Fisher'S Discriminant Analysis with Space Folding and Discriminant Analysis by the Posterior of Gaussian Mixtures(II)

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簡歷

基本資料

Project title

Code/計畫編號

MOST108-2221-E019-028-MY2

Translated Name/計畫中文名

協同空間摺疊操作之費雪判別分析與事後混合判別分析(II)

Project Coordinator/計畫主持人

Chin-Chun Chang

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Computer Science and Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=13328063

Year

2020

Start date/計畫起

01-08-2020

Expected Completion/計畫迄

31-07-2021

Bugetid/研究經費

748千元

ResearchField/研究領域

資訊科學--軟體

"費雪判別分析是一個常用的監督式降維/判別特徵抽取法。由於費雪判別分析假設資料具等分散性，它可能無法有效地處理具不等變異性 (heteroscedasticity) 或類別內資料具多峰性 (mulit-modality)的資料。在這兩年計畫，我們將發展兩個演算法來補強其弱點。使用線性整流函數(ReLU)為觸發函數的深向前傳導類神經網路(deep feedforward neural networks)，可藉由連續的空間摺疊，將數個在輸入空間的區域對映至相同輸出。由那個神經網路架構的啟發，我們將在第一年使用線性整流函數發展一個折疊費雪判別分析找不到判別資訊的子空間的演算法。藉由連續的空間摺疊幫助費雪判別分析找到更多判別資訊。第二年，我們將發展基於事後機率的混合判別分析演算法(mixture discriminant analysis)。目前混合判別分析與子類別分析(subclass discriminant analysis)都先學習每個類別的混合分布(mixture distribution)或子類別結構(subclass structure)，然後再做判別分析。擬發展的方法則是從事後機率(posterior probability)得到抽取判別特徵的轉換矩陣。由於事後機率直接關聯到類別判定，並且在這個問題，學習事後機率不會難於學習每個類別的混合分佈。所欲發展的演算法可期待優於目前的方法。這兩個將要發展的演算法都是新穎、可行並且可以補強費雪判別分析的弱點。他們將可擴大費雪判別分析的適用範圍。""Fisher's discriminant analysis (FDA) is a popular supervised dimensionality reduction/feature extraction method. Due to the assumption that the data have a Gaussian homoscedastic class structure, FDA can be incapable of dealing explicitly with heteroscedastic or multi-modal data. In this two-year project, we shall develop two algorithms to improve the weaknesses of FDA. Deep feedforward neural networks with rectified linear units (ReLUs) as activation functions can map many input neighborhoods to similar outputs by successively space folding. Inspired by that architecture of deep neural networks, in the first year, we shall develop an algorithm which can successively fold the subspace, where FDA fails to find discriminatory information, by ReLUs to help FDA to discover more discriminatory information. In the second year, we shall develop an algorithm for mixture discriminant analysis by the posterior probability. Existing algorithms of mixture discriminant analysis and subclass discriminant analysis usually perform discriminant analysis on the learned mixture distribution or the learned subclass structure for each class. Unlike the existing approach, the algorithm to develop learns the transformation matrix for extracting discriminatory features on the learned posterior probability. Because the posterior probability is directly relevant to discrimination, and learning the posterior probability in this circumstance is not more difficult than learning the mixture distribution for each class, it can be expected that the algorithm to develop can be superior to the existing algorithms. The two algorithms to develop are novel, feasible, and helpful for improving the weakness of FDA. These two algorithms will be useful for broadening the application of FDA."

Keyword(s)

費雪判別分析
線性整流函數
混合判別分析
Fisher's discriminant analysis
Rectified Linear Units
Mixture Discriminant Analysis

DSpace CRIS

Fisher'S Discriminant Analysis with Space Folding and Discriminant Analysis by the Posterior of Gaussian Mixtures(II)

基本資料

Description