The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distanc...The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distance and Tukey M-estimator.Firstly,we propose a k-distancebased method to compute user suspicion degree(USD).The reliable neighbor model can be constructed through incorporating the user suspicion degree into user neighbor model.The influence of attack profiles on the recommendation results is reduced through adjusting similarities among users.Then,Tukey M-estimator is introduced to construct robust matrix factorization model,which can realize the robust estimation of user feature matrix and item feature matrix and reduce the influence of attack profiles on item feature matrix.Finally,a robust collaborative recommendation algorithm is devised by combining the reliable neighbor model and robust matrix factorization model.Experimental results show that the proposed algorithm outperforms the existing methods in terms of both recommendation accuracy and robustness.展开更多
The purpose of this paper is to broaden the knowledge of mean difference and,<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="fon...The purpose of this paper is to broaden the knowledge of mean difference and,<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">in particular, of an important distribution model known as Tukey lambda, which is generally used to choose a model to fit data.<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">We have obtained compact formulas, which are not yet reported in literature, of mean deviation and mean difference related to the said distribution model.<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">These results made it possible to analyze the relationships among variability indexes, namely standard deviation, mean deviation and mean difference, regarding Tukey lambda model.展开更多
Tukey's halfspace median(HM), servicing as the multivariate counterpart of the univariate median,has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness pr...Tukey's halfspace median(HM), servicing as the multivariate counterpart of the univariate median,has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness property(the most outstanding property) of the univariate median. One of prevalent quantitative assessments of robustness is finite sample breakdown point(FSBP). Indeed, the FSBP of many multivariate medians have been identified, except for the most prevailing one—the Tukey's halfspace median. This paper presents a precise result on FSBP for Tukey's halfspace median. The result here depicts the complete prospect of the global robustness of HM in the finite sample practical scenario, revealing the dimension effect on the breakdown point robustness and complimenting the existing asymptotic breakdown point result.展开更多
Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey＇s halfspace median （1） has been obtained in the literature. In this paper, we establish the resu...Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey＇s halfspace median （1） has been obtained in the literature. In this paper, we establish the result under weaker assumptions imposed on underlying distribution （weak smoothness） and on data set （not necessary in general position）. The refined representation of Tukey＇s sample depth regions for data set not necessary in general position is also obtained, as a by-product of our derivation.展开更多
基金National Natural Science Foundation of China under Grant No.61379116，Natural Science Foundation of Hebei Province under Grant No.F2015203046 and No.F2013203124，Key Program of Research on Science and Technology of Higher Education Institutions of Hebei Province under Grant No.ZH2012028
文摘The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distance and Tukey M-estimator.Firstly,we propose a k-distancebased method to compute user suspicion degree(USD).The reliable neighbor model can be constructed through incorporating the user suspicion degree into user neighbor model.The influence of attack profiles on the recommendation results is reduced through adjusting similarities among users.Then,Tukey M-estimator is introduced to construct robust matrix factorization model,which can realize the robust estimation of user feature matrix and item feature matrix and reduce the influence of attack profiles on item feature matrix.Finally,a robust collaborative recommendation algorithm is devised by combining the reliable neighbor model and robust matrix factorization model.Experimental results show that the proposed algorithm outperforms the existing methods in terms of both recommendation accuracy and robustness.
文摘The purpose of this paper is to broaden the knowledge of mean difference and,<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">in particular, of an important distribution model known as Tukey lambda, which is generally used to choose a model to fit data.<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">We have obtained compact formulas, which are not yet reported in literature, of mean deviation and mean difference related to the said distribution model.<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">These results made it possible to analyze the relationships among variability indexes, namely standard deviation, mean deviation and mean difference, regarding Tukey lambda model.
基金supported by National Natural Science Foundation of China(Grant Nos.11601197,11461029,71463020,61263014 and 61563018),National Natural Science Foundation of China(Grant Nos.General program 11171331 and Key program 11331011)National Science Foundation of Jiangxi Province(Grant Nos.20161BAB201024,20142BAB211014,20143ACB21012 and 20151BAB211016)+3 种基金the Key Science Fund Project of Jiangxi Provincial Education Department(Grant Nos.GJJ150439,KJLD13033 and KJLD14034)the National Science Fund for Distinguished Young Scholars in China(Grant No.10725106)a grant from the Key Lab of Random Complex Structure and Data Science,Chinese Academy of SciencesNatural Science Foundation of Shenzhen University
文摘Tukey's halfspace median(HM), servicing as the multivariate counterpart of the univariate median,has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness property(the most outstanding property) of the univariate median. One of prevalent quantitative assessments of robustness is finite sample breakdown point(FSBP). Indeed, the FSBP of many multivariate medians have been identified, except for the most prevailing one—the Tukey's halfspace median. This paper presents a precise result on FSBP for Tukey's halfspace median. The result here depicts the complete prospect of the global robustness of HM in the finite sample practical scenario, revealing the dimension effect on the breakdown point robustness and complimenting the existing asymptotic breakdown point result.
基金Supported by NSF of China(Grant Nos.11601197,11461029 and 61563018)Ministry of Education Humanity Social Science Research Project of China(Grant No.15JYC910002)+2 种基金China Postdoctoral Science Foundation Funded Project(Grant Nos.2016M600511 and 2017T100475)NSF of Jiangxi Province(Grant Nos.20171ACB21030,20161BAB201024 and 20161ACB20009)the Key Science Fund Project of Jiangxi Provincial Education Department(Grant Nos.GJJ150439,KJLD13033 and KJLD14034)
文摘Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey＇s halfspace median （1） has been obtained in the literature. In this paper, we establish the result under weaker assumptions imposed on underlying distribution （weak smoothness） and on data set （not necessary in general position）. The refined representation of Tukey＇s sample depth regions for data set not necessary in general position is also obtained, as a by-product of our derivation.
