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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Singapore Management University

2007

Constraint theory

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Full-Text Articles in Physical Sciences and Mathematics

Learning Nonparametric Kernel Matrices From Pairwise Constraints, Steven C. H. Hoi, Rong Jin, Michael R. Lyu Jun 2007

Learning Nonparametric Kernel Matrices From Pairwise Constraints, Steven C. H. Hoi, Rong Jin, Michael R. Lyu

Research Collection School Of Computing and Information Systems

Many kernel learning methods have to assume parametric forms for the target kernel functions, which significantly limits the capability of kernels in fitting diverse patterns. Some kernel learning methods assume the target kernel matrix to be a linear combination of parametric kernel matrices. This assumption again importantly limits the flexibility of the target kernel matrices. The key challenge with nonparametric kernel learning arises from the difficulty in linking the nonparametric kernels to the input patterns. In this paper, we resolve this problem by introducing the graph Laplacian of the observed data as a regularizer when optimizing the kernel matrix with …


Gprune: A Constraint Pushing Framework For Graph Pattern Mining, Feida Zhu, Xifeng Yan, Jiawei Han, Philip S. Yu May 2007

Gprune: A Constraint Pushing Framework For Graph Pattern Mining, Feida Zhu, Xifeng Yan, Jiawei Han, Philip S. Yu

Research Collection School Of Computing and Information Systems

In graph mining applications, there has been an increasingly strong urge for imposing user-specified constraints on the mining results. However, unlike most traditional itemset constraints, structural constraints, such as density and diameter of a graph, are very hard to be pushed deep into the mining process. In this paper, we give the first comprehensive study on the pruning properties of both traditional and structural constraints aiming to reduce not only the pattern search space but the data search space as well. A new general framework, called gPrune, is proposed to incorporate all the constraints in such a way that they …