)
    # W1 = ...
    # b1 = ...
    # W2 = ...
    # b2 = ...
    # YOUR CODE STARTS HERE
    parameters_cp = copy.deepcopy(parameters)
    W1 = parameters_cp["W1"]
    b1 = parameters_cp["b1"]
    W2 = parameters_cp["W2"]
    b2 = parameters_cp["b2"]
    # YOUR CODE ENDS HERE
    
    # Retrieve each gradient from the dictionary "grads"
    #(≈ 4 lines of code)
    # dW1 = ...
    # db1 = ...
    # dW2 = ...
    # db2 = ...
    # YOUR CODE STARTS HERE
    dW1 = grads["dW1"]
    db1 = grads["db1"]
    dW2 = grads["dW2"]
    db2 = grads["db2"]
    # YOUR CODE ENDS HERE
    
    # Update rule for each parameter
    #(≈ 4 lines of code)
    # W1 = ...
    # b1 = ...
    # W2 = ...
    # b2 = ...
    # YOUR CODE STARTS HERE
    W1 = W1 - learning_rate * dW1
    b1 = b1 - learning_rate * db1
    W2 = W2 - learning_rate * dW2
    b2 = b2 - learning_rate * db2
    # YOUR CODE ENDS HERE
    
    parameters = {"W1": W1,
                  "b1": b1,
                  "W2": W2,
                  "b2": b2}
    
    return parameters

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55

# GRADED FUNCTION: nn_model

def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):
    """
    Arguments:
    X -- dataset of shape (2, number of examples)
    Y -- labels of shape (1, number of examples)
    n_h -- size of the hidden layer
    num_iterations -- Number of iterations in gradient descent loop
    print_cost -- if True, print the cost every 1000 iterations
    
    Returns:
    parameters -- parameters learnt by the model. They can then be used to predict.
    """
    
    np.random.seed(3)
    n_x = layer_sizes(X, Y)[0]
    n_y = layer_sizes(X, Y)[2]
    
    # Initialize parameters
    #(≈ 1 line of code)
    # parameters = ...
    # YOUR CODE STARTS HERE
    parameters = initialize_parameters(n_x, n_h, n_y)
    # YOUR CODE ENDS HERE
    
    # Loop (gradient descent)

    for i in range(0, num_iterations):
         
        #(≈ 4 lines of code)
        # Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache".
        # A2, cache = ...
        
        # Cost function. Inputs: "A2, Y". Outputs: "cost".
        # cost = ...
 
        # Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads".
        # grads = ...
 
        # Gradient descent parameter update. Inputs: "parameters, grads". Outputs: "parameters".
        # parameters = ...
        
        # YOUR CODE STARTS HERE
        A2, cache = forward_propagation(X, parameters)
        cost = compute_cost(A2, Y)
        grads = backward_propagation(parameters, cache, X, Y)
        parameters = update_parameters(parameters, grads)
        # YOUR CODE ENDS HERE
        
        # Print the cost every 1000 iterations
        if print_cost and i % 1000 == 0:
            print ("Cost after iteration %i: %f" %(i, cost))

    return parameters

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22

# GRADED FUNCTION: predict

def predict(parameters, X):
    """
    Using the learned parameters, predicts a class for each example in X
    
    Arguments:
    parameters -- python dictionary containing your parameters 
    X -- input data of size (n_x, m)
    
    Returns
    predictions -- vector of predictions of our model (red: 0 / blue: 1)
    """
    
    # Computes probabilities using forward propagation, and classifies to 0/1 using 0.5 as the threshold.
    #(≈ 2 lines of code)
    A2, cache = forward_propagation(X, parameters)
    predictions = np.round(A2)
    # YOUR CODE STARTS HERE
    # YOUR CODE ENDS HERE
    
    return predictions