Fisher大间距线性分类器

作为一种著名的特征抽取方法,Fisher线性鉴别分析的基本思想是选择使得Fisher准则函数达到最大值的向量(称为最优鉴别向量)作为最优投影方向,以便使得高维输入空间中的模式样本在该向量投影后,在类间散度达到最大的同时,类内散度最小。大间距线性分类器是寻找一个最优投影矢量(最优分隔超平面的法向量),它可使得投影后的两类样本之间的分类间距(Margin)最大。为了获得更佳的识别效果,结合Fisher线性鉴别分析和大间距分类器的优点,提出了一种新的线性投影分类算法——Fisher大间距线性分类器。该分类器的主要思想就是寻找最优投影矢量wbest(最优超平面的法向量),使得高维输入空间中的样本模式在wbest上投影后,在使类间间距达到最大的同时,使类内离散度尽可能地小。并从理论上讨论了与其他线性分类器的联系。在ORL人脸库和FERET人脸数据库上的实验结果表明,该线性投影分类算法的识别率优于其他分类器。     

超球体多类支持向量机理论

目前的多类分类器大多是经二分类器组合而成的,存在训练速度较慢的问题,在分类类别多的时候,会遇到很大困难,超球体多类支持向量机将超球体单类支持向量机扩展到多类问题,由于每类样本只参与一个超球体支持向量机的训练.因此,这是一种直接多类分类器,训练效率明显提高.为了有效训练超球体多类支持向量机,利用SMO算法思想,提出了超球体支持向量机的快速训练算法.同时对超球体多类支持向量机的推广能力进行了理论上的估计.数值实验表明,在分类类别较多的情况,这种分类器的训练速度有很大提高,非常适合解决类别数较多的分类问题.超球体多类支持向量机为研究快速直接多类分类器提供了新的思路.     

Linear dimensionality reduction via a heteroscedastic extension of LDA: the Chernoff criterion

We propose an eigenvector-based heteroscedastic linear dimension reduction (LDR) technique for multiclass data. The technique is based on a heteroscedastic two-class technique which utilizes the so-called Chernoff criterion, and successfully extends the well-known linear discriminant analysis (LDA). The latter, which is based on the Fisher criterion, is incapable of dealing with heteroscedastic data in a proper way. For the two-class case, the between-class scatter is generalized so to capture differences in (co)variances. It is shown that the classical notion of between-class scatter can be associated with Euclidean distances between class means. From this viewpoint, the between-class scatter is generalized by employing the Chernoff distance measure, leading to our proposed heteroscedastic measure. Finally, using the results from the two-class case, a multiclass extension of the Chernoff criterion is proposed. This criterion combines separation information present in the class mean as well as the class covariance matrices. Extensive experiments and a comparison with similar dimension reduction techniques are presented.     

A comparison of generalized linear discriminant analysis algorithms

Linear discriminant analysis (LDA) is a dimension reduction method which finds an optimal linear transformation that maximizes the class separability. However, in undersampled problems where the number of data samples is smaller than the dimension of data space, it is difficult to apply LDA due to the singularity of scatter matrices caused by high dimensionality. In order to make LDA applicable, several generalizations of LDA have been proposed recently. In this paper, we present theoretical and algorithmic relationships among several generalized LDA algorithms and compare their computational complexities and performances in text classification and face recognition. Towards a practical dimension reduction method for high dimensional data, an efficient algorithm is proposed, which reduces the computational complexity greatly while achieving competitive prediction accuracies. We also present nonlinear extensions of these LDA algorithms based on kernel methods. It is shown that a generalized eigenvalue problem can be formulated in the kernel-based feature space, and generalized LDA algorithms are applied to solve the generalized eigenvalue problem, resulting in nonlinear discriminant analysis. Performances of these linear and nonlinear discriminant analysis algorithms are compared extensively.     

Local likelihood regression in generalized linear single-index models with applications to microarray data

Searching for an effective dimension reduction space is an important problem in regression, especially for high-dimensional data such as microarray data. A major characteristic of microarray data consists in the small number of observations n and a very large number of genes p. This “large p, small n” paradigm makes the discriminant analysis for classification difficult. In order to offset this dimensionality problem a solution consists in reducing the dimension. Supervised classification is understood as a regression problem with a small number of observations and a large number of covariates. A new approach for dimension reduction is proposed. This is based on a semi-parametric approach which uses local likelihood estimates for single-index generalized linear models. The asymptotic properties of this procedure are considered and its asymptotic performances are illustrated by simulations. Applications of this method when applied to binary and multiclass classification of the three real data sets Colon, Leukemia and SRBCT are presented.     

