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Dm-KDE: dynamical kernel density estimation by sequences of KDE estimators with fixed number of components over data streams

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Abstract

In many data stream mining applications, traditional density estimation methods such as kernel density estimation, reduced set density estimation can not be applied to the density estimation of data streams because of their high computational burden, processing time and intensive memory allocation requirement. In order to reduce the time and space complexity, a novel density estimation method Dm-KDE over data streams based on the proposed algorithm m-KDE which can be used to design a KDE estimator with the fixed number of kernel components for a dataset is proposed. In this method, Dm-KDE sequence entries are created by algorithm m-KDE instead of all kernels obtained from other density estimation methods. In order to further reduce the storage space, Dm-KDE sequence entries can be merged by calculating their KL divergences. Finally, the probability density functions over arbitrary time or entire time can be estimated through the obtained estimation model. In contrast to the state-of-the-art algorithm SOMKE, the distinctive advantage of the proposed algorithm Dm-KDE exists in that it can achieve the same accuracy with much less fixed number of kernel components such that it is suitable for the scenarios where higher on-line computation about the kernel density estimation over data streams is required.We compare Dm-KDE with SOMKE and M-kernel in terms of density estimation accuracy and running time for various stationary datasets. We also apply Dm-KDE to evolving data streams. Experimental results illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Digital Media, Jiangnan University, Wuxi, 214122, China

    Min Xu, Xin Gu & Shitong Wang

  2. School of Internet of Things Technology, Wuxi Institute of Technology, Wuxi, 214121, China

    Min Xu

  3. Department of Computer Science, Osaka Prefecture University, Osaka, 599-8531, Japan

    Hisao Ishibuchi

Authors
  1. Min Xu
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  2. Hisao Ishibuchi
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  3. Xin Gu
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  4. Shitong Wang
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Corresponding author

Correspondence to Shitong Wang.

Additional information

Min Xu received the BS degree from Suzhou University, China in 2002 and the MS degree from Jiangnan University, China in 2009. Currently, she is a lecturer and pursuing a PhD degree in the School of Digital Media, Jiangnan University, China. Her current research interests include pattern recognition, information retrieval.

Hisao Ishibuchi received the BS, MS and PhD degrees in industrial engineering from Osaka Prefecture University, Osaka, Japan. Since 1999, he has been a full professor with Osaka Prefecture University. His research interests include artificial intelligence, neural fuzzy systems, and data mining. Dr. Ishibuchi is on the editorial boards of several journals, including the IEEE Transactions Fuzzy Systems and the IEEE Transactions on Systems, Man, and Cybernetics (B): Cybernetics.

Xin Gu received the BS degree from Southerneast University, China in 2001 and the MS degree from Jiangnan University in 2009. Currently, he is pursuing a PhD degree in the School of Digital Media, Jiangnan University, China. His current research interests include pattern recognition, information retrieval.

Shitong Wang received the MS degree in computer science from Nanjing University of Aeronautics and Astronautics, China in 1987. He visited London University and Bristol University in UK, Hiroshima International University in Japan, Hong Kong University of Science and Technology, Hong Kong Polytechnic University, as a research scientist, for over six years. Currently, he is a full professor of the School of Digital Media, Jiangnan University, China. His research interests include artificial intelligence, neuro-fuzzy systems, pattern recognition, and image processing. He has published about 80 papers in international/national journals and has authored seven books.

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Xu, M., Ishibuchi, H., Gu, X. et al. Dm-KDE: dynamical kernel density estimation by sequences of KDE estimators with fixed number of components over data streams. Front. Comput. Sci. 8, 563–580 (2014). https://doi.org/10.1007/s11704-014-3105-y

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  • DOI: https://doi.org/10.1007/s11704-014-3105-y

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