偵測改變點之模糊逐段迴歸模式

Abstract

Tanaka and Ishibuchi 所提出的模糊迴歸分析法當資料變異非常大時，可能性模式所構成的區間很寬而必然性模式則無法算出；此外，他們的方法所求出的模式，其係數常不是模糊數。為處理資料變異大的問題，本文提一模糊逐段迴歸模式，並且也採用二次規劃來處理模糊數寬度為零的現象。本研究所提出模糊逐段迴歸模式有兩個優點：一、可同時算出模糊逐段迴歸模式和改變點位置；二、可透過自動區隔資料偵測到離群值。

The possibilistic regression analysis proposed by Tanaka and Ishibuchi, which is extremely sensitive to outliers, may not able to find feasible solution. Besides, when they use linear programming in possibilistic regression analysis, some coefficients are limited to be crisp because of the characteristic of linear programming. To overcome large variation problem, we propose fuzzy piecewise regression method. Our method can also treat the problem with crisp coefficients by utilizing quadratic programming approach. The proposed fuzzy piecewise regression method has two advantages: (a) It can detect the positions of change-points and can estimate the fuzzy piecewise regression model simultaneously; (b) It can deal with outliers by automatically segmenting the data.