感知机Python代码优化与运行结果

#-*- coding:utf-8 -*-

'''

Purpose: implement perceptron algorithm; the perceptron algorithm is a binary classification algorithm, and is used to handle data sets that are linearly seperable.

Author: hittlle

QQ: 519234757

Email: hittlle@163.com

'''

importnumpy

classPerceptron:

def__init__(self, training_set = [], iterations =5, learning_rate =0.5):

self._training_set = training_set

self._iterations = iterations

self._learning_rate = learning_rate

self._setup()

def_setup(self):

iflen(self._training_set) >:

self._weight = numpy.zeros(len(self._training_set[][:-1]))

self._bias =0.0

self._alpha = numpy.zeros(len(self._training_set))

else:

self._weight =None

self._bias =None

self._alpha =None

#感知机原始形式training

defraw_training(self):

self._setup()

ifself._weightisNone:

return

foriterinxrange(self._iterations):

forsampleinself._training_set:

prediction = numpy.dot(self._weight, sample[:-1]) +self._bias

ifsample[-1] * prediction

self._weight =self._weight + numpy.multiply(self._learning_rate * sample[-1], sample[:-1])

self._bias =self._bias +self._learning_rate * sample[-1]

print("[+] Raw Perceptron - Stochatic Gradient Descent")

print("[+] weight ",self._weight)

print("[+] bias ",self._bias)

print("[+] learning rate ",self._learning_rate)

print("[+] iterations ",self._iterations)

#Gram矩阵计算

defcalculate_gram_matrix(self):

dim =len(self._training_set)

self._gram = numpy.zeros((dim,dim))

shape = numpy.shape(self._gram)

forrowinrange(shape[]):

forcolinrange(shape[1]):

self._gram[row][col] = numpy.dot(self._training_set[row][:-1],self._training_set[col][:-1])

print("[+] Gram matrix for duality training:")

print(self._gram)

#感知机对偶形式training

defduality_training(self):

self._setup()

ifself._weightisNone:

return

# calculate Gram Matrix

self.calculate_gram_matrix()

dim =len(self._training_set)

foriterinxrange(self._iterations):

sample_idx =

forsampleinself._training_set:

prediction =0.0

alpha_idx=

foridxinxrange(dim):

prediction +=self._alpha[idx] *self._training_set[idx][-1] *self._gram[sample_idx][idx]

prediction = sample[-1] * (prediction +self._bias)

ifprediction

self._alpha[sample_idx] =self._alpha[sample_idx] +self._learning_rate

self._bias =self._bias +self._learning_rate * sample[-1]

sample_idx +=1

#calculate weight

idx =

#_weight是training sample的线性组合

foriterinxrange(dim):

self._weight = numpy.add(numpy.multiply(self._alpha[idx] *self._training_set[iter][-1],self._training_set[iter][:-1]),self._weight)

idx+=1

print("[+] Duality Perceptron - Stochatic Gradient Descent")

print("[+] weight ",self._weight)

print("[+] bias ",self._bias)

print("[+] learning rate ",self._learning_rate)

print("[+] iterations ",self._iterations)

if__name__ =='__main__':

#test

training_set = [[3,3,1],[4,3,1],[1,1, -1]]

perceptron = Perceptron(training_set=training_set,iterations=5,learning_rate=1.0)

perceptron.raw_training()

perceptron.duality_training()

del(perceptron)

del(training_set)

training_set = [[12,32,11,12,10,1], [10,23,10,1,100, -1], [30,30,21,12,21,1], [11,10,12,13,12, -1]]

perceptron = Perceptron(training_set=training_set,iterations=100,learning_rate=0.0005)

perceptron.raw_training()

perceptron.duality_training()

上篇中的代码有一个小错误，虽无大的影响，但也不够严谨，这儿修正一下。下面是运行结果。

可以看到，对同一个数据集，原始形式和对偶形式算法得出的结果一样。笔者认为，对偶形式在训练样本比较少的时候有用，在训练样本比较多，而且维度比较高的情况下，计算Gram矩阵的开销就会比较大；而原始形式没有这样的问题。