앤드류응 교수님 딥러닝 학습일지 실습-(2) (부제:첫번째 인공신경망 구현!)

 

선형회귀는 명확한 한계가 존재합니다. 하나의 선을 기준으로 특정 값 이상이면 참, 아니면 거짓을 구분하기에 복잡한 형태의 데이터를 여러 기준으로 나누기에 적합하지 않습니다.

대표사진 삭제

사진 설명을 입력하세요.

다음과 같은 점들의 분포가 있다고 할 때 선형회귀를 통해서 구분 할 시 정확도는 47%에 불과합니다.

clf = sklearn.linear_model.LogisticRegressionCV();
clf.fit(X.T, Y.T);
plot_decision_boundary(lambda x: clf.predict(x), X, Y)
plt.title("Logistic Regression")

# Print accuracy
LR_predictions = clf.predict(X.T)
print ('Accuracy of logistic regression: %d ' % float((np.dot(Y,LR_predictions) + np.dot(1-Y,1-LR_predictions))/float(Y.size)*100) +
       '% ' + "(percentage of correctly labelled datapoints)")

 

다음 코드로 확인 할 수 있습니다. 그렇기 때문에 은닉층을 가진 인공신경망을 통해 분류를 하게 되는 것입니다.

import numpy as np
import matplotlib.pyplot as plt
from testCases_v2 import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets
np.random.seed(1)
X, Y = load_planar_dataset()
#Visualizing the data
plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);

shape_X=X.shape
shape_Y=Y.shape
m=X.shape[1]

# print("the shape of X is "+str(X.shape))
# print("the shape of Y is "+str(Y.shape))
# print("I have m= %d training examples " % m)

# 1. Define the neural network structure ( # of input units, # of hidden units, etc)
def layer_sizes(X,Y):
    n_x=X.shape[0]
    n_h=4
    n_y=Y.shape[0]
    return n_x,n_h,n_y


X_assess, Y_assess = layer_sizes_test_case()
# X.shape=(5,3) Y.shape=(2,3) ->각각의 특징은 5개,2개 데이터 개수가 3개인 것.
(n_x, n_h, n_y) = layer_sizes(X_assess, Y_assess)
# print("The size of the input layer is: n_x = " + str(n_x))
# print("The size of the hidden layer is: n_h = " + str(n_h))
# print("The size of the output layer is: n_y = " + str(n_y))

#2.Initialize the model's parameters
def initialize_parameters(n_x,n_h,n_y):

    np.random.seed(2)

    W1=np.random.randn(n_h,n_x)*0.01
    b1=np.zeros((n_h,1))
    W2=np.random.randn(n_y,n_h)*0.01
    b2=np.zeros((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

n_x, n_h, n_y = initialize_parameters_test_case()

# parameters = initialize_parameters(n_x, n_h, n_y)
# print("W1 = " + str(parameters["W1"]))
# print("b1 = " + str(parameters["b1"]))
# print("W2 = " + str(parameters["W2"]))
# print("b2 = " + str(parameters["b2"]))


def forward_propagation(X, parameters):
    """
    Argument:
    X -- input data of size (n_x, m)
    parameters -- python dictionary containing your parameters (output of initialization function)

    Returns:
    A2 -- The sigmoid output of the second activation
    cache -- a dictionary containing "Z1", "A1", "Z2" and "A2"
    """
    # Retrieve each parameter from the dictionary "parameters"
    ### START CODE HERE ### (≈ 4 lines of code)
    W1=parameters['W1']
    b1=parameters['b1']
    W2=parameters['W2']
    b2=parameters['b2']
    ### END CODE HERE ###

    # Implement Forward Propagation to calculate A2 (probabilities)
    ### START CODE HERE ### (≈ 4 lines of code)
    Z1=np.dot(W1,X)+b1
    A1=np.tanh(Z1)
    Z2=np.dot(W2,A1)+b2
    A2=sigmoid(Z2)
    ### END CODE HERE ###

    assert (A2.shape == (1, X.shape[1]))

    # Values needed in the backpropagation are stored in "cache". This will be given as an input to the backpropagation
    cache = {"Z1": Z1,
             "A1": A1,
             "Z2": Z2,
             "A2": A2}

    return A2, cache
X_assess, parameters = forward_propagation_test_case()
A2, cache = forward_propagation(X_assess, parameters)


def compute_cost(A2, Y, parameters):
    """
    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)
    parameters -- python dictionary containing your parameters W1, b1, W2 and b2
    [Note that the parameters argument is not used in this function,
    but the auto-grader currently expects this parameter.
    Future version of this notebook will fix both the notebook
    and the auto-grader so that `parameters` is not needed.
    For now, please include `parameters` in the function signature,
    and also when invoking this function.]