A bilevel framework for joint optimization of session compensation and classification for speaker identification

The i-vector framework based system is one of the most popular systems in speaker identification (SID). In this system, session compensation is usually employed first and then the classifier. For any session-compensated representation of i-vector, there is a corresponding identification result, so that both the stages are related. However, in current SID systems, session compensation and classifier are usually optimized independently. An incomplete knowledge about the session compensation to the identification task may lead to involving uncertainties. In this paper, we propose a bilevel framework to jointly optimize session compensation and classifier to enhance the relationship between the two stages. In this framework, we use the sparse coding (SC) to obtain the session-compensated feature by learning an overcomplete dictionary, and employ the softmax classifier and support vector machine (SVM) in classifying respectively. Moreover, we present a joint optimization of the dictionary and classifier parameters under a discriminative criterion for classifier with conditions for SC. In addition, the proposed methods are evaluated on the King-ASR-010, VoxCeleb and RSR2015 databases. Compared with typical session compensation techniques, such as linear discriminant analysis (LDA) and nonparametric discriminant analysis (NDA), our methods can be more robust to complex session variability. Moreover, compared with the typical classifiers in i-vector framework, i.e. the cosine distance scoring (CDS) and probabilistic linear discriminant analysis (PLDA), our methods can be more suitable for SID (multiclass task).     

A multiple maximum scatter difference discriminant criterion for facial feature extraction.

Maximum scatter difference (MSD) discriminant criterion was a recently presented binary discriminant criterion for pattern classification that utilizes the generalized scatter difference rather than the generalized Rayleigh quotient as a class separability measure, thereby avoiding the singularity problem when addressing small-sample-size problems. MSD classifiers based on this criterion have been quite effective on face-recognition tasks, but as they are binary classifiers, they are not as efficient on large-scale classification tasks. To address the problem, this paper generalizes the classification-oriented binary criterion to its multiple counterpart--multiple MSD (MMSD) discriminant criterion for facial feature extraction. The MMSD feature-extraction method, which is based on this novel discriminant criterion, is a new subspace-based feature-extraction method. Unlike most other subspace-based feature-extraction methods, the MMSD computes its discriminant vectors from both the range of the between-class scatter matrix and the null space of the within-class scatter matrix. The MMSD is theoretically elegant and easy to calculate. Extensive experimental studies conducted on the benchmark database, FERET, show that the MMSD out-performs state-of-the-art facial feature-extraction methods such as null space method, direct linear discriminant analysis (LDA), eigenface, Fisherface, and complete LDA.     

Solving the small sample size problem in face recognition using generalized discriminant analysis

The goal of face recognition is to distinguish persons via their facial images. Each person's images form a cluster, and a new image is recognized by assigning it to the correct cluster. Since the images are very high-dimensional, it is necessary to reduce their dimension. Linear discriminant analysis (LDA) has been shown to be effective at dimension reduction while preserving the cluster structure of the data. It is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters. The requirement that one of these matrices be nonsingular restricts its application to datasets in which the dimension of the data does not exceed the sample size. For face recognition, however, the dimension typically exceeds the number of images in the database, resulting in what is referred to as the small sample size problem. Recently, the applicability of LDA has been extended by using the generalized singular value decomposition (GSVD) to circumvent the nonsingularity requirement, thus making LDA directly applicable to face recognition data. Our experiments confirm that LDA/GSVD solves the small sample size problem very effectively as compared with other current methods.     

A novel Bayesian logistic discriminant model: An application to face recognition

The linear discriminant analysis (LDA) is a linear classifier which has proven to be powerful and competitive compared to the main state-of-the-art classifiers. However, the LDA algorithm assumes the sample vectors of each class are generated from underlying multivariate normal distributions of common covariance matrix with different means (i.e., homoscedastic data). This assumption has restricted the use of LDA considerably. Over the years, authors have defined several extensions to the basic formulation of LDA. One such method is the heteroscedastic LDA (HLDA) which is proposed to address the heteroscedasticity problem. Another method is the nonparametric DA (NDA) where the normality assumption is relaxed. In this paper, we propose a novel Bayesian logistic discriminant (BLD) model which can address both normality and heteroscedasticity problems. The normality assumption is relaxed by approximating the underlying distribution of each class with a mixture of Gaussians. Hence, the proposed BLD provides more flexibility and better classification performances than the LDA, HLDA and NDA. A subclass and multinomial versions of the BLD are proposed. The posterior distribution of the BLD model is elegantly approximated by a tractable Gaussian form using variational transformation and Jensen's inequality, allowing a straightforward computation of the weights. An extensive comparison of the BLD to the LDA, support vector machine (SVM), HLDA, NDA and subclass discriminant analysis (SDA), performed on artificial and real data sets, has shown the advantages and superiority of our proposed method. In particular, the experiments on face recognition have clearly shown a significant improvement of the proposed BLD over the LDA.     

