Abstract
Functional data clustering analysis becomes an urgent and challenging task in the new era of big data. In this paper, we propose a new framework for functional data clustering analysis, which adopts a similar structure as the k-means algorithm for the conventional clustering analysis. Under this framework, we clarify three issues: how to represent functions, how to measure distances between functions, and how to calculate centers of functions. We utilize Gaussian processes to represent the clusters of functions which are actually their sample curves or trajectories on a finite set of sample points. Moreover, we take the Wasserstein distance to measure the similarity between Gaussian distributions. With the choice of Wasserstein distance, the centers of Gaussian processes can be calculated analytically and efficiently. To demonstrate the effectiveness of the proposed method, we compare it with existing competitive clustering methods on synthetic datasets and the obtained results are encouraging. We finally apply the proposed method to three real-world datasets with satisfying results.
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Notes
- 1.
The details here are not so important, and the definition of Wasserstein 2-distance of Gaussian measures is enough for the development of this work. We present the formal definition here for completeness.
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Acknowledgements
This work was supported by the National Key R & D Program of China (2018YFC0808305).
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Li, T., Ma, J. (2020). Functional Data Clustering Analysis via the Learning of Gaussian Processes with Wasserstein Distance. In: Yang, H., Pasupa, K., Leung, A.CS., Kwok, J.T., Chan, J.H., King, I. (eds) Neural Information Processing. ICONIP 2020. Lecture Notes in Computer Science(), vol 12533. Springer, Cham. https://doi.org/10.1007/978-3-030-63833-7_33
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