基于核的广义Foley-Sammon鉴别分析

广义Foley-Sammon线性鉴别分析(GFSDA)是抽取线性特征的有效方法之一。本文提出了基于核的广义Foley-Sammon鉴别分析(KGFSDA)方法，首先建立KGFSDA的模型，然后从理论上给出KGFSDA模型的具体求解方法。分析表明，KGFSDA保留了GFSDA能从整体上考虑经过广义最佳鉴别变换后样本的可分性的优点，更重要的是该方法能够有效地抽取样本的非线性特征，是对GFSDA的进一步拓展。在ORL标准人脸库上的实验结果表明，该方法在识别性能上优于已有的广义Foley-Sammon线性鉴别分析，也比经典的Foley-Sammon线性鉴别分析更有效。     

快速核Foley—Sammon鉴别分析及其在人脸识别上的应用

核Foley-Sammon鉴别分析由于可以抽取得到原始样本的非线性正交特征,因此被广泛应用于模式识别的研究领域.但是该算法在具体求解每一个特征矢量过程中均需求解相应的广义特征方程,因此非常耗时.为了克服这一困难,提出了一种新的快速近似算法即核Foley-Sammon鉴别分析,有效地避免了多次求解广义特征方程.在ORL人脸数据库上的实验结果表明,该算法不仅在识别性能上优于核线性鉴别分析,而且在特征抽取速度上优于传统的核Foley-Sammon鉴别分析.     

人脸识别中基于核的子空间鉴别分析

尽管基于Fisher准则的线性鉴别分析被公认为特征抽取的有效方法之一，并被成功地用于人脸识别，但是由于光照变化、人脸表情和姿势变化，实际上的人脸图像分布是十分复杂的，因此，抽取非线性鉴别特征显得十分必要。为了能利用非线性鉴别特征进行人脸识别，提出了一种基于核的子空间鉴别分析方法。该方法首先利用核函数技术将原始样本隐式地映射到高维（甚至无穷维）特征空间；然后在高维特征空间里，利用再生核理论来建立基于广义Fisher准则的两个等价模型；最后利用正交补空间方法求得最优鉴别矢量来进行人脸识别。在ORL和NUST603两个人脸数据库上，对该方法进行了鉴别性能实验，得到了识别率分别为94％和99．58％的实验结果，这表明该方法与核组合方法的识别结果相当，且明显优于KPCA和Kernel fisherfaces方法的识别结果。     

一种基于正交投影的特征抽取方法

本文结合Fisher鉴别准则给出了一组正交投影矢量，并引入了一种度量投影矢量相关性的简捷方法，与经典的Foley-Sammon鉴别分别法相比，所提出的正交投影法具有较强的消除样本特征之间相关性的能力和良好的鉴别能力，最后，在CENPARMI手写体阿拉伯数字库的试验结果证实了该特征抽取方法明显优于Foley-Sammon鉴别分析法。     

正交化Fisher鉴别向量集及其应用

在正交化Fisher鉴别分析的基础上提出了正交化核Fisher鉴别分析方法。该方法具有理论简单、计算方便、特征表示能力强等优点。在CENPARMI手写体阿拉伯数字数据库、NUST603HW手写体汉字样本库和FERET人脸图像数据库上的仿真实验结果表明，正变化Fisher鉴别和正交化核Fisher鉴别方法在特征抽取能力和特征抽取效率方面均分别优于FoleySammon鉴别和核Foley-Sammon鉴别方法。     

一种新颖的核鉴别通用矢量集算法

为了进一步增强鉴别通用矢量集算法的性能,提出一种核鉴别通用矢量集算法.首先利用核函数将原始样本隐式地映射到高维特征空间;然后在高维特征空间里利用再生核理论建立鉴别通用矢量集算法的等价求解模型;最后根据新的求解模型,应用二次Gram-Schmidt正交化方法求出核类内零空间中的鉴别矢量集.在人脸库上的实验结果验证了文中算法的有效性.     

一种新的核线性鉴别分析算法及其在人脸识别上的应用

基于核策略的核Fisher鉴别分析（KFD）算法已成为非线性特征抽取的最有效方法之一。但是先前的基于核Fisher鉴别分析算法的特征抽取过程都是基于2值分类问题而言的。如何从重叠（离群）样本中抽取有效的分类特征没有得到有效的解决。本文在结合模糊集理论的基础上,利用模糊隶属度函数的概念,在特征提取过程中融入了样本的分布信息,提出了一种新的核Fisher鉴别分析方法——模糊核鉴别分析算法。在ORL人脸数据库上的实验结果验证了该算法的有效性。     

