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

【摘要】：經(jīng)典的康托集合理論中,一個(gè)對(duì)象與一個(gè)樣本的關(guān)系只可能有兩種:屬于和不屬于。這樣帶來(lái)了計(jì)算的方便性,但是現(xiàn)實(shí)中的很多問(wèn)題無(wú)法描述,Zadeh教授的模糊集理論成功解決了這一問(wèn)題。但是需要計(jì)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(jì)算方法常需要指定特定函數(shù)進(jìn)行擬合,依賴(lài)與專(zhuān)家的經(jīng)驗(yàn)。為此我們提出一種基于標(biāo)簽語(yǔ)義學(xué)和原型理論的模糊重構(gòu)方法,用來(lái)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(gè)標(biāo)簽集的原型,然后使用原型重構(gòu)每個(gè)樣本,同時(shí)我們?cè)谥貥?gòu)時(shí)加入熵正則項(xiàng),限制重構(gòu)系數(shù)在區(qū)間[0,1]中,且所有的重構(gòu)系數(shù)和為1。其中求解的目標(biāo)為:argmin‖x-WP‖2/2+λPIn(PT),s.t.∑wi≤1,wi0。求解的目標(biāo)為最小化重構(gòu)誤差,最大化熵。此目標(biāo)函數(shù)可以保證在盡可能小的重構(gòu)誤差的基礎(chǔ)上,每個(gè)點(diǎn)都盡可能的參與重構(gòu)的過(guò)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(gòu)系數(shù)有物理意義。根據(jù)重構(gòu)系數(shù)可以得到標(biāo)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(biāo)簽語(yǔ)義學(xué)和原型理論的模糊重構(gòu)方法求解隸屬度函數(shù),可以保證隸屬度函數(shù)具有標(biāo)簽集相關(guān)性、重構(gòu)性和保序性。在手寫(xiě)數(shù)字、人臉、聲吶信號(hào)等數(shù)據(jù)集上的模糊重構(gòu)的分類(lèi)實(shí)驗(yàn)表明,實(shí)驗(yàn)結(jié)果與傳統(tǒng)的算法相比具有較強(qiáng)的魯棒性,且對(duì)不同的數(shù)據(jù)分布不敏感,分類(lèi)效果均能達(dá)到較為先進(jìn)的水平。由此可以證明基于標(biāo)簽語(yǔ)義學(xué)和原型理論的模糊重構(gòu)方法可以得到與實(shí)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(hào)：2080017