推荐引擎（一）

推荐引擎算法大体上分为两种：
（一）基于内容的
暂时不分析
（二）协同过滤
一个协同过滤算法通常的做法是对一大群人进行搜索，从中找到与我们品味相近的一小群人，算法会对这些人所偏爱的其他内容进行考查，并把他们组合成一个经过排名的推荐列表。
1，首先我们先找与我们品味相同的用户
我们常用的两套计算相似度评价值得体系：欧几里德距离和皮尔逊相关度
例子：

# set of movies
critics={'Lisa Rose': {'Lady in the Water': 2.5, 'Snakes on a Plane': 3.5,
 'Just My Luck': 3.0, 'Superman Returns': 3.5, 'You, Me and Dupree': 2.5, 
 'The Night Listener': 3.0},
'Gene Seymour': {'Lady in the Water': 3.0, 'Snakes on a Plane': 3.5, 
 'Just My Luck': 1.5, 'Superman Returns': 5.0, 'The Night Listener': 3.0, 
 'You, Me and Dupree': 3.5}, 
'Michael Phillips': {'Lady in the Water': 2.5, 'Snakes on a Plane': 3.0,
 'Superman Returns': 3.5, 'The Night Listener': 4.0},
'Claudia Puig': {'Snakes on a Plane': 3.5, 'Just My Luck': 3.0,
 'The Night Listener': 4.5, 'Superman Returns': 4.0, 
 'You, Me and Dupree': 2.5},
'Mick LaSalle': {'Lady in the Water': 3.0, 'Snakes on a Plane': 4.0, 
 'Just My Luck': 2.0, 'Superman Returns': 3.0, 'The Night Listener': 3.0,
 'You, Me and Dupree': 2.0}, 
'Jack Matthews': {'Lady in the Water': 3.0, 'Snakes on a Plane': 4.0,
 'The Night Listener': 3.0, 'Superman Returns': 5.0, 'You, Me and Dupree': 3.5},
'Toby': {'Snakes on a Plane':4.5,'You, Me and Dupree':1.0,'Superman Returns':4.0}}

欧几里德距离

from math import sqrt

# Returns a distance-based similarity score for person1 and person2
def sim_distance(prefs,person1,person2):
  # Get the list of shared_items
  si={}
  for item in prefs[person1]: 
    if item in prefs[person2]: si[item]=1

  # if they have no ratings in common, return 0
  if len(si)==0: return 0

  # Add up the squares of all the differences
  sum_of_squares=sum([pow(prefs[person1][item]-prefs[person2][item],2) 
                      for item in prefs[person1] if item in prefs[person2]])

  return 1/(1+sum_of_squares)

运行：
>>> import myset
>>> myset.sim_distance(myset.critics,'Lisa Rose','Gene Seymour')
0.14814814814814814
上述执行过程给出了Lisa Rose和Gene Seymour之间的相似度评价
皮尔逊相关度
如果某人总是倾向于给出比另一个人更高的分值，而二者的分值之差又始终保持一致，则他们依然可能会存在很好的相关性，前面的欧几里德距离就显得不合适了。我们看下皮尔逊相关度评价。

def sim_pearson(prefs,p1,p2):
  # Get the list of mutually rated items
  si={}
  for item in prefs[p1]: 
    if item in prefs[p2]: si[item]=1

  # if they are no ratings in common, return 0
  if len(si)==0: return 0

  # Sum calculations
  n=len(si)
  
  # Sums of all the preferences
  sum1=sum([prefs[p1][it] for it in si])
  sum2=sum([prefs[p2][it] for it in si])
  
  # Sums of the squares
  sum1Sq=sum([pow(prefs[p1][it],2) for it in si])
  sum2Sq=sum([pow(prefs[p2][it],2) for it in si])	
  
  # Sum of the products
  pSum=sum([prefs[p1][it]*prefs[p2][it] for it in si])
  
  # Calculate r (Pearson score)
  num=pSum-(sum1*sum2/n)
  den=sqrt((sum1Sq-pow(sum1,2)/n)*(sum2Sq-pow(sum2,2)/n))
  if den==0: return 0

  r=num/den

  return r

发现一篇介绍推荐引擎的文章写得很不错
http://www.oschina.net/question/12_17362