Fuzzy multiset is applicable as a model of information retrieval because it has the mathematical structure which expresses the number and the degree of attribution of an element simultaneously. Therefore fuzzy multisets can be used also as a suitable model for document clustering. This paper aims at developing clustering algorithms based on a fuzzy multiset model for document clustering. The st...

In this paper, we deal with the pattern recognition problem using non-linear statistical models based on Kernel Principal Component Analysis. Objects that we try to recognize are defined by ordered sets of points. We present here two types of models: the first one uses an explicit projection function, the second one uses the Kernel trick. The present work attempts to estimate the localization o...

A simple, yet powerful, learning method is presented by combining the famed kernel trick and the least-mean-square (LMS) algorithm, called the KLMS. General properties of the KLMS algorithm are demonstrated regarding its well-posedness in very high dimensional spaces using Tikhonov regularization theory. An experiment is studied to support our conclusion that the KLMS algorithm can be readily u...

Kernel trick is a powerful tool being used for solving complex pattern classification problem. As long as a linear feature extraction algorithm can be expressed exclusively by dot-products, it can be extended to non-linear version by combining kernel method. In this paper, we present such an improved iterative algorithm used for linear discriminant analysis. By mapping data onto high dimensiona...

The term kernel is derived from a word that can be traced back to c. 1000 and originally meant a seed (contained within a fruit) or the softer (usually edible) part contained within the hard shell of a nut or stone-fruit. The former meaning is now obsolete. It was first used in mathematics when it was defined for integral equations in which the kernel is known and the other function(s) unknown,...

Face recognition has been a research topic of pattern recognition and feature extraction is an important step toward face recognition. In this paper, we first propose a method to transform from LDA to PCA with the discriminative information embedded in a whitening transformation, and then we propose a support vector machine (SVM) method of LDA. The kernel algorithm of the SVM solution to LDA ha...

We present the first model and algorithm for L1-norm kernel PCA. While L2-norm kernel PCA has been widely studied, there has been no work on L1-norm kernel PCA. For this non-convex and non-smooth problem, we offer geometric understandings through reformulations and present an efficient algorithm where the kernel trick is applicable. To attest the efficiency of the algorithm, we provide a conver...

Mika et al. [1] apply the “kernel trick” to obtain a non-linear variant of Fisher’s linear discriminant analysis method, demonstrating state-of-the-art performance on a range of benchmark datasets. We show that leave-one-out cross-validation of kernel Fisher discriminant classifiers can be implemented with a computational complexity of only O(l3) operations rather than the O(l4) of a näıve impl...

Reproducing Kernel Hilbert Spaces (RKHS) have been found incredibly useful in the machine learning community. Their theory has been around for quite some time and has been used in the statistics literature for at least twenty years. More recently, their application to perceptron-style algorithms, as well as new classes of learning algorithms (specially large-margin or other regularization machi...

Kernel discriminant analysis (KDA) is effective to extract nonlinear discriminative features of input samples using the kernel trick. However, the conventional KDA algorithm endures the kernel selection which has significant impact on the performances of KDA. In order to overcome this limitation, a novel nonlinear feature extraction method called adaptive quasiconformal kernel discriminant anal...