前言

不管是兴趣还是趋势，笔者开始尝试入坑机器学习，慢慢做一点笔记学习下。。由于是菜鸟，数学原理就不写了，贴一些流程和公式，专业词汇可能也有点不到位问题。这里记录的是怎么训练一个识别猫的程序（来源是Coursera）

用到的python库

numpy 矩阵计算必备
PIL和scipy将图片转为矩阵

import numpy as np
import scipy
from PIL import Image
from scipy import ndimage

训练数据定义

数据来源是Coursera上面的,注意文中所有的矩阵都是numpy.array类型哦

train_set_x_orig, train_set_y, test_set_x_orig, test_set_y = load_dataset()

train_set_x_orig是训练图片集209张图片，每张图片 64x64x3（RGB）
所以是(209,64,64,3)的矩阵
test_set_x_orig 是测试用图片集 ,基本同上，就是图片数量不一样，50个，所以是
(50,64,64,3)

train_set_y 是训练用的结果集合，是一个一维的矩阵，每一个值对应的是训练用图片的正确输出值
，显然这个是人工录好的，在这个识别猫的程序里，图片是猫就输出1，不是就输出0，这是一个
（1，209）的矩阵
test_set_y则是测试的结果矩阵，同上，也是数量不一样,为(1,50)
然后根据训练集拿到一些有用的参数

#训练图片数
m_train = len(train_set_x_orig)
#测试图片数
m_test = len(test_set_x_orig)
#像素宽
num_px = train_set_x_orig[0].shape[0]

操作流程

1.把图集平铺开，每张图是由 64,64,3的矩阵构成，那么可以转为64x64x3的一维矩阵
所以图集也可变为(64x64x3,209)的矩阵,测试图集也是一样

train_set_x_flatten = train_set_x_orig.reshape(m_train , -1).T
test_set_x_flatten =  test_set_x_orig.reshape(m_test, -1).T
#rgb的值就是255，除以255得到对应的小数,这样能加快计算效率，这里 train_set_x_flatten和test_set_x_flatten的类型都是
#numpy.array哦
train_set_x = train_set_x_flatten/255.
test_set_x = test_set_x_flatten/255.

sigmoid函数，处理数据用

sigmoid

def sigmoid(z):
    """
    Compute the sigmoid of z

    Arguments:
    z -- A scalar or numpy array of any size.

    Return:
    s -- sigmoid(z)
    """
    s = 1/(1+np.exp(-z))   
    return s

初始化一些参数

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)
    """
    w = np.zeros((dim ,1))
    b = 0
    assert(w.shape == (dim, 1))
    assert(isinstance(b, float) or isinstance(b, int))
    
    return w, b

前向传播和反向传播，已经获得降低cost
下面几个公式很有用
A是预测结果的函数，最终目标就是找到最优的w和b的值，然后
输入图片，通过A函数求值，判断输出

cost J 公式如下，cost理论上越小越好

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
   
    """
    
    m = X.shape[1]
    # FORWARD PROPAGATION (FROM X TO COST)
   
    A = sigmoid(np.dot(w.T,X)+b)
    # compute activation
    cost = np.sum(Y*np.log(A)+np.log(1-A)*(1-Y))/-m    
    print(cost)
    # compute cost

    
    # BACKWARD PROPAGATION (TO FIND GRAD)
  
    dw = np.dot(X,(A-Y).T)/m
    db = np.sum(A-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

然后对cost 这些参数可以优化，拿到个局部最优解

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):
        
        
        # Cost and gradient calculation
        grads, cost = propagate(w,b,X,Y)
   
        
        # Retrieve derivatives from grads
        dw = grads["dw"]
        db = grads["db"]
        
        # update rule 
       
        w = w-learning_rate*dw
        b = b-learning_rate*db
     
        
        # 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

预测结果

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

    A = sigmoid(np.dot(w.T,X)+b)
    
    
    for i in range(A.shape[1]):
        
        # Convert probabilities A[0,i] to actual predictions p[0,i]
        
        Y_prediction[0,i]=0 if A[0,i]<=0.5 else 1
        
    
    assert(Y_prediction.shape == (1, m))
    
    return Y_prediction

整个代码组合下就是

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.
    """
    
   
    
    # initialize parameters with zeros 
    w, b = initialize_with_zeros(len(X_train))

    # Gradient descent
    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
    Y_prediction_test = predict(w,b,X_test)
    Y_prediction_train = predict(w,b,X_train)



    # 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

跑了model函数以后的，验证代码

d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 3000, learning_rate = 0.007, print_cost = True)
my_image = "timg.jpg"   # change this to the name of your image file 

# We preprocess the image to fit your algorithm.
fname = "images/" + my_image
image = np.array(ndimage.imread(fname, flatten=False))
my_image = scipy.misc.imresize(image, size=(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)#在ui上显示图片
print("y = " + str(np.squeeze(my_predicted_image)) + ")

结语

有些线代方面的知识已经还给老师了，有时间还是要搞本周志华老师的西瓜书看看，总之还是好好学习天天向上吧。