Extraction of Signals With Specific Temporal Structure Using Kernel Methods

This paper proposes a blind source extraction (BSE) method on the basis of several time-delay autocorrelations from primary sources. This method is a second-order statistic learning algorithm, which can extract a desired biomedical signal while it shows a specific temporal structure. In contrast to conventional BSE methods, it is simple and do not need to choose any learning step size. Computer simulations on biomedical measurements demonstrate its validity and high performance in the process of revealing the underlying desired signal.

Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.

This paper presents a novel algorithm - robust kernel principal component analysis (robust KPCA), on the basis of the research of kernel principal component analysis (KPCA) and robust principal component analysis (RPCA). First, this algorithm sets the radius of the images of the training samples in the feature space using kernel tricks, then determines whether the samples are outliers or not, and finally analyzes the training samples which have eliminated the outliers using KPCA algorithm. The improved KPCA algorithm not only retains the non-linearity property of KPCA algorithm but also gets better robustness. Because the effects of outliers are eliminated, robust KPCA algorithm gets higher accuracy than KPCA algorithm for data analysis. The simulation experiments show that the robust KPCA algorithm developed is better than the KPCA algorithm.

The inherent physical characteristics of many real-life phenomena, including biological and physiological aspects, require adapted nonlinear tools. Moreover, the additive nature in some situations involve solutions expressed as positive combinations of data. In this paper, we propose a nonlinear feature extraction method, with a non-negativity constraint. To this end, the kernel principal component analysis is considered to define the most relevant features in the reproducing kernel Hilbert space. These features are the nonlinear principal components with high-order correlations between input variables. A pre-image technique is required to get back to the input space. With a non-negative constraint, we show that one can solve the pre-image problem efficiently, using a simple iterative scheme. Furthermore, the constrained solution contributes to the stability of the algorithm. Experimental results on event-related potentials (ERP) illustrate the efficiency of the proposed method.

Principal component analysis (PCA) has been proven to be an efficient method in dimensionality reduction, feature extraction and pattern recognition. Kernel principal component analysis (KPCA) can be considered as a natural nonlinear generalization of PCA, which performs linear PCA in a high dimensional space implicitly by using kernel trick. However, both conventional PCA and KPCA suffer from the deficiency of being sensitive to outliers. Existing robust KPCA has to eigen-decompose the gram matrix directly in each step and is much more computationally infeasible due to the large size of the matrix when the number of training samples is large. By extending existing robust PCA algorithm using kernel methods, we present a novel robust adaptive algorithm for calculating the kernel principal components. The proposed method not only preserves the characteristic of capturing underlying nonlinear structure of KPCA but also is robust against outliers by restraining the effect of outlying samples. Compared with existing robust KPCA methods, our method is performed without having to store the kernel matrix, which can reduce significantly the storage burden. In addition, our method shows the potential of expansibility to the incremental learning version. Experimental results on synthetic data indicate that our improved algorithm is effective and promising.

We present a novel data embedding that significantly reduces the estimation error of locality sensitive hashing (LSH) technique when used in reproducing kernel Hilbert space (RKHS). Efficient and accurate kernel approximation techniques either involve the kernel principal component analysis (KPCA) approach or the Nystrom approximation method. In this work we show that extant LSH methods in this space suffer from a bias problem, that moreover is difficult to estimate apriori. Consequently, the LSH estimate of a kernel is different from that of the KPCA/Nystrom approximation. We provide theoretical rationale for this bias, which is also confirmed empirically. We propose an LSH algorithm that can reduce this bias and consequently our approach can match the KPCA or the Nystrom methods’ estimation accuracy while retaining the traditional benefits of LSH. We evaluate our algorithm on a wide range of realworld image datasets (for which kernels are known to perform well) and show the efficacy of our algorithm using a variety of principled evaluations including mean estimation error, KL divergence and the Kolmogorov-Smirnov test.

We propose a data analysis method that combines the objectives of nonlinear principal component analysis and nonlinear discriminant analysis with the kernel method in a reproducing kernel Hilbert space. This method addresses nonlinear data analysis problems in high-dimensional spaces, specifically the reproducing kernel Hilbert space, through the use of the kernel trick. Our proposed method can be considered as a semi-supervised data analysis approach. We evaluate our proposed method using various kernel functions and datasets, both visually and quantitatively. The evaluation results demonstrate that our proposal outperforms kernel principal component analysis and generalized discriminant analysis in terms of classification performance. This indicates the advantages and originality of our proposed method. Furthermore, we analyze and discuss our findings based on the evaluation results, and highlight potential areas for further research and future work related to our proposal.

In kernel methods, choosing a suitable kernel is in dispensable for favorable results. No well-founded methods, however, have been established in general for unsupervised learning. We focus on kernel Princ ipal Component Analysis (kernel PCA), which is a nonlinear extension of principal component analysis and ha s been used electively for extracting nonlinear featu res and reducing dimensionality. As a kernel method , kernel PCA also suffers from the problem of kernel choice. Although cross-validation is a popular meth od for choosing hyperparameters, it is not applicable straightforwardly to choose a kernel in kernel PCA because of the incomparable norms given by differen t kernels. It is important, thus, to develop a well founded method for choosing a kernel in kernel PCA. This study proposes a method for choosing hyperparameters in kernel PCA (kernel and the number of components) based on cross-validation for the comparable reconstruction errors of pre-images in t he original space. The experimental results on synthesized and real-world datasets demonstrate tha t the proposed method successfully selects an appropriate kernel and the number of components in kernel PCA in terms of visualization and classification errors on the principal components. The results imply that the proposed method enables automatic design of hyperparameters in kernel PCA.

Kernel discriminant analysis (KDA) and the kernel principal component analysis (KPCA), which are the extension of the linear discriminant analysis (LDA) and the principal component analysis (PCA), respectively, from linear domain to nonlinear domain via the kernel trick, are two very popular nonlinear feature extraction methods. In this paper, we present a new feature extraction algorithm by combing KDA and KPCA, and then apply it to the face recognition task. The experimental results on Yale face dataset show that the proposed method can significantly improve the performance both KDA and KPCA.

Subspace methods that utilize principal component analysis (PCA) are widely used for pattern classification or detection problems. Kernel PCA (KPCA) that is an extension of PCA is also applied to subspace methods. However, its computational cost is very high since the computational cost mainly depends on the number of samples in kernel methods. Recently, subset KPCA (SKPCA) has been proposed in order to reduce its computational complexity. In this paper, we apply SKPCA to subspace methods, and compare SKPCA with KPCA using some sample selection methods. Experimental results demonstrate advantages of subspace methods using SKPCA.

A local–global mixed kernel with reproducing property

A novel Gabor-Kernel face recognition method is proposed in this paper. This involves convolving a face image with a series of Gabor wavelets at different scales, locations, and orientations and extracting features from resulting Gabor filtered images. kernel discriminant analysis (KDDA) is then applied to the feature vectors for dimension reduction as well as class separability enhancement. A database of 600 frontal-view face images from the FERET face database is used to test the method. Experimental results demonstrate the advantage of KDDA over other Kernel methods such as kernel principal component analysis (KPCA) and general discriminant analysis (GDA). Significant improvements are also observed when features are extracted from Gabor filtered images instead of the original images. A 94% accuracy has been observed for the novel Gabor + KDDA method on the FERET database using a simple classifier, which could be further improved by employing a more complex classifier and distance measurer.

Support Vector Machines and Kernel methods have become very popular as methods for learning from examples. In this paper, in order to solve the non-linear and the time of recognition problem, recent advanced techniques are presented. For example, Kernel Principal Components and Proximal Support Vector Machines, Kernel Principal Components Analysis can describe multiple correlations between pixels in the image recognition, and can handle the high order statistics of the original data, at the same time the nonlinear features of the image can be preferably extracted. Proximal Support Vector Machines is an improvement for these characters of Support Vector Machines, combines the proximal algorithm with Support Vector Machines, has a better ability of nonlinear mapping and a stronger generalization capability, and the pace of Proximal Support Vector Machines is very enhanced. In this paper, the computer simulation was progressed based on ORL face database, the effectiveness of the Proximal Support Vector Machines algorithm and Kernel Principal Components Analysis algorithm were shown by experimental results.

There is a trend in recent machine learning community to construct a nonlinear version of a linear algorithm using the 'kernel method', e.g. Support Vector Machines (SVMs), kernel principal component analysis, kernel fisher discriminant analysis and the recent kernel clustering algorithms. In unsupervised clustering algorithms using kernel method, typically, a nonlinear mapping is used first to map the data into a potentially much higher feature space, where clustering is then performed. A drawback of these kernel clustering algorithms is thatthe clustering prototypes lie in high dimensional feature space and hence lack clear and intuitive descriptions unless using additional projection approximation from the feature to the data space as done in the existing literatures. In this paper, a novel clustering algorithm using the 'kernel method' based on the classical fuzzy clustering algorithm (FCM) is proposed and called as kernel fuzzy c-means algorithm (KFCM). KFCM adopts a new kernel-induced metric in the data space to replace the original Euclidean norm metric in FCM and the clustered prototypes still lie in the data space so that the clustering results can be reformulated and interpreted in the original space. Our analysis shows that KFCM is robust to noise and outliers and also tolerates unequal sized clusters. And finally this property is utilized to cluster incomplete data. Experiments on two artificial and one real datasets show that KFCM hasbetter clustering performance and more robust than several modifications of FCM for incomplete data clustering.

A deep kernel method for lithofacies identification using conventional well logs