GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity of increasing plus-convex-along-rays(IPCAR)functions defined on a real normed linear space X.We also study,for this class of functions,some concepts of abstract convexity,such as support sets and subdifferentials.Finally,as an application,we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.

NIA2: A fast indirect association mining algorithm

Indirect association is a high level relationship between items and frequent item sets in data. There are many potential applications for indirect associations, such as database marketing, intelligent data analysis, web -log analysis, recommended system, etc. Existing indirect association mining algorithms are mostly based on the notion of post - processing of discovery of frequent item sets. In the mining process, all frequent item sets need to be generated first, and then they are fihered and joined to form indirect associations. We have presented an indirect association mining algorithm （NIA） based on anti -monotonicity of indirect associations whereas k candidate indirect associations can be generated directly from k - 1 candidate indirect associations, without all frequent item sets generated. We also use the frequent itempair support matrix to reduce the time and memory space needed by the algorithm. In this paper, a novel algorithm （NIA2） is introduced based on the generation of indirect association patterns between itempairs through one item mediator sets from frequent itempair support matrix. A notion of mediator set support threshold is also presented. NIA2 mines indirect association patterns directly from the dataset, without generating all frequent item sets. The frequent itempair support matrix and the notion of using tm as the support threshold for mediator sets can significantly reduce the cost of joint operations and the search process compared with existing algorithms. Results of experiments on a real - word web log dataset have proved NIA2 one order of magnitude faster than existing algorithms.

Iterative subspace matching pursuit for joint sparse recovery

Joint sparse recovery(JSR)in compressed sensing(CS)is to simultaneously recover multiple jointly sparse vectors from their incomplete measurements that are conducted based on a common sensing matrix.In this study,the focus is placed on the rank defective case where the number of measurements is limited or the signals are significantly correlated with each other.First,an iterative atom refinement process is adopted to estimate part of the atoms of the support set.Subsequently,the above atoms along with the measurements are used to estimate the remaining atoms.The estimation criteria for atoms are based on the principle of minimum subspace distance.Extensive numerical experiments were performed in noiseless and noisy scenarios,and results reveal that iterative subspace matching pursuit(ISMP)outperforms other existing algorithms for JSR.