Weighted embedding and outlier detection of metric space data
: Heinonen, Lauri; Nyberg, Henri; Virta, Joni
Publisher: SPRINGER HEIDELBERG
: HEIDELBERG
: 2025
: Advances in Data Analysis and Classification
: ADVANCES IN DATA ANALYSIS AND CLASSIFICATION
: ADV DATA ANAL CLASSI
: 37
: 1862-5347
: 1862-5355
DOI: https://doi.org/10.1007/s11634-025-00627-8
: https://link.springer.com/article/10.1007/s11634-025-00627-8
: https://research.utu.fi/converis/portal/detail/Publication/485205296
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.
:
Open Access funding provided by University of Turku (including Turku University Central Hospital). The work of Lauri Heinonen was supported by the Research Council of Finland (Grants 321968 and 353769). The work of Henri Nyberg was supported by the Research Council of Finland (Grant 321968) and the Foundation for Economic Education (Liikesivistysrahasto, Grant 220246). The work of Joni Virta was supported by the Research Council of Finland (Grants 335077, 347501 and 353769).