    Returns:
    cost -- cross-entropy cost given equation (13)

    """

    m = Y.shape[1]  # number of example

    # Compute the cross-entropy cost
    ### START CODE HERE ### (≈ 2 lines of code)
    logprobs=np.multiply(np.log(A2),Y)+np.multiply(np.log(1-A2),(1-Y))
    cost=np.sum(logprobs)/(-m)
    ### END CODE HERE ###

    cost = float(np.squeeze(cost))  # makes sure cost is the dimension we expect.
    # E.g., turns [[17]] into 17
    assert (isinstance(cost, float))

    return cost
A2, Y_assess, parameters = compute_cost_test_case()

# print("cost = " + str(compute_cost(A2, Y_assess, parameters)))

 

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".
    ### START CODE HERE ### (≈ 2 lines of code)
    W1=parameters['W1']
    b1=parameters['b1']
    W2=parameters['W2']
    b2=parameters['b2']
    ### END CODE HERE ###

    # Retrieve also A1 and A2 from dictionary "cache".
    ### START CODE HERE ### (≈ 2 lines of code)
    A1=cache['A1']
    Z1=cache['Z1']
    A2=cache['A2']
    Z2=cache['Z2']
    ### END CODE HERE ###

    # Backward propagation: calculate dW1, db1, dW2, db2.
    ### START CODE HERE ### (≈ 6 lines of code, corresponding to 6 equations on slide above)
    dZ2=A2-Y
    dW2=(1/m)*np.dot(dZ2,A1.T)
    db2=(1/m)*np.sum(dZ2,axis=1,keepdims=True)
    dZ1=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)
    ### END CODE HERE ###

    grads = {"dW1": dW1,
             "db1": db1,
             "dW2": dW2,
             "db2": db2}

    return grads
parameters, cache, X_assess, Y_assess = backward_propagation_test_case()

grads = backward_propagation(parameters, cache, X_assess, Y_assess)
print ("dW1 = "+ str(grads["dW1"]))
print ("db1 = "+ str(grads["db1"]))
print ("dW2 = "+ str(grads["dW2"]))
print ("db2 = "+ str(grads["db2"]))


def update_parameters(parameters, grads, learning_rate):
    """
    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 each parameter from the dictionary "parameters"
    ### START CODE HERE ### (≈ 4 lines of code)
    W1=parameters['W1']
    b1=parameters['b1']
    W2=parameters['W2']
    b2=parameters['b2']
    ### END CODE HERE ###

    # Retrieve each gradient from the dictionary "grads"
    ### START CODE HERE ### (≈ 4 lines of code)
    dW1=grads['dW1']
    db1=grads['db1']
    dW2=grads['dW2']
    db2=grads['db2']
    ## END CODE HERE ###

    # Update rule for each parameter
    ### START CODE HERE ### (≈ 4 lines of code)
    W1=W1-dW1*learning_rate
    b1=b1-db1*learning_rate
    W2=W2-dW2*learning_rate
    b2=b2-db2*learning_rate

    ### END CODE HERE ###

    parameters = {"W1": W1,
                  "b1": b1,
                  "W2": W2,
                  "b2": b2}

    return parameters
parameters, grads = update_parameters_test_case()
parameters = update_parameters(parameters, grads,1.2)

def nn_model(X, Y, n_h, learning_rate, num_iterations=10000, print_cost=False):
    n_x=layer_sizes(X,Y)[0]
    n_h=layer_sizes(X,Y)[1]
    n_y = layer_sizes(X, Y)[2]

    # Initialize parameters
    parameters = initialize_parameters(n_x, n_h, n_y)
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]

    # Loop (gradient descent)
    for i in range(0, num_iterations):
        # Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache"
        A2,cache=forward_propagation(X,parameters)
        # Cost function. Inputs: "A2, Y, parameters". Outputs: "cost"
        cost=compute_cost(A2,Y,parameters)
        # Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads"
        grads=backward_propagation(parameters,cache,X,Y)
            # Update rule for each parameter
        parameters=update_parameters(parameters,grads,learning_rate)
            # If print_cost=True, Print the cost every 1000 iterations
        if print_cost and i % 1000 == 0:
            print("Cost after iteration %i: %f" % (i, cost))
    # Returns parameters learnt by the model. They can then be used to predict output
    return parameters


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.
    ### START CODE HERE ### (≈ 2 lines of code)
    A2,parameters=forward_propagation(X,parameters)
    predictions=(A2>0.5)
    ### END CODE HERE ###

    return predictions

 

기억할 것은 은닉층의 수에 따라 차원 맞춰주는 것만 잘하면 된다는 것입니다.

이것 외에는 크게 기억 할 것이 없답니다!

슬슬 블로그에 쓰기에는 길이가 기네여..깃허브 사용법을 얼른 익혀서 깃허브에 올려야겠어요.