Multivariate online kernel density estimation with Gaussian kernels |
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| Authors: | Matej Kristan Ale? Leonardis Danijel Sko?aj |
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| Affiliation: | 1. Faculty of Computer and Information Science, University of Ljubljana, Slovenia;2. Faculty of Electrical Engineering, University of Ljubljana, Slovenia;1. ECARES, Université libre de Bruxelles CP114/4, B-1050 Brussels, Belgium;2. The Institute of Information Theory and Automation of the Czech Academy of Sciences, Pod Vodárenskou vě?í 4, CZ-182 08 Prague 8, Czech Republic;1. State Key Laboratory of Power Transmission Equipment and System Security, Chongqing University, Chongqing 400044, China;2. School of Electrical Engineering and Automation, Hefei University of Technology, Anhui 230009, China;3. University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada;4. Department of Electrical and Computer Engineering, University of Tulsa, Tulsa, OK 74104, USA;5. Chongqing Electric Power Research Institute, Yubei District, Chongqing 401123, China;1. University of Vigo, Lagoas–Marcosende, 36 310 Vigo, Spain;2. Institute of Statistics, Biostatistics and Actuarial Sciences, Université catholique de Louvain, Voie du Roman Pays 20, B 1348 Louvain-la-Neuve, Belgium;1. School of Electrical and Computer Engineering, Yazd University, Yazd, Iran;2. Department of Nursing, Yazd Branch, Islamic Azad University, Yazd, Iran;3. Hematology and Oncology Research Center, Shahid Sadoughi University of Medical Science and Health System, Yazd, Iran |
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| Abstract: | We propose a novel approach to online estimation of probability density functions, which is based on kernel density estimation (KDE). The method maintains and updates a non-parametric model of the observed data, from which the KDE can be calculated. We propose an online bandwidth estimation approach and a compression/revitalization scheme which maintains the KDE's complexity low. We compare the proposed online KDE to the state-of-the-art approaches on examples of estimating stationary and non-stationary distributions, and on examples of classification. The results show that the online KDE outperforms or achieves a comparable performance to the state-of-the-art and produces models with a significantly lower complexity while allowing online adaptation. |
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