In [1]:
from numpy import *
from numpy import linalg as la
import pandas as pd
import pdb
import numpy as np
In [2]:
def loadData():
    M =    [[0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 5],
           [0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 3],
           [0, 0, 0, 0, 4, 0, 0, 1, 0, 4, 0],
           [3, 3, 4, 0, 0, 0, 0, 2, 2, 0, 0],
           [5, 4, 5, 0, 0, 0, 0, 5, 5, 0, 0],
           [0, 0, 0, 0, 5, 0, 1, 0, 0, 5, 0],
           [4, 3, 4, 0, 0, 0, 0, 5, 5, 0, 1],
           [0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4],
           [0, 0, 0, 2, 0, 2, 5, 0, 0, 1, 2],
           [0, 0, 0, 0, 5, 0, 0, 0, 0, 4, 0],
           [1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0],
           [2, 1, 0, 2, 0, 5, 3, 0, 1, 0, 1]]
    return(np.mat(M))
In [3]:
def euclidSim(inA,inB):
    return 1.0/(1.0 + la.norm(inA - inB))

def pearsonSim(inA,inB):
    if len(inA) < 3 : return 1.0
    return 0.5+0.5*corrcoef(inA, inB, rowvar = 0)[0][1]

def cosineSim(inA,inB):
    num = float(inA.T*inB)
    denom = la.norm(inA)*la.norm(inB)
    return 0.5+0.5*(num/denom)
In [4]:
A = np.array([2,3,0,1,0,4,-5])
B = np.array([0,1,2,-4,2,0,3])
A = mat(A)
B = mat(B)
In [5]:
print(euclidSim(A.T,B.T))

0.08333333333333333
In [6]:
print(cosineSim(A.T,B.T))

0.3150010839748479
In [7]:
print(pearsonSim(A.T,B.T))

0.2665380020120951
In [8]:
def standEst(dataMat, user, simMeas, item):
    n = shape(dataMat)[1]
    simTotal = 0.0; ratSimTotal = 0.0
    for j in range(n):
        userRating = dataMat[user,j]
        if userRating == 0: 
            continue
        overLap = nonzero(logical_and(dataMat[:,item]>0, dataMat[:,j]>0))[0]
        if len(overLap) == 0: 
            similarity = 0
        else: 
            similarity = simMeas(dataMat[overLap,item], dataMat[overLap,j])
        #print('the %d and %d similarity is: %f' % (item, j, similarity))
        simTotal += similarity
        ratSimTotal += similarity * userRating
    if simTotal == 0: return 0
    else: return ratSimTotal/simTotal
In [9]:
def svdEst(dataMat, user, simMeas, item):
    n = shape(dataMat)[1]
    simTotal = 0.0; ratSimTotal = 0.0
    data=mat(dataMat)
    U,Sigma,VT = la.svd(data)
    Sig4 = mat(eye(4)*Sigma[:4]) #arrange Sig4 into a diagonal matrix
    xformedItems = data.T * U[:,:4] * Sig4.I  #create transformed items
    for j in range(n):
        userRating = data[user,j]
        if userRating == 0 or j==item: continue
        similarity = simMeas(xformedItems[item,:].T, xformedItems[j,:].T)
        #print('the %d and %d similarity is: %f' % (item, j, similarity))
        simTotal += similarity
        ratSimTotal += similarity * userRating
    if simTotal == 0: return 0
    else: return ratSimTotal/simTotal
In [10]:
def recommend(dataMat, user, N=3, simMeas=cosineSim, estMethod=standEst):
    unratedItems = nonzero(dataMat[user,:].A==0)[1] #find unrated items 
    if len(unratedItems) == 0: return 'you rated everything'
    itemScores = []
    for item in unratedItems:
        estimatedScore = estMethod(dataMat, user, simMeas, item)
        itemScores.append((item, estimatedScore))
    return sorted(itemScores, key=lambda jj: jj[1], reverse=True)[:N]
In [11]:
data = loadData()
print(data)

[[0 0 0 0 0 4 0 0 0 0 5]
 [0 0 0 3 0 4 0 0 0 0 3]
 [0 0 0 0 4 0 0 1 0 4 0]
 [3 3 4 0 0 0 0 2 2 0 0]
 [5 4 5 0 0 0 0 5 5 0 0]
 [0 0 0 0 5 0 1 0 0 5 0]
 [4 3 4 0 0 0 0 5 5 0 1]
 [0 0 0 4 0 4 0 0 0 0 4]
 [0 0 0 2 0 2 5 0 0 1 2]
 [0 0 0 0 5 0 0 0 0 4 0]
 [1 0 0 0 0 0 0 1 2 0 0]
 [2 1 0 2 0 5 3 0 1 0 1]]
In [12]:
D=mat(data)
U,Sigma,VT = la.svd(D)
Sig4 = mat(eye(4)*Sigma[:4]) #arrange Sig4 into a diagonal matrix
xItems = data.T * U[:,:4] * Sig4.I  #create transformed items
print(xItems)

[[-0.45889187  0.03170418 -0.01809311  0.11036907]
 [-0.3622062   0.04692163 -0.01141864  0.04254964]
 [-0.45537578  0.10423397 -0.00800224 -0.05403528]
 [-0.051868   -0.39701598 -0.05950012  0.06753374]
 [-0.01726089 -0.08392364  0.71965471 -0.13098077]
 [-0.09964753 -0.67126432 -0.11207725 -0.04038616]
 [-0.04619366 -0.25745027  0.05860349  0.87744841]
 [-0.45397947  0.09523267  0.03757744 -0.09430203]
 [-0.46909953  0.0672883  -0.0131357   0.00911101]
 [-0.01955354 -0.10798751  0.67233514  0.01344801]
 [-0.09629148 -0.52832652 -0.09176174 -0.42505074]]
In [13]:
user = 4
recommendations = recommend(data, user, N=4, simMeas=cosineSim, estMethod=standEst)
print(recommendations)

[(4, 5.0), (9, 5.0), (10, 4.804196825932594), (3, 4.666666666666667)]
In [14]:
print("Recommended Items for User", user, ":\n")
for i, p in recommendations:
    print("Item ", i, "with predicted rating: ", p, "\n")

Recommended Items for User 4 :

Item  4 with predicted rating:  5.0 

Item  9 with predicted rating:  5.0 

Item  10 with predicted rating:  4.804196825932594 

Item  3 with predicted rating:  4.666666666666667
In [15]:
user = 4
recommendations = recommend(data, user, N=4, simMeas=cosineSim, estMethod=svdEst)
print(recommendations)

[(10, 4.808129974963378), (4, 4.80785278924504), (9, 4.803516888538971), (5, 4.79538416477759)]
In [16]:
print("Recommended Items for User", user, ":\n")
for i, p in recommendations:
    print("Item ", i, "with predicted rating: ", p, "\n")

Recommended Items for User 4 :

Item  10 with predicted rating:  4.808129974963378 

Item  4 with predicted rating:  4.80785278924504 

Item  9 with predicted rating:  4.803516888538971 

Item  5 with predicted rating:  4.79538416477759
In [ ]: