February 2025
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17 Reads
Advances in Data Analysis and Classification
This work discusses weighted kernel point projection (WKPP), a new method for embedding metric space or kernel data. WKPP is based on an iteratively weighted generalization of multidimensional scaling and kernel principal component analysis, and one of its main uses is outlier detection. After a detailed derivation of the method and its algorithm, we give theoretical guarantees regarding its convergence and outlier detection capabilities. Additionally, as one of our mathematical contributions, we give a novel characterization of kernelizability, connecting it also to the classical kernel literature. In our empirical examples, WKPP is benchmarked with respect to several competing outlier detection methods, using various different datasets. The obtained results show that WKPP is computationally fast, while simultaneously achieving performance comparable to state-of-the-art methods.
![Percentage of correctly estimated dimensions d as a function of the degree of freedom ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document} of the multivariate t-distribution in the tail thickness simulation. The sample size is n=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 100$$\end{document} throughout](https://www.researchgate.net/publication/376376469/figure/fig1/AS:11431281257896258@1719917121621/Percentage-of-correctly-estimated-dimensions-d-as-a-function-of-the-degree-of-freedom_Q320.jpg)
![Mean of the error in dimension estimation as a function of the degree of freedom ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document} of the multivariate t-distribution in the tail thickness simulation. The sample size is n=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 100$$\end{document} throughout](https://www.researchgate.net/publication/376376469/figure/fig2/AS:11431281257915823@1719917125419/Mean-of-the-error-in-dimension-estimation-as-a-function-of-the-degree-of-freedom_Q320.jpg)
![Average absolute errors of the dimension estimates as a function of the underlying dimension d when sample size is n=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 100$$\end{document} (top panel) or n=1000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 1000$$\end{document} (bottom panel)](https://www.researchgate.net/publication/376376469/figure/fig3/AS:11431281257887078@1719917129092/Average-absolute-errors-of-the-dimension-estimates-as-a-function-of-the-underlying_Q320.jpg)
![The monthly log returns (in percentages) of five stocks (IBM, HPQ, INTC, JPM, BAC) from January 1990 to December 2008. See [Tsay (2010), Section 9]](https://www.researchgate.net/publication/376376469/figure/fig5/AS:11431281257953507@1719917136512/The-monthly-log-returns-in-percentages-of-five-stocks-IBM-HPQ-INTC-JPM-BAC-from_Q320.jpg)
