Generalized null space uncorrelated Fisher discriminant analysis for linear dimensionality reduction

We propose a generalized null space uncorrelated Fisher discriminant analysis (GNUFDA) technique integrating the uncorrelated discriminant analysis and weighted pairwise Fisher criterion. The GNUFDA can effectively deal with the small sample-size problem and perform satisfactorily when the dimensionality of the null space decreases with increase in the number of training samples per class and/or classes, C. The proposed GNUFDA can extract at most C-1 optimal uncorrelated discriminative vectors without being influenced by the null-space dimensionality.     

累积正态分布函数的逼近函数综述

Fisher z变换是一个显式的初等函数,用来逼近累积正态分布函数（标准正态分布的累积分布函数）。介绍了累积正态分布函数逼近函数的评价标准,对有代表性的逼近函数表达式及相应的最大距离误差值进行归纳总结。     

多流形判别分析在人脸识别中的研究

局部保持投影LPP(Locality Preserving Projection)是一种有效的非线性降维方法,能够使投影降维后的数据与原输入空间中的相似局部结构保持一致,但是该方法没有充分利用类间样本点的权重等重要信息。为了解决这个问题,提出基于Fisher准则的多流形判别分析FMMDA(Fisher Multi-Manifold Discriminant Analysis)方法。结合Fisher准则训练样本类内拉普拉斯图和样本均值类间拉普拉斯图,既保持了原样本的相似局部结构,又充分地利用了不同类别之间的权重。在ORL及Yale人脸库上验证了该方法的有效性。与其他几种最先进的方法相比,FMMDA方法取得了更好的识别效果。     

基于Fisher 准则和最大熵原理的SVM核参数选择方法

针对支持向量机(SVM)核参数选择困难的问题,提出一种基于Fisher准则和最大熵原理的SVM核参数优选方法.首先,从SVM分类器原理出发,提出SVM核参数优劣的衡量标准;然后,根据此标准利用Fisher准则来优选SVM核参数,并引入最大熵原理进一步调整算法的优选性能.整个模型采用粒子群优化算法(PSO)进行参数寻优.UCI标准数据集实验表明了所提方法具有良好的参数选择效果,优选出的核参数能够使SVM具有较高的泛化性能.     

基于核Fisher判别和加权码书映射的音频信号削波修复方法

本文基于核Fisher判别（Kernel Fisher Discriminant, KFD）和加权码书映射（Weighted Codebook Mapping, WCBM）,提出了一种MDCT（Modified Discrete Cosine Transform）域的音频信号削波修复方法。首先根据音频信号的MDCT系数提取子带包络等四种削波特征参数;其次,利用这些特征参数训练检测音频信号出现削波的核Fisher分类器;最后,利用子带包络的WCBM来修复音频信号的削波。测试结果表明,本文所提方法能有效修复音频信号的削波,其性能优于现有的几种削波修复方法。     

Fisher discrimination based low rank matrix recovery for face recognition

In this paper, we consider the issue of computing low rank (LR) recovery of matrices with sparse errors. Based on the success of low rank matrix recovery in statistical learning, computer vision and signal processing, a novel low rank matrix recovery algorithm with Fisher discrimination regularization (FDLR) is proposed. Standard low rank matrix recovery algorithm decomposes the original matrix into a set of representative basis with a corresponding sparse error for modeling the raw data. Motivated by the Fisher criterion, the proposed FDLR executes low rank matrix recovery in a supervised manner, i.e., taking the with-class scatter and between-class scatter into account when the whole label information are available. The paper shows that the formulated model can be solved by the augmented Lagrange multipliers and provides additional discriminating power over the standard low rank recovery models. The representative bases learned by the proposed method are encouraged to be closer within the same class, and as far as possible between different classes. Meanwhile, the sparse error recovered by FDLR is not discarded as usual, but treated as a feedback in the following classification tasks. Numerical simulations demonstrate that the proposed algorithm achieves the state of the art results.     

Integrated Fisher linear discriminants: An empirical study

This paper studies Fisher linear discriminants (FLDs) based on classification accuracies for imbalanced datasets. An optimal threshold is found out from a series of empirical formulas developed, which is related not only to sample sizes but also to distribution regions. A mixed binary–decimal coding system is suggested to make the very dense datasets sparse and enlarge the class margins on condition that the neighborhood relationships of samples are nearly preserved. The within-class scatter matrices being or approximately singular should be moderately reduced in dimensionality but not added with tiny perturbations. The weight vectors can be further updated by a kind of epoch-limited (three at most) iterative learning strategy provided that the current training error rates come down accordingly. Putting the above ideas together, this paper proposes a type of integrated FLDs. The extensive experimental results over real-world datasets have demonstrated that the integrated FLDs have obvious advantages over the conventional FLDs in the aspects of learning and generalization performances for the imbalanced datasets.