On the Trace of Scatter Matrix Difference: A Convex Approximate Discriminant Analysis Formulation and Its Mechanism Research in Imperial Examination System

2015 ◽  
Vol 24 (05) ◽  
pp. 1550015
Author(s):  
Kun Li ◽  
Yongsheng Qian ◽  
Dejie Xu ◽  
Junwei Zeng ◽  
Min Wang ◽  
...  

In this paper, we present a convex discriminant analysis formulation, which is extended to solve multi-label classification problems. The original Linear Discriminant Analysis energy optimization function is turned into another form as a convex formulation (namely, convex Approximate LDA, denoted as “convexALDA” for short) using the generalized eigen-decomposition. We give applications by incorporating convexALDA as a regularizer into discriminant regression analysis. Extensive experimental results on multi-label classification tasks and an extensive application scenario on communication characteristics of imperial examination system are provided. In this way we have a brand-new comprehension for it, and a new idea and method was also put forward for studying the system.

Author(s):  
David Zhang ◽  
Fengxi Song ◽  
Yong Xu ◽  
Zhizhen Liang

In this chapter, we mainly present three kinds of weighted LDA methods. In Sections 5.1, 5.2 and 5.3, we respectively present parameterized direct linear discriminant analysis, weighted nullspace linear discriminant analysis and weighted LDA in the range of within-class scatter matrix. We offer a brief summery of the chapter in Section 5.4.


2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Zhicheng Lu ◽  
Zhizheng Liang

Linear discriminant analysis has been widely studied in data mining and pattern recognition. However, when performing the eigen-decomposition on the matrix pair (within-class scatter matrix and between-class scatter matrix) in some cases, one can find that there exist some degenerated eigenvalues, thereby resulting in indistinguishability of information from the eigen-subspace corresponding to some degenerated eigenvalue. In order to address this problem, we revisit linear discriminant analysis in this paper and propose a stable and effective algorithm for linear discriminant analysis in terms of an optimization criterion. By discussing the properties of the optimization criterion, we find that the eigenvectors in some eigen-subspaces may be indistinguishable if the degenerated eigenvalue occurs. Inspired from the idea of the maximum margin criterion (MMC), we embed MMC into the eigen-subspace corresponding to the degenerated eigenvalue to exploit discriminability of the eigenvectors in the eigen-subspace. Since the proposed algorithm can deal with the degenerated case of eigenvalues, it not only handles the small-sample-size problem but also enables us to select projection vectors from the null space of the between-class scatter matrix. Extensive experiments on several face images and microarray data sets are conducted to evaluate the proposed algorithm in terms of the classification performance, and experimental results show that our method has smaller standard deviations than other methods in most cases.


2014 ◽  
Vol 556-562 ◽  
pp. 4825-4829 ◽  
Author(s):  
Kai Li ◽  
Peng Tang

Linear discriminant analysis (LDA) is an important feature extraction method. This paper proposes an improved linear discriminant analysis method, which redefines the within-class scatter matrix and introduces the normalized parameter to control the bias and variance of eigenvalues. In addition, it makes the between-class scatter matrix to weight and avoids the overlapping of neighboring class samples. Some experiments for the improved algorithm presented by us are performed on the ORL, FERET and YALE face databases, and it is compared with other commonly used methods. Experimental results show that the proposed algorithm is the effective.


Author(s):  
Shariq Mohammed ◽  
Dipak K. Dey

Background and Aim: We aim to build a classifier to distinguish between malaria-infected red blood cells (RBCs) and healthy cells using the two-dimensional (2D) microscopic images of RBCs. We demonstrate the process of cell segmentation and feature extraction from the 2D images. Methods and Materials: We describe an approach to address the problem using mixture discriminant analysis (MDA) on the 2D image profiles of the RBCs. The extracted features are used with Gaussian MDA to distinguish between healthy and malaria infected cells. We also use the neutral zone classifiers where ambiguous cases are identified separately by the classifier. Results: We compare the classification results from the regular classifiers such as linear discriminant analysis (LDA) or MDA and the methods where neutral zone classifiers are used. We see that including the neutral zone improves the classification results by controlling the false positive and false negatives. The number of misclassifications are seen to be lower than the case without neutral zone classifiers. Conclusion: This paper presents an alternative approach for classification by incorporating neutral zone classifier approach, where a prediction is not made for the ambiguous cases. From the data analysis we see that this approach based on neutral zone classifiers presents a useful alternative in classification problems for various applications.


