設計的VC維度

Abstract

對一t-(v,k,λ)區族設計D=(X,B)而言，其VC維度定義為X 中滿足下列條件的子集A： 每一個A 的子集合C 都存在一個在區族集B中的區族B，使得 C=A∩B。在這篇論文我們探討t-(v,k,λ) 區族設計的VC維度的基本性質，並且運用他們完整的決定當 λ = 1 且t = 2 和t = 3 時，這兩類區族設計的VC維度。

The Vapnik-Chervonenkis dimension of a t-(v,k,λ) design D =(X, B) is the largest cardinality of a subset A of X such that for each subset C there exists a block Β∈B such that C=A∩B. In this thesis we give some general properties of the Vapnik-Chervonenkis dimension of a t-(v,k,λ) design, and use them to completely determine the Vapnik-Chervonenkis dimension of a t-(v,k,1) design for t = 2 and t = 3.