發(fā)布時間：2018-06-29 00:26

  本文選題：模糊重構 + 原型理論��； 參考：《浙江大學》2017年碩士論文

【摘要】：經(jīng)典的康托集合理論中,一個對象與一個樣本的關系只可能有兩種:屬于和不屬于。這樣帶來了計算的方便性,但是現(xiàn)實中的很多問題無法描述,Zadeh教授的模糊集理論成功解決了這一問題。但是需要計算隸屬度函數(shù),隸屬度函數(shù)在模糊集理論中占有舉足輕重的地位。經(jīng)典的隸屬集函數(shù)計算方法常需要指定特定函數(shù)進行擬合,依賴與專家的經(jīng)驗。為此我們提出一種基于標簽語義學和原型理論的模糊重構方法,用來確定模糊集的隸屬度函數(shù)。首先我們依據(jù)原型理論求解出每個標簽集的原型,然后使用原型重構每個樣本,同時我們在重構時加入熵正則項,限制重構系數(shù)在區(qū)間[0,1]中,且所有的重構系數(shù)和為1。其中求解的目標為:argmin‖x-WP‖2/2+λPIn(PT),s.t.∑wi≤1,wi0。求解的目標為最小化重構誤差,最大化熵。此目標函數(shù)可以保證在盡可能小的重構誤差的基礎上,每個點都盡可能的參與重構的過程。加入系數(shù)的限制可以保證所有的系數(shù)都在區(qū)間[0,1]中,使重構系數(shù)有物理意義。根據(jù)重構系數(shù)可以得到標簽的概率密度函數(shù),依據(jù)概率密度函數(shù)可以求出隸屬度函數(shù)。使用基于標簽語義學和原型理論的模糊重構方法求解隸屬度函數(shù),可以保證隸屬度函數(shù)具有標簽集相關性、重構性和保序性。在手寫數(shù)字、人臉、聲吶信號等數(shù)據(jù)集上的模糊重構的分類實驗表明,實驗結果與傳統(tǒng)的算法相比具有較強的魯棒性,且對不同的數(shù)據(jù)分布不敏感,分類效果均能達到較為先進的水平。由此可以證明基于標簽語義學和原型理論的模糊重構方法可以得到與實際數(shù)據(jù)相符的隸屬度函數(shù)分布。
[Abstract]:In the classical Cantor set theory, there are only two kinds of relations between an object and a sample: belonging and not belonging. This leads to the convenience of calculation, but many problems in reality can not be described. Professor Zadeh's fuzzy set theory successfully solves this problem. But it is necessary to calculate membership function, which plays an important role in fuzzy set theory. The classical calculation method of membership set function often needs to specify a specific function to fit, depending on the experience of experts. Therefore, we propose a fuzzy reconstruction method based on label semantics and prototype theory, which can be used to determine the membership function of fuzzy sets. First, we solve the prototype of each tag set according to the prototype theory, then reconstruct each sample using the prototype. At the same time, we add the entropy canonical term to the reconstruction, limiting the reconstruction coefficient to be in the interval [0], and all the reconstruction coefficients sum up to 1. The target of solution is: 2 / 2 位 Pin (PT) s.t. 鈭，

本文編號：2080017