Unsupervised Functional Data Clustering Based on Adaptive Weights
- 1 School of Sciences, Hebei University of Technology, Tianjin, China
- 2 School of Sciences, Beijing Institute of Petrochemical Technology, Beijing, China
Abstract
In recent years, functional data has been widely used in finance, medicine, biology and other fields. The current clustering analysis can solve the problems in finite-dimensional space, but it is difficult to be directly used for the clustering of functional data. In this paper, we propose a new unsupervised clustering algorithm based on adaptive weights. In the absence of initialization parameter, we use entropy-type penalty terms and fuzzy partition matrix to find the optimal number of clusters. At the same time, we introduce a measure based on adaptive weights to reflect the difference in information content between different clustering metrics. Simulation experiments show that the proposed algorithm has higher purity than some algorithms.
- Ramsay, J.O. (1982) When the Data Are Functions. Psychometrika, 47, 379-396. https://doi.org/10.1007/BF02293704
- Bouveyron, C., Girard, S. and Schmid, C. (2007) High-Dimensional Data Clustering. Computational Statistics & Data Analysis, 52, 502-519. https://doi.org/10.1016/j.csda.2007.02.009
- Zhu, J. and Chen, K. (2007) The Cluster Analysis of Panel Data and Its Application. Statistical Research, 24, 11-14.
- Tarpey, T. and Kinateder, K.K.J. (2003) Clustering Functional Data. Journal of Classification, 20, 93-114. https://doi.org/10.1007/s00357-003-0007-3
- Tokushige, S., Yadohisa, H. and Inada, K. (2007) Crisp and Fuzzy K-Means Clustering Algorithms for Multivariate Functional Data. Computational Statistics, 22, 1-16. https://doi.org/10.1007/s00180-006-0013-0
- Antoniadis, A., Brossat, X., Cugliari, J. and Poggi, J.M. (2013) Clustering Functional Data Using Wavelets. International Journal of Wavelets, Multiresolution and Information Processing, 11, 1350003. https://doi.org/10.1142/S0219691313500033
- Wang, D., Zhu, J. and Wang, D. (2015) Research of Clustering Analysis for Functional Data Based on Adaptive Weighting. Journal of Applied Statistics and Management, 34, 84-92.
- Delaigle, A., Hall, P. and Pham, T. (2019) Clustering Functional Data into Groups by Using Projections. Journal of the Royal Statistical Society: Series B: Statistical Methodology, 81, 271-304. https://doi.org/10.1111/rssb.12310
- Hardle, W., Kerkyacharian, G., Picard, D. and Tsybakov, A. (2012) Wavelets, Approximation, and Statistical Applications. Springer Science & Business Media, Berlin.
- Fryzlewicz, P. (2007) Unbalanced Haar Technique for Nonparametric Function Estimation. Journal of the American Statistical Association, 102, 1318-1327. https://doi.org/10.1198/016214507000000860
- Sharp, A. and Browne, R. (2021) Functional Data Clustering by Projection into Latent Generalized Hyperbolic Subspaces. Advances in Data Analysis and Classification, 15, 735-757. https://doi.org/10.1007/s11634-020-00432-5
- Wu, R., Wang, B. and Xu, A. (2022) Functional Data Clustering Using Principal Curve Methods. Communications in Statistics-Theory and Methods, 51, 7264-7283. https://doi.org/10.1080/03610926.2021.1872636
- Wang, D., Zhu, J. and Xie, B. (2012) Research on Clustering Analysis for Functional Data Based on Adaptive Iteration. Statistical Research, 4, 91-96.