基于带偏倚最大间隔二值矩阵分解的多值矩阵分层填充
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摘要
最大间隔矩阵分解是解决矩阵填充的重要方法,它通过将每个项目投影到低维特征空间,构建出每个用户的超平面,对每个项目进行分类来完成矩阵填充.然而传统的最大间隔矩阵分解方法对二值矩阵进行分解时都假设所构造的超平面经过原点.为了使超平面具有普适性,提高分类效果,将超平面移动一定的偏倚量,提出了带偏倚的最大间隔二值矩阵分解方法.对于多值矩阵的填充问题,通过多次采用上述改进的二值矩阵分解方法,对多值矩阵进行分层填充,并采用交替优化的方法进行求解.在真实数据集Movielens上的实验结果优于目前已有的方法,并且在较低维的特征空间中就能够完成矩阵分解,能有效提高矩阵分解速度,减少计算内存.
The matrix factorization based on collaborative filtering is an important method in matrix completion,and in the bi-level Maximum margin matrix factorization,we can vieweach item in a lowrank feature space,for each user,there is a hyperplane to classify each item,therefore we can compute the unobserved data by compute the hyperplane. However,all of the hyperplanes pass through the origin in the feature space,and this may result in a classified loss. So,we move each hyperplane from the origin so that there is a bias in each user. Based on this we propose binary maximum margin matrix factorization with bias. Furthermore,for the multi-valued matrix,we complete it by using several binary classifiers. The experimental result on the real data set Movielens is better than the other ten well-known algorithms,we also showthat our method can be achieve in a very lowrank feature space,and this can improve the speed of matrix factorization.
The matrix factorization based on collaborative filtering is an important method in matrix completion,and in the bi-level Maximum margin matrix factorization,we can vieweach item in a lowrank feature space,for each user,there is a hyperplane to classify each item,therefore we can compute the unobserved data by compute the hyperplane. However,all of the hyperplanes pass through the origin in the feature space,and this may result in a classified loss. So,we move each hyperplane from the origin so that there is a bias in each user. Based on this we propose binary maximum margin matrix factorization with bias. Furthermore,for the multi-valued matrix,we complete it by using several binary classifiers. The experimental result on the real data set Movielens is better than the other ten well-known algorithms,we also showthat our method can be achieve in a very lowrank feature space,and this can improve the speed of matrix factorization.
引文
[1]Kumar V,Pujari A K,Sahu S K,et al.Collaborative filtering using multiple binary maximum margin matrix factorizations[J].Information Sciences,2017,380(C):1-11.
[2]Lee D.Learning the parts of objects with nonnegative matrix factorization[J].Nature,1999,401(6755):788-791.
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[5]Rennie J D M,Srebro N.Fast maximum margin matrix factorization for collaborative prediction[C].International Conference,DBLP,2005:713-719.
[6]Liu Y,Zhang H H,Wu Y.Hard or soft classification?large-margin unified machines[J].Journal of the American Statistical Association,2011,106(493):166-177.
[7]Decoste D.Collaborative prediction using ensembl-es of maximum margin matrix factorizations[C].International Conference,2006:249-256.
[8]Weimer M,Karatzoglou A,Smola A.Improving maximum margin matrix factorization[J].M achine Learning,2008,72(3):263-276.
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[11]Yu G W,Yu G W.Effective latent models for binary feedback in recommender systems[C].International ACM SIGIR Conference on Research and Development in Information Retrieval,ACM,2015:313-322.
[12]Rendle S,Freudenthaler C,Gantner Z,et al.BPR:Bayesian personalized ranking from implicit feed-back[C].Conference on Uncertainty in Artificial Intelligence,AUAI Press,2009:452-461.
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[14]Zhong E,Fan W,Yang Q.Contextual collab-orative?ltering via hierarchical matrix factorization[C].Proceedings of SIAM International Conference on Data M ining,2012:744-755.
[15]Zhao Jun,Wang Hong,Yin Fang-yong.Collaborative recommendation for sparse rating w ith spammer[J].Journal of Chinese Computer Systems,2017,38(3):472-477.
[16]Sun Hong,Han Zhen.Improved collaborative filtering algorithm based on popularity of items[J].Journal of Chinese Computer Systems,2018,39(4):638-643.
[17]Tong Z,Oles F J.Text categorization based on regularized linear classification methods[J].Information Retrieval,2001,4(1):5-31.
[18]Paatero P.Least squares formulation of robust no-nnegative factor analysis[J].Chemometrics&Intelligent Laboratory Systems,1997,37(1):23-35.
[19]Fazel M,Hindi H,Boyd SP.A rank minimizationheuristic with application to minimum order system approximation[C].American Control Conference,Proceedings of the.IEEE,2001:4734-4739.
[20]Marlin B.Modeling user rating profiles for collaborative filtering[C].International Conference on Neural Information Processing Systems,M IT Press,2003:627-634.
