顺手贴笔记 2.Pearson Correlation Score

# A dictionary of movie critics and their ratings of a small
# set of movies
from math import sqrt
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}}
# 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 no rating 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
倒推出来其实就是公式：
(x1, y1) (x2, y2) ......(xn, yn)
x1 is the score of person1's item1, y1 is the score of person2's item1.
x2 is the score of person1's item2, y2 is the score of person2's item2.
so:
s1 = x1 + x2 +....+ xn
s2 = y1 + y2 +....+ yn
sq1 = x1^2 + x2^2 + ....+ xn^2
sq2 = y1^2 + y2^2 + ....+ yn^2
sp = x1*y1 + x2*y2 + .... + xn * yn
the correlation line rate:
(sp - s1 * s2/n)
------------------------------
sqrt((sq1-s1^2/n)*(sq2-s2^2/n))
It corrects for grade inflation.