一种用于人脸识别的非线性鉴别特征融合方法

最近，在人脸等图像识别领域，用于抽取非线性特征的核方法如核Fisher鉴别分析(KFDA)已经取得成功并得到了广泛应用，但现有的核方法都存在这样的问题，即构造特征空间中的核矩阵所耗费的计算量非常大．而且，抽取得到的单类特征往往不能获得到令人满意的识别结果．提出了一种用于人脸识别的非线性鉴别特征融合方法，即首先利用小波变换和奇异值分解对原始输入样本进行降雏变换，抽取同一样本空间的两类特征，然后利用复向量将这两类特征组合在一起，构成一复特征向量空间，最后在该空间中进行最优鉴别特征抽取．在ORL标准人脸库上的试验结果表明所提方法不仅在识别性能上优于现有的核Fisher鉴别分析方法，而且，在ORL人脸库上的特征抽取速度提高了近8倍．     

求解广义最佳鉴别矢量集的一种迭代算法及人脸识别

广义最佳鉴别矢量集是Foley-Sammon最佳鉴别矢量集的一种推广,它与Foley-Sammon最佳鉴别矢量集的不同之处在于广义最佳鉴别矢量集从整体上考虑投影集的可分性,即样本在广义最佳鉴别矢量上的投影集从整体上具有最佳的可分性。该文给出了广义最佳鉴别矢量的定义,对求解广义最佳鉴别矢量集的已有算法从理论上作了分析,指出了其中的不足之处,给出了一种迭代算法,从理论上证明了迭代结果收敛于精确解,并对其误差作了分析。最后,将此方法用于人脸识别,结果显示,新方法比已有的方法更有效。     

一种改进的核特征抽取方法及其在人脸识别中的应用

首先利用核函数技术将原始样本隐式地映射到高维特征空间;然后在高维空间里利用再生核理论建立基于Fisher鉴别极小准则的2个等价模型;最后在该空间的核类间散布矩阵的非零空间和零空间中应用Fisher极小鉴别准则求取核鉴别矢量.在人脸库上的实验结果验证了该算法的有效性.     

A comparison of machine learning techniques with a qualitative response model for auditor’s going concern reporting

Audit reports can take the form of a non-going concern (clean) report or Going concern (financial distress) report. If a firm is facing going concern uncertainty problems the auditor has a further choice of issuing two types of audit reports, namely the modified report or the disclaimer report. The issuance of the wrong type of report can have consequences for the auditor. Prior studies have developed models in an attempt to predict the type of audit report that should be issued to clients. However, all these studies, without exception, focused on the decision whether to issue a non-going concern report or a going concern report. The present study extends this area of research by comparing three predictive models that can help facilitate the decision on the type of going concern report that should be issued. Two of the predictive models are on based machine learning techniques (Artificial Neural Networks and Expert Systems) while the third is a qualitative model (Multiple Discriminant Analysis). The validity of the models are tested by comparing their predictive ability of the type of audit report which should be issued to the client. The results of the study indicate that the artificial neural network model has a superior predictive ability in determining the type of going concern audit report that should be issued to the client.     

Penalized Fisher Discriminant Analysis and Its Application to Image-Based Morphometry

Image-based morphometry is an important area of pattern recognition research, with numerous applications in science and technology (including biology and medicine). Fisher linear discriminant analysis (FLDA) techniques are often employed to elucidate and visualize important information that discriminates between two or more populations. We demonstrate that the direct application of FLDA can lead to undesirable errors in characterizing such information and that the reason for such errors is not necessarily the ill conditioning in the resulting generalized eigenvalue problem, as usually assumed. We show that the regularized eigenvalue decomposition often used is related to solving a modified FLDA criterion that includes a least-squares-type representation penalty, and derive the relationship explicitly. We demonstrate the concepts by applying this modified technique to several problems in image-based morphometry, and build discriminant representative models for different data sets.     

苹果近红外光谱的特征提取和分类研究

采用近红外光谱分析法对不同种类的苹果样品进行分类,提出一种基于非相关判别转换的苹果近红外光谱定性分析新方法。实验分别采用主成分分析、Fisher判别分析和非相关判别转换三种方法对苹果光谱数据进行特征提取,并使用K-近邻分类算法建立三种苹果分类识别模型,最后使用"留一"交叉验证法进行模型检验。结果表明,使用非相关判别转换方法建立的模型正确识别率优于使用主成分分析和Fisher判别分析建立的模型。     

Error rate estimation on the basis of posterior probabilities

The so-called posterior probability estimator, e, formed by averaging the minimum of the posterior probabilities over a set of initial or additional observations (which need not be classified) is considered in the context of estimating the overall actual error rate for the linear discriminant function appropriate for two multivariate normal populations with a common covariance matrix. The bias of e is examined by deriving asymptotic approximations under three different models, the normal, logistic, and mixture models. The properties of e are investigated further by a series of simulation experiments for the logistic and mixture models for which there are few other available estimators.     

特征迁移中投影子空间的分析与构造

近年来,针对实际应用场景中可匹配的训练数据不足的问题,科研人员发展出了迁移学习的概念,希望通过提取源域数据的特征信息进行迁移,从而提升目标域的学习效果.本文根据迁移学习所处理的不同数据类型,构造了两种典型的模型:单类别投影基构造模型与监督多类别投影模型.由于子空间投影可以在一定程度上反映原始样本空间的特征性质.因此,本文应用线性判别分析的技巧以及最大均值差异的思想,分别构造了上述模型的求解算法并对相应的非线性核方法进行了推广.     

