Maximal pattern complexity, optimal solution to the pattern recognition problem, uniform set and super-stationary set

2019 Fiscal Year Final Research Report

• Project/Area Number: 26400121
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Osaka City University
• Principal Investigator: Kamae Teturo 大阪市立大学, 大学院理学研究科, 特任教授 (80047258)
• Project Period (FY): 2014-04-01 – 2020-03-31
• Keywords: 最大型複雑さ / パターン認識 / エントロピー

Outline of Final Research Achievements

We introduced the notion of the maximal pattern complexity for a family D of pictures on a canvas C. That is, let A be a finite set of the informations about colors, etc. at one point on the canbas. Then, an element in the power set (A to D) becomes a picture drawn on the canbas C, and a subset D of it becomes a family of pictures on C. The maximal pattern complexity p(D,k)(k=1,2,...) is defined as the maximum number of pictures in D distinguished by the observation at k sampling points. We call a k samling point optimal if it attains p(D,k). We studied for various families of pictures what is the maximal pattrn complexity, what is an optimal sampling points. Our studies have applications to the pattern recognition problem.

Free Research Field

エルゴード理論と記号力学系

Academic Significance and Societal Importance of the Research Achievements

有限個所の観測から全体のパターンを認識し識別することがパターン認識の基本原理である．このことの可能性や能率の良さ・限界について理論的考察を行った．これは実際問題への応用をもつとともに，問題の本質を明確化する大事な意味をもっている．さらに，n個の観測から得られる最大の情報量（最大型複雑さ）についての研究を行った．nに関するこれの漸近増加量P(n)Exp(an)のaはエントロピーとして知られている．これ次ぐ新たな量として多項式Pの次元を考察した．