2011 ◽  
Vol 128-129 ◽  
pp. 58-61
Author(s):  
Shi Ping Li ◽  
Yu Cheng ◽  
Hui Bin Liu ◽  
Lin Mu

Linear Discriminant Analysis (LDA) [1] is a well-known method for face recognition in feature extraction and dimension reduction. To solve the “small sample” effect of LDA, Two-Dimensional Linear Discriminant Analysis (2DLDA) [2] has been used for face recognition recently,but its could hardly take use of the relationship between the adjacent scatter matrix. In this paper, I improved the between-class scatter matrix, proposed paired-class scatter matrix for face representation and recognition. In this new method, a paired between-class scatter matrix distance metric is used to measure the distance between random paired between-class scatter matrix. To test this new method, ORL face database is used and the results show that the paired between-class scatter matrix based 2DLDA method (N2DLDA) outperforms the 2DLDA method and achieves higher classification accuracy than the 2DLDA algorithm.


T oung Pao ◽  
2015 ◽  
Vol 101 (1-3) ◽  
pp. 168-207
Author(s):  
Shiuon Chu

This article investigates the practice of returning marked papers to rejected candidates in late imperial Chinese examinations. The practice—common from the sixteenth century to the abolition of imperial examinations in 1905—established a sense of personal communication between examiners and examinees and was an opportunity for rejected candidates to benefit from the examination system. The failed papers returned to their authors enabled them to make sense of their performance by interpreting, when not misconstruing, examiners’ comments. The examiners sometimes praised the papers and blamed the decision to fail on other examiners. As a result, most rejected candidates tended not to challenge the examiners through official channels or take collective action against the examination system. Thus, in the late imperial examination system, the ways in which rejecting decisions could be negotiated and construed were no less important than the awarding of degrees to an extremely small proportion of participants.
Cet article s’intéresse à la pratique, particulière à la période impériale tardive, consistant à rendre leurs copies aux candidats ayant échoué aux examens. Courante depuis le xvie siècle et jusqu’à l’abolition des examens mandarinaux en 1905, cette pratique créait l’impression d’une relation personnelle entre les examinateurs et les candidats et était un moyen pour ceux qui avaient échoué de tirer profit du système. Les copies rejetées retournées à leurs auteurs permettaient à ces derniers de donner un sens à leur performance en interprétant, voire en dévoyant, les commentaires des examinateurs. Il arrivait que les examinateurs fassent l’éloge des copies et attribuent à autrui la décision de les rejeter. De ce fait, la plupart des candidats malheureux évitaient de contester les examinateurs par la voie réglementaire ou de manifester collectivement contre le système. Ainsi, dans le système des examens à la fin de la période impériale, la manière dont les décisions négatives pouvaient être négociées ou interprétées n’était pas moins importante que l’attribution de rangs académiques à une toute petite proportion de ceux qui concouraient.



Author(s):  
XIPENG QIU ◽  
LIDE WU

Linear Discriminant Analysis (LDA) is a popular feature extraction technique in statistical pattern recognition. However, it often suffers from the small sample size problem when dealing with high-dimensional data. Moreover, while LDA is guaranteed to find the best directions when each class has a Gaussian density with a common covariance matrix, it can fail if the class densities are more general. In this paper, a novel nonparametric linear feature extraction method, nearest neighbor discriminant analysis (NNDA), is proposed from the view of the nearest neighbor classification. NNDA finds the important discriminant directions without assuming the class densities belong to any particular parametric family. It does not depend on the nonsingularity of the within-class scatter matrix either. Then we give an approximate approach to optimize NNDA and an extension to k-NN. We apply NNDA to the simulated data and real world data, the results demonstrate that NNDA outperforms the existing variant LDA methods.


Author(s):  
WEN-SHENG CHEN ◽  
PONG C. YUEN ◽  
JIAN HUANG

This paper presents a new regularization technique to deal with the small sample size (S3) problem in linear discriminant analysis (LDA) based face recognition. Regularization on the within-class scatter matrix Sw has been shown to be a good direction for solving the S3 problem because the solution is found in full space instead of a subspace. The main limitation in regularization is that a very high computation is required to determine the optimal parameters. In view of this limitation, this paper re-defines the three-parameter regularization on the within-class scatter matrix [Formula: see text], which is suitable for parameter reduction. Based on the new definition of [Formula: see text], we derive a single parameter (t) explicit expression formula for determining the three parameters and develop a one-parameter regularization on the within-class scatter matrix. A simple and efficient method is developed to determine the value of t. It is also proven that the new regularized within-class scatter matrix [Formula: see text] approaches the original within-class scatter matrix Sw as the single parameter tends to zero. A novel one-parameter regularization linear discriminant analysis (1PRLDA) algorithm is then developed. The proposed 1PRLDA method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. The average recognition accuracies of 50 runs for ORL and FERET databases are 96.65% and 94.00%, respectively. Comparing with existing LDA-based methods in solving the S3 problem, the proposed 1PRLDA method gives the best performance.


Sign in / Sign up

Export Citation Format

Share Document