Orthogonal nonnegative learning for sparse feature extraction and approximate combinatorial optimization

作     者：Erkki OJA Zhirong YANG 

作者机构：Department of Information and Computer ScienceAalto UniversityFI-00076 AaltoEspooFinland 

出 版 物：《Frontiers of Electrical and Electronic Engineering in China》 (中国电气与电子工程前沿（英文版）)

年 卷 期：2010年第5卷第3期

页      面：261-273页

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

主　　题：nonnegative factorization sparse feature extraction orthogonal learning clustering 

摘      要：Nonnegativity has been shown to be a powerful principle in linear matrix decompositions,leading to sparse component matrices in feature analysis and data *** classical method is Lee and Seung’s Nonnegative Matrix Factorization.A standard way to form learning rules is by multiplicative updates,maintaining ***,a generic principle is presented for forming multiplicative update rules,which integrate an orthonormality constraint into nonnegative *** principle,called Orthogonal Nonnegative Learning(ONL),is rigorously derived from the Lagrangian *** examples,the proposed method is applied for transforming Nonnegative Matrix Factorization(NMF)and its variant,Projective Nonnegative Matrix Factorization(PNMF),into their orthogonal *** general,it is well-known that orthogonal nonnegative learning can give very useful approximative solutions for problems involving non-vectorial data,for example,binary *** optimization is replaced by continuous-space gradient optimization which is often computationally *** is shown how the multiplicative updates rules obtained by using the proposed ONL principle can find a nonnegative and highly orthogonal matrix for an approximated graph partitioning *** empirical results on various graphs indicate that our nonnegative learning algorithms not only outperform those without the orthogonality condition,but also surpass other existing partitioning approaches.