svd 做协同过滤

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Jun 20 21:02:58 2018

@author: luogan
"""

#coding=UTF-8
from numpy import *
from numpy import linalg as la

def loadExData():
    return[[0, 0, 0, 2, 2],
           [0, 0, 0, 3, 3],
           [0, 0, 0, 1, 1],
           [1, 1, 1, 0, 0],
           [2, 2, 2, 0, 0],
           [5, 5, 5, 0, 0],
           [1, 1, 1, 0, 0]]

def loadExData2():
    return[[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]]

def ecludSim(inA,inB):
    return 1.0/(1.0 + la.norm(inA - inB))

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

def cosSim(inA,inB):
    num = float(inA.T*inB)
    denom = la.norm(inA)*la.norm(inB)
    return 0.5+0.5*(num/denom)

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].A>0, \
                                      dataMat[:,j].A>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

def svdEst(dataMat, user, simMeas, item):
    n = shape(dataMat)[1]
    simTotal = 0.0; ratSimTotal = 0.0
    U,Sigma,VT = la.svd(dataMat)
    Sig4 = mat(eye(4)*Sigma[:4]) #arrange Sig4 into a diagonal matrix
    xformedItems = dataMat.T * U[:,:4] * Sig4.I  #create transformed items
    Sig = mat(eye(n)*Sigma) #arrange Sig4 into a diagonal matrix
    #print Sig
    #print U * Sig * VT #back up source mat
    #print xformedItems #item feature begin compute item similer
    #print "user feature:"
    #xformedUsers = dataMat * VT[:,:4] * Sig4
    #print xformedUsers
    #print  xformedUsers * xformedItems.T
    #print dataMat
    for j in range(n):
        userRating = dataMat[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

def recommend(dataMat, user, N=3, simMeas=cosSim, estMethod=standEst):
    #print 'type', dataMat[:,:4] #the number user line or col
    print (nonzero(dataMat[user,:].A==0)) # to array
    unratedItems=nonzero(dataMat[user,:].A==0)[1]
    print (unratedItems)
    #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]

def printMat(inMat, thresh=0.8):
    for i in range(32):
        for k in range(32):
            if float(inMat[i,k]) > thresh:
                print (1),
            else: print( 0),
        print ('')

def imgCompress(numSV=3, thresh=0.8):
    myl = []
    for line in open('0_5.txt').readlines():
        newRow = []
        for i in range(32):
            newRow.append(int(line[i]))
        myl.append(newRow)
    myMat = mat(myl)
    print ("****original matrix******")
    printMat(myMat, thresh)
    U,Sigma,VT = la.svd(myMat)
    SigRecon = mat(zeros((numSV, numSV)))
    for k in range(numSV):#construct diagonal matrix from vector
        SigRecon[k,k] = Sigma[k]
    reconMat = U[:,:numSV]*SigRecon*VT[:numSV,:]
    print ("****reconstructed matrix using %d singular values******" % numSV)
    printMat(reconMat, thresh)
if __name__ == '__main__':
    print ("begin")
    myData=loadExData2()
    myMat=mat(myData)
    #myMat = mat(loadExData)
    recommend(myMat, 2, 3, cosSim, svdEst)

begin
(array([0, 0, 0, 0, 0, 0, 0, 0]), array([ 0,  1,  2,  3,  5,  6,  8, 10]))
[ 0  1  2  3  5  6  8 10]
the 0 and 4 similarity is: 0.487100
the 0 and 7 similarity is: 0.996341
the 0 and 9 similarity is: 0.490280
the 1 and 4 similarity is: 0.485583
the 1 and 7 similarity is: 0.995886
the 1 and 9 similarity is: 0.490272
the 2 and 4 similarity is: 0.485739
the 2 and 7 similarity is: 0.995963
the 2 and 9 similarity is: 0.490180
the 3 and 4 similarity is: 0.450495
the 3 and 7 similarity is: 0.482175
the 3 and 9 similarity is: 0.522379
the 5 and 4 similarity is: 0.506795
the 5 and 7 similarity is: 0.494716
the 5 and 9 similarity is: 0.496130
the 6 and 4 similarity is: 0.434401
the 6 and 7 similarity is: 0.479543
the 6 and 9 similarity is: 0.583833
the 8 and 4 similarity is: 0.490037
the 8 and 7 similarity is: 0.997067
the 8 and 9 similarity is: 0.490078
the 10 and 4 similarity is: 0.512896
the 10 and 7 similarity is: 0.524970
the 10 and 9 similarity is: 0.493617