MM-001 25 基于SVD的推荐系统代码实现

Code implementation of SVD- d recommendation system

Data Example：

Coding Part：

\'\'\'
SVD(singular value decomposition) is widely used in Recommendation System.
Here we want to offer suggestions for visitors  d on the grades on all kinds of spots 
Because of the sparsity of the visitor-grades matrix, we choose SVD method,
which can compress the large matrix to a smaller one to save the computation time
\'\'\'
import numpy as np
import pandas as pd
#Using liner algebra module in numpy
from numpy import linalg as la

#Using test data for validation
def DataInput():
    f=open(\'C:/Users/Tinky/Desktop/data.csv\')
    M0=pd.read_csv(f)
    M=M0.iloc[:,1:]#M is a visitor-grades matrix
    return np.mat(M)

#Calculate the cosine similarity between vector X and vector Y
def cosSim(X,Y):
    vec_product=float(X.T*Y)
    norm_product=la.norm(X)*la.norm(Y)
    normalize=0.5*(vec_product/norm_product) +0.5#Normalization
    return normalize

#Calculate the threshold value of singular value proportion(K)
def sig_percentage(sig,percentage):
    tol_sig_Squaresum=sum(sig**2)
    initK_sig_Squaresum=K=0
    for i in sig:
        initK_sig_Squaresum+=i**2
        K+=1
        if initK_sig_Squaresum>=tol_sig_Squaresum*percentage:
            break
    return K

#Dimension reduction
def Reduction(data,percentage):
    U,S,Vt=la.svd(data)
    k=sig_percentage(S,percentage)
    sigK=np.mat(np.eye(k)*S[:k])  #The singular value matrix of SVD
    Vk=data.T*U[:,:k]*sigK.I  #Converted data of SPOT in k dimension linear space
    return Vk

#Evaluate the spots that visitors haven\'t been to by similarities
def Predict_score(data,visitor_Id,spot,percentage):
    n=np.shape(data)[1]#Read the column(size of the matrix\'s Second Dimension)
    tol_similarity=Gtol_similarity=0
    SVDreduction=Reduction(data,percentage)
    for j in range(n):
        visitorgrades=data[visitor_Id,j]
        if visitorgrades==0 or j==spot:
            continue
        similarity=cosSim(SVDreduction[spot,:].T,SVDreduction[j,:].T) #Calculate the similarity
        tol_similarity+=similarity
        Gtol_similarity+=similarity*visitorgrades
    if tol_similarity==0:
        return 0
    else:
        predict_score=Gtol_similarity/tol_similarity#Calculate the predict score
        return  predict_score

#Recommend the first k highest-score spots fot visitors
def recommend(data,visitor_Id,highest_k,percentage=0.9):
    unvisited_spot=np.nonzero(data[visitor_Id,:].A==0)[1]
    if len(unvisited_spot)==0:
        return 0
    Scores=[]
    # Predict the score
    for spot in unvisited_spot:
        Score=Predict_score(data,visitor_Id,spot,percentage)
        Scores.append((spot,Score))
    # Descending order
    Scores=sorted(Scores,key=lambda x:x[1],reverse=True)
    return Scores[:highest_k]

visitor_Id=10#Use visitor10 for example to test the model
result=pd.Data (recommend(DataInput(),visitor_Id,highest_k=5))
result.rename(columns={0:\'spot Id\',1:\'spot score\'}, inplace = True)
print(\"For visitor No.{}, we recommend:\".format(visitor_Id))
print(result)

Output：