优化线性辨别分析在人脸识别中的应用(英文)

国内外学者研究发现,类间方差最大化的方向与类内方差最大化的方向之间的角度对传统的线性辨别分析方法的准确性影响显著,并且,当这两个方向平行的时候,传统的线性方法往往不能得到很好的结果。经过的研究和实验,发现传统线性方法的准确性与类间方差和类内方差之间的角度没有直接的决定关系,它的最大问题在于线性地对类间方差和类内方差的加和不能完全保留类别之间的辨别信息。提出了一种优化的线性辨别分析的方法(OLDA)来解决这个问题。首先,引入了辨别能量的概念,能够给任意两个类之间的辨别信息赋予同样的权重;其次,引入了一种梯度下降的算法来计算最终的判别向量,并且加速迭代算子的引入能够更加有效地解决运算复杂度的问题。最后,为了解决非线性问题,预先的聚类算法能够将非线性问题转化成为线性问题,从而使数据集能够被有效地分辨出来。采用了一个人脸数据集和一个虚拟数据集进行了实现,实验结果表明提出的优化辨别分析的方法能够有效地解决数据集的分类问题。     

Forecasting business failure using two‐stage ensemble of multivariate discriminant analysis and logistic regression

A major drawback associated with the use of classical statistical methods for business failure prediction on top of financial distress is their lack of high accuracy rate. This work analyses the use of the two‐stage ensemble of multivariate discriminant analysis (MDA) and logit to improve predictive performance of classical statistical methods. All possible ratios are firstly built from the quantities involved and then the three common filters, that is stepwise MDA, stepwise logit, and t‐test, are used to choose another three convenient subsets of ratios. Four principal components spaces (PCSs) are, respectively, produced on the four different feature spaces by using principal components analysis. MDA and logit are used to produce predictions on the four PCSs. After that, two levels of ensemble are implemented: one based on predictions inside each of the same type of model (i.e. MDA or logit) and another based on the former two ensembles and one best model. Each of the eight models is weighted on the base of ranking order information of its predictive accuracy in ensemble by majority voting. MDA and logit and the new challenge model of support vector machine respectively in their best standalone modes are used for comparisons. Empirical results indicate that the two‐stage ensemble of MDA and logit compares favourably with the three comparative models and all its component models.     

局部和全局加权的二维统计不相关鉴别分析

传统的统计不相关鉴别分析方法使用样本的均值来估计期望,计算出总体散度矩阵。这些方法在数据不满足高斯分布的情况下会出现大的偏差,影响最优鉴别特征的提取。为了解决该问题,文中结合二维鉴别分析的思想,分别提出了基于局部的二维统计不相关鉴别变换（L2DUDT）方法和基于全局加权的二维统计不相关鉴别变换（WG2DUDT）方法。L2DUDT通过用样本的近邻中心来定义每个样本的期望,而WG2DUDT用样本间的欧几里得距离加权来定义期望。基于AR和FERET人脸数据库的实验表明,文中提出的方法与一些相关方法相比,有效地提高了识别性能。     

Assessment of a New Three-Group Software Quality Classification Technique: An Empirical Case Study

The primary aim of risk-based software quality classification models is to detect, prior to testing or operations, components that are most-likely to be of high-risk. Their practical usage as quality assurance tools is gauged by the prediction-accuracy and cost-effective aspects of the models. Classifying modules into two risk groups is the more commonly practiced trend. Such models assume that all modules predicted as high-risk will be subjected to quality improvements. Due to the always-limited reliability improvement resources and the variability of the quality risk-factor, a more focused classification model may be desired to achieve cost-effective software quality assurance goals. In such cases, calibrating a three-group (high-risk, medium-risk, and low-risk) classification model is more rewarding. We present an innovative method that circumvents the complexities, computational overhead, and difficulties involved in calibrating pure or direct three-group classification models. With the application of the proposed method, practitioners can utilize an existing two-group classification algorithm thrice in order to yield the three risk-based classes. An empirical approach is taken to investigate the effectiveness and validity of the proposed technique. Some commonly used classification techniques are studied to demonstrate the proposed methodology. They include, the C4.5 decision tree algorithm, discriminant analysis, and case-based reasoning. For the first two, we compare the three-group model calibrated using the respective techniques with the one built by applying the proposed method. Any two-group classification technique can be employed by the proposed method, including those that do not provide a direct three-group classification model, e.x., logistic regression and certain binary classification trees, such as CART. Based on a case study of a large-scale industrial software system, it is observed that the proposed method yielded promising results. For a given classification technique, the expected cost of misclassification of the proposed three-group models were significantly better (generally) when compared to the techniques direct three-group model. In addition, the proposed method is also evaluated against an alternate indirect three-group classification method.