Analysis-Synthesis Dictionary Learning for Universality-Particularity Representation Based Classification

Dictionary learning has played an important role in the success of sparse representation. Although synthesis dictionary learning for sparse representation has been well studied for universality representation (i.e., the dictionary is universal to all classes) and particularity representation (i.e., the dictionary is class-particular), jointly learning an analysis dictionary and a synthesis dictionary is still in its infant stage. Universality-particularity representation can well match the intrinsic characteristics of data (i.e., different classes share commonality and distinctness), while analysis-synthesis dictionary can give a more complete view of data representation (i.e., analysis dictionary is a dual-viewpoint of synthesis dictionary). In this paper, we proposed a novel model of analysis-synthesis dictionary learning for universality-particularity (ASDL-UP) representation based classification. The discrimination of universality and particularity representation is jointly exploited by simultaneously learning a pair of analysis dictionary and synthesis dictionary. More specifically, we impose a label preserving term to analysis coding coefficients for universality representation. Fisher-like regularizations for analysis coding coefficients and the subsequent synthesis representation are introduced to particularity representation. Compared with other state-of-the-art dictionary learning methods, ASDL-UP has shown better or competitive performance in various classification tasks.