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作业方面，暂时只关注需要编程的题目了，用python完成代码。
Q15~Q17应用的是传统PLA算法，给定的数据集也是保证线性可分的。
代码需要完成的就是实现一个简单的PLA，并且“W = W + speed*yX”中的speed是可以配置的（即学习速率）
代码1
#encoding=utf8 import sys import numpy as np import math if __name__ == ‘__main__‘: W = [ 0.0, 0.0, 0.0, 0.0, 0.0 ] halts = 0 for line in open("train.dat").readlines(): items = line.strip().split(‘\t‘) y = items[1].strip() X = items[0].strip().split(‘ ‘) X.insert(0,1) # gurantee the length of W and X if ( len(W)!=len(X) ): sys.exit(-1) # initial score 0 score = 0.0 # calculate W‘X for i in range(0,len(X)): score = score + float(X[i]) * float(W[i]) print "score" + str(score) # transfer score to sign sign = 1 if score>0.0 else -1 if sign != int(y) : halts = halts + 1 for i in range(0,len(X)): W[i] = float(W[i]) + float(y)*float(X[i]) for w in W: print w print "halts:" + str(halts)
代码2（随机打乱样本顺序）
#encoding=utf8 import sys import numpy as np import math from random import * if __name__ == ‘__main__‘: # params TIMES = 2000 sum_halts = 0 SPEED = 0.5 # read raw data raw_data = [] for line in open("train.dat").readlines(): raw_data.append(line.strip()) # iteratively a = Random() for i in range(0,TIMES): W = [ 0.0, 0.0, 0.0, 0.0, 0.0 ] halts = 0 # randomly shuffle data a.seed(i) a.shuffle(raw_data) # pla process for line in raw_data: items = line.strip().split(‘\t‘) y = items[1].strip() X = items[0].strip().split(‘ ‘) X.insert(0,1) # gurantee the length of W and X if ( len(W)!=len(X) ): sys.exit(-1) # initial score 0 score = 0.0 # calculate W‘X for i in range(0,len(X)): score = score + float(X[i]) * float(W[i]) # transfer score to sign sign = 1 if score>0.0 else -1 if sign != int(y) : halts = halts + 1 for i in range(0,len(X)): W[i] = float(W[i]) + SPEED*float(y)*float(X[i]) print "halts:" + str(halts) # accumulate sum of halts sum_halts = sum_halts + halts print "average halts:" + str(sum_halts/(TIMES-1))
这几道题的可以得到的结论就是：如果更新学习的速率，打乱样本顺序，可能会对收敛的次数产生影响。
另外，还有一个细节就是：一定不要忘记加上偏执W0（即常数项截距），否则会一直保持一个误差无法做到收敛。
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作业Q18~Q20考查的是pocket pla
即，train数据不是线性可分的情况（实际中也多是如此），改进成pocket pla的方法。
之前一直没理解好pocket的意思，后来参考了讨论区的内容，理解了Pocket的意思。
简而言之就是，“pocket不影响pla的正常运行，每轮W该更新还是要更新；pocket只需要维护历史出现的W中，在train_data上error最小的那个即可”
#encoding=utf8 import sys import numpy as np import math from random import * def error_on_data(data, W): error_W = 0 for line in data: items = line.strip().split(‘\t‘) y = items[1].strip() X = items[0].strip().split(‘ ‘) X.insert(0,1) # calculate scores of W score_W = 0.0 for i in range(0,len(X)): score_W = score_W + float(X[i]) * float(W[i]) # judge W sign_W = 1 if score_W>0.0 else -1 if sign_W != int(y) : error_W = error_W + 1 return error_W def pocket_algorithm(train_data, r): best_W = [ 0, 0, 0, 0, 0 ] best_error = error_on_data(train_data, best_W) W = [ 0, 0, 0, 0, 0 ] rounds = 0 while rounds<100: line = train_data[r.randint(0,len(train_data)-1)] items = line.strip().split(‘\t‘) y = items[1].strip() X = items[0].strip().split(‘ ‘) X.insert(0,1) # initial score 0 score = 0.0 # calculate W‘X for i in range(0,len(X)): score = score + float(X[i]) * float(W[i]) # wrong judgement : transfer score to sign sign = 1 if score>0.0 else -1 if sign != int(y) : rounds = rounds + 1 for i in range(0,len(X)): W[i] = float(W[i]) + float(y)*float(X[i]) # update best_W curr_error = error_on_data(train_data,W) print "curr_error:" + str(curr_error) + ",best_error:" + str(best_error) if curr_error<best_error: for i in range(0,len(best_W)): best_W[i]=W[i] best_error = curr_error return best_W #return W if __name__ == ‘__main__‘: # read raw data train_data = [] for line in open("train2.dat").readlines(): train_data.append(line.strip()) test_data = [] for line in open("test2.dat").readlines(): test_data.append(line.strip()) # iteratively pocket algorithm iterative_times = 100 total_error_times = 0 r = Random() for i in range(0,iterative_times): # each round initialize a random seed r.seed(i) # conduct one round pocket algorithm W = pocket_algorithm(train_data, r) # accmulate error times error_times = error_on_data(test_data, W) total_error_times = total_error_times + error_times print str( (1.0*total_error_times)/(iterative_times*len(test_data)) )
这个参考资料解释了Pocket 算法是怎么样运行的
https://class.coursera.org/ntumlone-002/forum/thread?thread_id=79
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原文地址：http://www.cnblogs.com/xbf9xbf/p/4578521.html
