{{c:swap:recommendations_toby.pdf|Reading material}}
# 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')]
^ Critic ^ Similarity ^ Night ^ S.xNight ^ Lady ^ S.xLady ^ Luck ^ S.xLuck ^
| Rose | 0.99 | 3 | 2.97 | 2.5 | 2.48 | 3 | 2.97 |
| Seymour | 0.38 | 3 | 1.14 | 3 | 1.14 | 1.5 | 0.57 |
| Puig | 0.89 | 4.5 | 4.02 | | | 3 | 2.68 |
| LaSalle | 0.92 | 3 | 2.77 | 3 | 2.77 | 2 | 1.85 |
| Matthews | 0.66 | 3 | 1.99 | 3 | 1.99 | | |
| Total | | | 12.89 | | 8.38 | | 8.07 |
| Sim.Sum | | | 3.84 | | 2.95 | | 3.18 |
| Total/Sim.Sum | | | 3.35 | | 2.83 | | 2.53 |
# 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__
# 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