[21]Salakhutdinov R,Mnih A.Probabilistic matrix factorization[C].International Conference on Neural Information Processing Systems,Curran Associates Inc,2007:1257-1264.
[22]Salakhutdinov R,Mnih A.Bayesian probabilistic matrix factorization using M arkov chain monte carlo[C].International Conference on M achine Learning,ACM,2008:880-887.
[23]Lawrence N D,Urtasun R.Non-linear matrix factorization with Gaussian processes[C].International Conference on M achine Learning,ACM,2009:601-608.
[15]赵军,王红,殷方勇.一种面向稀疏和虚假评分的协同推荐方法[J].小型微型计算机系统,2017,38(3):472-477.
[16]孙红,韩震.融合物品热门因子的协同过滤改进算法[J].小型微型计算机系统,2018,39(4):638-643.
[2]Lee D.Learning the parts of objects with nonnegative matrix factorization[J].Nature,1999,401(6755):788-791.
[3]Sarwar B,Konstan J,Riedl J.Incremental singular value decomposition algorithms for highly[C].International Conference on Computer&Information Science,2002:27-28.
[4]Srebro N,Rennie J D M,Jaakkola T.Maximum-margin matrix factorization[J].Advances in Neural Information Processing Systems,2005,37(2):1329-1336.
[5]Rennie J D M,Srebro N.Fast maximum margin matrix factorization for collaborative prediction[C].International Conference,DBLP,2005:713-719.
[6]Liu Y,Zhang H H,Wu Y.Hard or soft classification?large-margin unified machines[J].Journal of the American Statistical Association,2011,106(493):166-177.
[7]Decoste D.Collaborative prediction using ensembl-es of maximum margin matrix factorizations[C].International Conference,2006:249-256.
[8]Weimer M,Karatzoglou A,Smola A.Improving maximum margin matrix factorization[J].M achine Learning,2008,72(3):263-276.
[9]Xu M,Zhu J,Zhang B.Bayesian nonparametric maximum margin matrix factorization for collaborative prediction[C].Advances in Neural Information Processing Systems,2012:64-72.
[10]Xu M,Zhu J,Zhang B.Fast max-margin matrix factorization with data augmentation[C].International Conference on M achine Learning,2013:978-986.
[11]Yu G W,Yu G W.Effective latent models for binary feedback in recommender systems[C].International ACM SIGIR Conference on Research and Development in Information Retrieval,ACM,2015:313-322.
[12]Rendle S,Freudenthaler C,Gantner Z,et al.BPR:Bayesian personalized ranking from implicit feed-back[C].Conference on Uncertainty in Artificial Intelligence,AUAI Press,2009:452-461.
[13]Kumar V,Pujari A K,Sahu S K,et al.Proximal maximum margin matrix factorization for collabor-ative filtering[J].Pattern Recognition Letters,2016,86(2017):62-67.
[14]Zhong E,Fan W,Yang Q.Contextual collab-orative?ltering via hierarchical matrix factorization[C].Proceedings of SIAM International Conference on Data M ining,2012:744-755.
[15]Zhao Jun,Wang Hong,Yin Fang-yong.Collaborative recommendation for sparse rating w ith spammer[J].Journal of Chinese Computer Systems,2017,38(3):472-477.
[16]Sun Hong,Han Zhen.Improved collaborative filtering algorithm based on popularity of items[J].Journal of Chinese Computer Systems,2018,39(4):638-643.
[17]Tong Z,Oles F J.Text categorization based on regularized linear classification methods[J].Information Retrieval,2001,4(1):5-31.
[18]Paatero P.Least squares formulation of robust no-nnegative factor analysis[J].Chemometrics&Intelligent Laboratory Systems,1997,37(1):23-35.
[19]Fazel M,Hindi H,Boyd SP.A rank minimizationheuristic with application to minimum order system approximation[C].American Control Conference,Proceedings of the.IEEE,2001:4734-4739.
[20]Marlin B.Modeling user rating profiles for collaborative filtering[C].International Conference on Neural Information Processing Systems,M IT Press,2003:627-634.
[21]Salakhutdinov R,Mnih A.Probabilistic matrix factorization[C].International Conference on Neural Information Processing Systems,Curran Associates Inc,2007:1257-1264.
[22]Salakhutdinov R,Mnih A.Bayesian probabilistic matrix factorization using M arkov chain monte carlo[C].International Conference on M achine Learning,ACM,2008:880-887.
[23]Lawrence N D,Urtasun R.Non-linear matrix factorization with Gaussian processes[C].International Conference on M achine Learning,ACM,2009:601-608.
[15]赵军,王红,殷方勇.一种面向稀疏和虚假评分的协同推荐方法[J].小型微型计算机系统,2017,38(3):472-477.
[16]孙红,韩震.融合物品热门因子的协同过滤改进算法[J].小型微型计算机系统,2018,39(4):638-643.
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