机器学习基石第二讲 Learning to Answer Yes/No

一.Perceptron Hypothesis Set

二.Perceptron Learning Algorithm (PLA)

PLA算法流程：

三.Guarantee of PLA

下面是对PLA的证明：

 

四.Non-Separable Data

在学习完percetron算法后，我自己编写了一个识别0，1的程序，训练集和测试集使用的是Yann LeCun大神很有名的MNIST数字images，经过训练之后，测试集的正确率有70%左右，代码如下：

import cv2
import os
import numpy
import glob

class Percetron(object):
    def __init__(self, image_x_dimension, image_y_dimension, positive_dimension, negtive_dimension):
        self.image_x_dimension = image_x_dimension
        self.image_y_dimension = image_y_dimension
        self.positive_dimension = positive_dimension
        self.negtive_dimension = negtive_dimension
        self.dimension = self.image_x_dimension * self.image_y_dimension + 1
        self.count = self.positive_dimension + self.negtive_dimension

    def image2vector(self, filename):
        returnVect = numpy.zeros((1,self.dimension))
        file_matrix = cv2.imread(filename, cv2.IMREAD_GRAYSCALE)
        returnVect[0, 0] = 1
        for i in range(self.image_x_dimension):
            for j in range(self.image_y_dimension):
                returnVect[0, self.image_y_dimension * i + j + 1] = float(file_matrix[i, j])
        return returnVect

    def image2Matrix(self):
        X_train = numpy.zeros((self.count, self.dimension))
        i = 0
        for bmp in glob.glob(".\*.bmp"):
            X_train[i, :] = self.image2vector(bmp)
            i += 1
        return X_train

    def yMatrix(self):
        y_train = numpy.zeros((self.count, 1))
        for i in range(self.negtive_dimension):
            y_train[i] = -1
        for i in range(self.positive_dimension):
            y_train[i + self.negtive_dimension] = 1
        return y_train

    def opPercetron(self):
        w = numpy.zeros((self.dimension, 1))
        X_train = self.image2Matrix()
        y_train = self.yMatrix()
        while True:
            flag = 0
            num = 0
            for i in range(self.count):
                if  numpy.dot(X_train[i, :], w)[0] * y_train[i] <= 0:
                    w += y_train[i, 0] * X_train[i,:].reshape(self.dimension, 1)
                    flag = 1
            if flag == 0:
                break
        return w

    def accuracy(self, w):
        num = 0
        X_test = self.image2Matrix()
        y_test = self.yMatrix()
        for i in range(self.count):
            if numpy.dot(X_test[i, :], w)[0] * y_test[i] > 0:
                num += 1
        print float(num) / self.count


my_train_Percetron = Percetron(28, 28, 800, 800)
os.chdir("C:\Users\samsung\Desktop\Perceptron_train")
w = my_train_Percetron.opPercetron()
my_train_Percetron.accuracy(w)

my_test_Percetron = Percetron(28, 28, 180, 335)
os.chdir("C:\Users\samsung\Desktop\Perceptron_test")
my_test_Percetron.accuracy(w)