The Kernel Common Vector Method: A Novel Nonlinear Subspace Classifier for Pattern Recognition

Abstract

Abstract-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.

Extended least squares support vector machines for ordinal regression

“…To obtain our nonlinear classifier for ordinal regression, similar to other kernel-based learning algorithms, we can use the kernel-based idea [37]. Define the nonlinear function u : R p !…”

Feature Extraction Using a Complete Kernel Extension of Supervised Graph Embedding

“…For FERET face database, three images of each individual are selected for training and the remaining images for testing. Figures 4,5,6,7,8,and 9 report the result the accuracies of different methods. As expected, our methods outperform other kernel-based methods, which indicate that making full use of irregular and regular discriminative information is efficient for face recognition.…”

“…Similar to LDA, KFD also encounters the ill-posed problem in its real-world applications. A number of regularization techniques to alleviate this problem have been suggested [5,6,15,16,19,21,22,27,34,36]. Zheng et al [36] further presented a modified algorithm for the KFD method by addressing the issue of several eigenvectors associating with the same eigenvalue.…”

“…However, the optimal weight of the within-class scatter matrix is difficult to determine. Cevikalp et al [5,6] developed a kernel discriminative common vector (KDCV) technique for face recognition. However, KDCV could be suboptimal because it only makes use of the discriminant information in the null space of within-class scatter matrix.…”

Array of Multilayer Perceptrons with No-class Resampling Training for Face Recognition

“…El kernel empleado para los métodos basados en subespacios no lineales es de tipo gausiano, porqué es el normalmente utilizado en tareas de clasificación de patrones, como en [4,5,16,20].…”