物流网络,LogisticNeuralNetwork

发表时间:2020-11-16
import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage
from lr_utils import load_dataset

%matplotlib inline
train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()

每张图片为一个训练样本,需要将其转换成(m,n)的数据格式,m代表数据条数,n代表特征数(三通道图片展开即可),
之后转置,改变成nxm的形状,列为样本数,行为特征,方便计算

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

归一化

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

定义sigmoid函数,参数初始化,定义损失函数,损失函数导数,梯度下降方法,预测函数

def sigmoid(z):
    s = 1/(1+np.exp(-z))
    return s
    
def initialize_with_zeros(dim):   
    w,b = np.zeros((dim,1)),0
    assert(w.shape == (dim, 1))
    assert(isinstance(b, float) or isinstance(b, int))
    return w, b

def propagate(w, b, X, Y):
    m = X.shape[1]    
    s =  sigmoid(w.T.dot(X)+b)
    cost = -np.sum(Y*np.log(s) + (1-Y)*np.log(1-s))/m
    dw = X.dot((s - Y).T)/m
    db = np.sum(s-Y)/m

    assert(dw.shape == w.shape)
    assert(db.dtype == float)
    cost = np.squeeze(cost)
    assert(cost.shape == ())
    
    grads = {"dw": dw,
             "db": db}
    
    return grads, cost
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.

    """
    
    costs = []
    
    for i in range(num_iterations):
        
        grads,cost  = propagate(w, b, X, Y)
        dw = grads["dw"]
        db = grads["db"]
        w  = w - learning_rate*dw
        b =  b - learning_rate *db
        if i % 100 == 0:
            costs.append(cost)

        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
    
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)
    A =  sigmoid(w.T.dot(X)+b)

    for i in range(A.shape[1]):
        if A[0,i] <= 0.5:
            Y_prediction[0,i] = 0
        else:
            Y_prediction[0,i] = 1
    
    assert(Y_prediction.shape == (1, m))
    return Y_prediction

将上述函数整合,给定初始参数,按照给定损失函数和损失函数导数进行梯度迭代


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.
    """
    
    w,b = initialize_with_zeros(X_train.shape[0])
    params, grads, costs =  optimize(w, b, X_train,Y_train, num_iterations, learning_rate, print_cost = False)
    w,b = params['w'],params['b']
    
    Y_prediction_train = predict(w, b, X_train)
    Y_prediction_test = predict(w, b, X_test)

    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)
结果:
train accuracy: 99.04306220095694 %
test accuracy: 70.0 %

绘制学习曲线
在这里插入图片描述

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()

不同学习率下cost函数变化情况(学习率过大出现上下波动,越过了最低点到另一侧)
在这里插入图片描述

learning_rates = [0.01, 0.001, 0.0001]
models = {}
for i in learning_rates:
    print ("learning rate is: " + str(i))
    models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 1500, learning_rate = i, print_cost = False)
    print ('\n' + "-------------------------------------------------------" + '\n')

for i in learning_rates:
    plt.plot(np.squeeze(models[str(i)]["costs"]), label= str(models[str(i)]["learning_rate"]))

plt.ylabel('cost')
plt.xlabel('iterations')

legend = plt.legend(loc='upper center', shadow=True)
frame = legend.get_frame()
frame.set_facecolor('0.90')
plt.show()


结果:
learning rate is: 0.01
train accuracy: 99.52153110047847 %
test accuracy: 68.0 %

-------------------------------------------------------

learning rate is: 0.001
train accuracy: 88.99521531100478 %
test accuracy: 64.0 %

-------------------------------------------------------

learning rate is: 0.0001
train accuracy: 68.42105263157895 %
test accuracy: 36.0 %

文章来源互联网,如有侵权,请联系管理员删除。邮箱:417803890@qq.com / QQ:417803890

微配音

Python Free

邮箱:417803890@qq.com
QQ:417803890

皖ICP备19001818号
© 2019 copyright www.pythonf.cn - All rights reserved

微信扫一扫关注公众号:

联系方式

Python Free