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Full-Text Articles in Physical Sciences and Mathematics
Pattern Avoiding Partitions, Sequence A054391 And The Kernel Method, Toufik Mansour, Mark Shattuck
Pattern Avoiding Partitions, Sequence A054391 And The Kernel Method, Toufik Mansour, Mark Shattuck
Applications and Applied Mathematics: An International Journal (AAM)
Sequence A054391 in OEIS, which we will denote by an , counts a certain two-pattern avoidance class of the permutations of size n . In this paper, we provide additional combinatorial interpretations for these numbers in terms of finite set partitions. In particular, we identify six classes of the partitions of size n , all of which have cardinality an and each avoiding two classical patterns. We use both algebraic and combinatorial methods to establish our results. In one apparently more difficult case, to show the result, we make use of the kernel method in solving a system …
Double Updating Online Learning, Peilin Zhao, Steven C. H. Hoi, Rong Jin
Double Updating Online Learning, Peilin Zhao, Steven C. H. Hoi, Rong Jin
Research Collection School Of Computing and Information Systems
In most kernel based online learning algorithms, when an incoming instance is misclassified, it will be added into the pool of support vectors and assigned with a weight, which often remains unchanged during the rest of the learning process. This is clearly insufficient since when a new support vector is added, we generally expect the weights of the other existing support vectors to be updated in order to reflect the influence of the added support vector. In this paper, we propose a new online learning method, termed Double Updating Online Learning, or DUOL for short, that explicitly addresses this problem. …