Class-dependent PCA, MDC and LDA: A combined classifier for pattern classification

Several pattern classifiers give high classification accuracy but their storage requirements and processing time are severely expensive. On the other hand, some classifiers require very low storage requirement and processing time but their classification accuracy is not satisfactory. In either of the cases the performance of the classifier is poor. In this paper, we have presented a technique based on the combination of minimum distance classifier (MDC), class-dependent principal component analysis (PCA) and linear discriminant analysis (LDA) which gives improved performance as compared with other standard techniques when experimented on several machine learning corpuses.     

Multiclass Support Vector Machines for Classification of ECG Data with Missing Values

The article presents an experimental study on multiclass Support Vector Machine (SVM) methods over a cardiac arrhythmia dataset that has missing attribute values for electrocardiogram (ECG) diagnostic application. The presence of an incomplete dataset and high data dimensionality can affect the performance of classifiers. Imputation of missing data and discriminant analysis are commonly used as preprocessing techniques in such large datasets. The article proposes experiments to evaluate performance of One-Against-All (OAA) and One-Against-One (OAO) approaches in kernel multiclass SVM for a heartbeat classification problem with imputation and dimension reduction techniques. The results indicate that the OAA approach has superiority over OAO in multiclass SVM for ECG data analysis with missing values.     

Enhanced iterative projection for subclass discriminant analysis under EM-alike framework

Mixture discriminant analysis (MDA) and subclass discriminant analysis (SDA) belong to the supervised classification approaches. They have advantage over the standard linear discriminant analysis (LDA) in large sample size problems, since both of them divide the samples in each class into subclasses which keep locality but LDA does not. However, since the current MDA and SDA algorithms perform subclass division in just one step in the original data space before solving the generalized eigenvalue problem, two problems are exposed: (1) they ignore the relation among classes since subclass division is performed in each isolated class; (2) they cannot guarantee good performance of classifiers in the transformed space, because locality in the original data space may not be kept in the transformed space. To address these problems, this paper presents a new approach for subclass division based on k-means clustering in the projected space, class by class using the iterative steps under EM-alike framework. Experiments are performed on the artificial data set, the UCI machine learning data sets, the CENPARMI handwritten numeral database, the NUST603 handwritten Chinese character database, and the terrain cover database. Extensive experimental results demonstrate the performance advantages of the proposed method.     

A heuristic supervised Euclidean data difference dimension reduction for KNN classifier and its application to visual place classification

In this paper, we propose a novel supervised dimension reduction algorithm based on K-nearest neighbor (KNN) classifier. The proposed algorithm reduces the dimension of data in order to improve the accuracy of the KNN classification. This heuristic algorithm proposes independent dimensions which decrease Euclidean distance of a sample data and its K-nearest within-class neighbors and increase Euclidean distance of that sample and its M-nearest between-class neighbors. This algorithm is a linear dimension reduction algorithm which produces a mapping matrix for projecting data into low dimension. The dimension reduction step is followed by a KNN classifier. Therefore, it is applicable for high-dimensional multiclass classification. Experiments with artificial data such as Helix and Twin-peaks show ability of the algorithm for data visualization. This algorithm is compared with state-of-the-art algorithms in classification of eight different multiclass data sets from UCI collection. Simulation results have shown that the proposed algorithm outperforms the existing algorithms. Visual place classification is an important problem for intelligent mobile robots which not only deals with high-dimensional data but also has to solve a multiclass classification problem. A proper dimension reduction method is usually needed to decrease computation and memory complexity of algorithms in large environments. Therefore, our method is very well suited for this problem. We extract color histogram of omnidirectional camera images as primary features, reduce the features into a low-dimensional space and apply a KNN classifier. Results of experiments on five real data sets showed superiority of the proposed algorithm against others.     

