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The common vector (CV) method is a linear subspace classifier method which allows one to discriminate between classes of data sets, such as those arising in image and word recognition. This method utilizes subspaces that represent classes during classification. Each subspace is modeled such that common features of all samples in the corresponding class are extracted. To accomplish this goal, the method eliminates features that are in the direction of the eigenvectors corresponding to the nonzero eigenvalues of the covariance matrix of each class. In this paper, we introduce a variation of the CV method, which will be referred to as the modified CV (MCV) method. Then, a novel approach is proposed to apply the MCV method in a nonlinearly mapped higher dimensional feature space. In this approach, all samples are mapped into a higher dimensional feature space using a kernel mapping function, and then, the MCV method is applied in the mapped space. Under certain conditions, each class gives rise to a unique CV, and the method guarantees a 100% recognition rate with respect to the training set data. Moreover, experiments with several test cases also show that the generalization performance of the proposed kernel method is comparable to the generalization performances of other linear subspace classifier methods as well as the kernel-based nonlinear subspace method. While both the MCV method and its kernel counterpart did not outperform the support vector machine (SVM) classifier in most of the reported experiments, the application of our proposed methods is simpler than that of the multiclass SVM classifier. In addition, it is not necessary to adjust any parameters in our approach. Index Terms--Common vector (CV), kernel-based subspace method, pattern recognition, subspace classifier.

In this paper, covariance behavior of several features (signature identifiers) that are determined from the voltage waveform within a time window for power-quality (PQ) event detection and classification is analyzed. A feature vector using selected signature identifiers such as local wavelet transform extrema at various decomposition levels, spectral harmonic ratios, and local extrema of higher order statistical parameters, is constructed. It is observed that the feature vectors corresponding to power quality event instances can be efficiently classified according to the event type using a covariance based classifier known as the common vector classifier. Arcing fault (high impedance fault) type events are successfully classified and distinguished from motor startup events under various load conditions. It is also observed that the proposed approach is even able to discriminate the loading conditions within the same class of events at a success rate of 70%. In addition, the common vector approach provides a redundancy and usefulness information about the feature vector elements. Implication of this information is experimentally justified with the fact that some of the signature identifiers are more important than others for the discrimination of PQ event types. Index Terms--Covariance analysis, event classification, higher order statistics, power-quality (PQ) analysis.

In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the within-class scatter matrix is singular and the Linear Discriminant Analysis (LDA) method cannot be applied directly. This problem is known as the "small sample size" problem. In this paper, we propose a new face recognition method called the Discriminative Common Vector method based on a variation of Fisher's Linear Discriminant Analysis for the small sample size case. Two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database. One algorithm uses the within-class scatter matrix of the samples in the training set while the other uses the subspace methods and the Gram-Schmidt orthogonalization procedure to obtain the discriminative common vectors. Then, the discriminative common vectors are used for classification of new faces. The proposed method yields an optimal solution for maximizing the modified Fisher's Linear Discriminant criterion given in the paper. Our test results show that the Discriminative Common Vector method is superior to other methods in terms of recognition accuracy, efficiency, and numerical stability. Index Terms--Common vectors, discriminative common vectors, face recognition, Fisher's linear discriminant analysis, principal component analysis, small sample size, subspace methods.

Common vector approach (CVA), discriminative common vector approach (DCVA), and linear regression classification (LRC) are subspace methods used in pattern recognition. Up to now, there were two well-known algorithms to calculate the common vectors: (i) by using the Gram-Schmidt orthogonalization process, (ii) by using the within-class covariance matrices. The purpose of this paper is to introduce a new implementation algorithm for the derivation of the common vectors using the linear regression idea. The derivation of the discriminative common vectors through LRC is also included in this paper. Two numerical examples are given to clarify the proposed derivations. An experimental work is given in AR face database to compare the recognition performances of CVA, DCVA, and LRC. Additionally, the three implementation algorithms of common vector are compared in terms of processing time efficiency. [ABSTRACT FROM AUTHOR]

The common vector (CV) method is a linear subspace classifier method which allows one to discriminate between classes of data sets, such as those arising in image and word recognition. This. method utilizes subspaces that represent classes during classification. Each subspace is modeled such that common features of all samples in the corresponding class are extracted. To accomplish this goal, the method eliminates features that are in the direction of the eigenvectors corresponding to the nonzero eigenvalues of the covariance matrix of each class. In this paper, we introduce a variation of the CV method, which will be referred to as the modified CV (MCV) method. Then, a novel approach is proposed to apply the MCV method in a nonlinearly mapped higher dimensional feature space. In this approach, all samples are mapped into a higher dimensional feature space using a kernel mapping function, and then, the MCV method is applied in the mapped space. Under certain conditions, each class gives rise to a unique CV, and the method guarantees a 100% recognition rate with respect to the training set data. Moreover, experiments with several test cases also show that the generalization performance of the proposed kernel method is comparable to the generalization performances of other linear subspace classifier methods as well as the kernel-based nonlinear subspace method. While both the MCV method and its kernel counterpart did not outperform the support vector machine (SVM) classifier in most of the reported experiments, the application of our proposed methods is simpler than that of the multiclass SVM classifier. In addition, it is not necessary to adjust any parameters in our approach. [ABSTRACT FROM AUTHOR]

In this work, the cross-sectional areas of the vocal tract are determined for the lossy and lossless cases by using the pole-zero models obtained from the electrical equivalent circuit model of the vocal tract and the system identification method. The cross-sectional areas are used to compare the lossy and lossless cases. In the lossy case, the internal losses due to wall vibration, heat conduction, air friction and viscosity are considered, that is, the complex poles and zeros obtained from the models are used directly. Whereas, in the lossless case, only the imaginary parts of these poles and zeros are used. The vocal tract shapes obtained for the lossy case are close to the actual ones. [ABSTRACT FROM AUTHOR]