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# A dictionary of movie critics and their ratings of a small
# 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}}

>> from math import sqrt
>> sqrt(pow(4.5-4,2)+pow(2-1,2))
1.118033988749895

>> 1/(1+sqrt(pow(5-4,2)+pow(4-1,2)))
0.4721359549995794

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)

similarity between two users.

>>> reload(recommendations)
>>> recommendations.sim_distance(recommendations.critics,
... 'Lisa Rose','Gene Seymour')
0.148148148148

for python 3.xx

>>> import recommendations
imp.reload(recommendations)
>>> recommendations.sim_distance(recommendations.critics,
... 'Lisa Rose','Gene Seymour')
0.148148148148

Pearson correlation Score
r = See, http://onlinestatbook.com/2/describing_bivariate_data/calculation.html

# Returns the Pearson correlation coefficient for p1 and p2
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
 
  # Find the number of elements
  n=len(si)
 
  # if they are no ratings in common, return 0
  if n==0: return 0
 
  # Add up all the preferences
  sum1=sum([prefs[p1][it] for it in si])
  sum2=sum([prefs[p2][it] for it in si])
 
  # Sum up 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 up the products
  pSum=sum([prefs[p1][it]*prefs[p2][it] for it in si])
 
  # Calculate 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

>>> reload(recommendations)
>>> print recommendations.sim_pearson(recommendations.critics,
... 'Lisa Rose','Gene Seymour')
0.396059017191

Ranking the Critics

# Returns the best matches for person from the prefs dictionary.
# Number of results and similarity function are optional params.
def topMatches(prefs,person,n=5,similarity=sim_pearson):
  scores=[(similarity(prefs,person,other),other)
                  for other in prefs if other!=person]

  # Sort the list so the highest scores appear at the top
  scores.sort( )
  scores.reverse( )
  return scores[0:n]

>> reload(recommendations)
>> recommendations.topMatches(recommendations.critics,'Toby',n=3)
[(0.99124070716192991, 'Lisa Rose'), (0.92447345164190486, 'Mick LaSalle'),
(0.89340514744156474, 'Claudia Puig')]

# Gets recommendations for a person by using a weighted average
# of every other user's rankings
def getRecommendations(prefs,person,similarity=sim_pearson):
  totals={}
  simSums={}
  for other in prefs:
    # don't compare me to myself
    if other==person: continue
    sim=similarity(prefs,person,other)

    # ignore scores of zero or lower
    if sim<=0: continue
    for item in prefs[other]:

      # only score movies I haven't seen yet
      if item not in prefs[person] or prefs[person][item]==0:
        # Similarity * Score
        totals.setdefault(item,0)
        totals[item]+=prefs[other][item]*sim
        # Sum of similarities
        simSums.setdefault(item,0)
        simSums[item]+=sim

  # Create the normalized list
  rankings=[(total/simSums[item],item) for item,total in totals.items( )]

  # Return the sorted list
  rankings.sort( )
  rankings.reverse( )
  return rankings

>>> reload(recommendations)
>>> recommendations.getRecommendations(recommendations.critics,'Toby')
[(3.3477895267131013, 'The Night Listener'), (2.8325499182641614, 'Lady in the
Water'), (2.5309807037655645, 'Just My Luck')]
>>> recommendations.getRecommendations(recommendations.critics,'Toby',
... similarity=recommendations.sim_distance)
[(3.5002478401415877, 'The Night Listener'), (2.7561242939959363, 'Lady in the
Water'), (2.4619884860743739, 'Just My Luck')]

def transformPrefs(prefs):
  result={}
  for person in prefs:
    for item in prefs[person]:
      result.setdefault(item,{})
 
      # Flip item and person
      result[item][person]=prefs[person][item]
    return result

>> reload(recommendations)
>> movies=recommendations.transformPrefs(recommendations.critics)
>> recommendations.topMatches(movies,'Superman Returns')
[(0.657, 'You, Me and Dupree'), (0.487, 'Lady in the Water'), (0.111, 'Snakes on a
Plane'), (-0.179, 'The Night Listener'), (-0.422, 'Just My Luck')]

Whole script, recommendations.py

recommendations.py

# A dictionary of movie critics and their ratings of a small
# 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}}
 
 
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)
 
# Returns the Pearson correlation coefficient for p1 and p2
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
 
# Returns the best matches for person from the prefs dictionary. 
# Number of results and similarity function are optional params.
def topMatches(prefs,person,n=5,similarity=sim_pearson):
  scores=[(similarity(prefs,person,other),other) 
                  for other in prefs if other!=person]
  scores.sort()
  scores.reverse()
  return scores[0:n]
 
# Gets recommendations for a person by using a weighted average
# of every other user's rankings
def getRecommendations(prefs,person,similarity=sim_pearson):
  totals={}
  simSums={}
  for other in prefs:
    # don't compare me to myself
    if other==person: continue
    sim=similarity(prefs,person,other)
 
    # ignore scores of zero or lower
    if sim<=0: continue
    for item in prefs[other]:
 
      # only score movies I haven't seen yet
      if item not in prefs[person] or prefs[person][item]==0:
        # Similarity * Score
        totals.setdefault(item,0)
        totals[item]+=prefs[other][item]*sim
        # Sum of similarities
        simSums.setdefault(item,0)
        simSums[item]+=sim
 
  # Create the normalized list
  rankings=[(total/simSums[item],item) for item,total in totals.items()]
 
  # Return the sorted list
  rankings.sort()
  rankings.reverse()
  return rankings
 
def transformPrefs(prefs):
  result={}
  for person in prefs:
    for item in prefs[person]:
      result.setdefault(item,{})
 
      # Flip item and person
      result[item][person]=prefs[person][item]
  return result
 
 
def calculateSimilarItems(prefs,n=10):
  # Create a dictionary of items showing which other items they
  # are most similar to.
  result={}
  # Invert the preference matrix to be item-centric
  itemPrefs=transformPrefs(prefs)
  c=0
  for item in itemPrefs:
    # Status updates for large datasets
    c+=1
    if c%100==0: print "%d / %d" % (c,len(itemPrefs))
    # Find the most similar items to this one
    scores=topMatches(itemPrefs,item,n=n,similarity=sim_distance)
    result[item]=scores
  return result
 
def getRecommendedItems(prefs,itemMatch,user):
  userRatings=prefs[user]
  scores={}
  totalSim={}
  # Loop over items rated by this user
  for (item,rating) in userRatings.items( ):
 
    # Loop over items similar to this one
    for (similarity,item2) in itemMatch[item]:
 
      # Ignore if this user has already rated this item
      if item2 in userRatings: continue
      # Weighted sum of rating times similarity
      scores.setdefault(item2,0)
      scores[item2]+=similarity*rating
      # Sum of all the similarities
      totalSim.setdefault(item2,0)
      totalSim[item2]+=similarity
 
  # Divide each total score by total weighting to get an average
  rankings=[(score/totalSim[item],item) for item,score in scores.items( )]
 
  # Return the rankings from highest to lowest
  rankings.sort( )
  rankings.reverse( )
  return rankings
 
def loadMovieLens(path='/data/movielens'):
  # Get movie titles
  movies={}
  for line in open(path+'/u.item'):
    (id,title)=line.split('|')[0:2]
    movies[id]=title
 
  # Load data
  prefs={}
  for line in open(path+'/u.data'):
    (user,movieid,rating,ts)=line.split('\t')
    prefs.setdefault(user,{})
    prefs[user][movies[movieid]]=float(rating)
  return prefs