Ridge regression-based feature extraction for hyperspectral data

Feature extraction based on ridge regression (FERR) is proposed in this article. In FERR, a feature vector is defined in each spectral band using the mean of all classes in that dimension. Then, it is modelled using a linear combination of its farthest neighbours from among other defined feature vectors. The representation coefficients obtained by solving the ridge regression model compose the projection matrix for feature extraction. FERR can extract each desired number of features while the other methods such as linear discriminant analysis (LDA) and generalized discriminant analysis (GDA) have limitations in the number of extracted features. Experimental results on four popular real hyperspectral images show that the efficiency of FERR is superior to those of other supervised feature extraction methods in small sample-size situations. For example, for the Indian Pines dataset, the comparison between the highest average classification accuracies achieved by different feature extraction methods using a support vector machine (SVM) classifier and 16 training samples per class shows that FERR is 7% more accurate than nonparametric weighted feature extraction and is also 9% better than GDA. LDA, having the singularity problem in the small sample-size situations, has 40% less accuracy than FERR. The experiments show that generally the performance of FERR using the SVM classifier is better than when using the maximum likelihood classifier.     

Canonical correlation analysis using within-class coupling

Fisher’s linear discriminant analysis (LDA) is one of the most popular supervised linear dimensionality reduction methods. Unfortunately, LDA is not suitable for problems where the class labels are not available and only the spatial or temporal association of data samples is implicitly indicative of class membership. In this study, a new strategy for reducing LDA to Hotelling’s canonical correlation analysis (CCA) is proposed. CCA seeks prominently correlated projections between two views of data and it has been long known to be equivalent to LDA when the data features are used in one view and the class labels are used in the other view. The basic idea of the new equivalence between LDA and CCA, which we call within-class coupling CCA (WCCCA), is to apply CCA to pairs of data samples that are most likely to belong to the same class. We prove the equivalence between LDA and such an application of CCA. With such an implicit representation of the class labels, WCCCA is applicable both to regular LDA problems and to problems in which only spatial and/or temporal continuity provides clues to the class labels.     

小样本情况下Fisher线性鉴别分析的理论及其验证

线性鉴别分析是特征抽取中最为经典和广泛使用的方法之一。近几年,在小样本情况下如何抽取F isher最优鉴别特征一直是许多研究者关心的问题。本文应用投影变换和同构变换的原理,从理论上解决了小样本情况下最优鉴别矢量的求解问题,即最优鉴别矢量可在一个低维空间里求得;给出了特征抽取模型,并给出求解模型的PPCA+LDA算法;在ORL人脸库3种分辨率灰度图像上进行实验。实验结果表明,PPCA+LDA算法抽取的鉴别向量有较强的特征抽取能力,在普通的最小距离分类器下能达到较高的正确识别率,而且识别结果十分稳定。     

三种判别分析方法在元音库上的分类

分别用降秩线性判别分析(RRLDA)、降秩二次判别分析(RRQDA)和主成分分析+线性判别分析(PCA+LDA)三种模型对数据进行了分析,并在元音测试数据集上进行了测试.分别画出了这三种模型的误分类率曲线,画出了RRLDA和PCA+LDA分别降至二维后的最优分类面.从实验结果中可以发现,RRLDA模型的实验结果优于PC...     

基于主元和判别集成分析的模拟电路故障诊断

提出了主元和线性判别的集成分析算法以实施模拟故障数据的特征提取过程和方法。该集成分析方法首先对模拟故障数据进行主元分析,然后在主元变换空间实行线性判别分析,最后将所获得的最优判别特征模式应用于模式分类器进行故障诊断。仿真结果表明,所提出的方法能够充分利用线性方法的计算简便优势,增强单一主元分析或线性判别分析的特征提取性能,获取故障数据集的本质特征,简化模式分类器的结构,降低系统运行的计算成本。     

Performance Evaluation Indicator (PEI): A new paradigm to evaluate the competence of machine learning classifiers in predicting rockmass conditions

To illustrate an unprejudiced comparison among machine learning classifiers established on proprietary databases, and to guarantee the validity and robustness of these classifiers, a Performance Evaluation Indicator (PEI) and the corresponding failure criterion are proposed in this study. Three types of machine learning classifiers, including the strictly binary classifier, the normal multiclass classifier and the misclassification cost-sensitive classifier, are trained on four datasets recorded from a water drainage TBM project. The results indicate that: (1) the PEI successfully compares the competence of classifiers under different scenarios by isolating the effects of different overlapping-degree of rockmass classes, and (2) the cost-sensitive algorithm is warranted to classify rockmasses when the ratio of inter-class classes is more than 8:1. The contributions of this research are to fill the gap in performance evaluations of a classifier for imbalanced training data, and to identify the best situation to apply this classifier.