# Review of Clustering Methods for Functional Data

arXiv: https://arxiv.org/abs/2210.00847 · HTML: https://mlsanity.com/paper/2210.00847/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 130 references that are in the map.
- First posted on arXiv 3 Oct 2022.

## Builds on (most cited first, 24 of 24)

- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data](https://mlsanity.com/paper/1706.03161/) (2017)
- [Clustering with Deep Learning: Taxonomy and New Methods](https://mlsanity.com/paper/1801.07648/) (2018)
- [Spatio-Temporal Data Mining: A Survey of Problems and Methods](https://mlsanity.com/paper/1711.04710/) (2017)
- [Functional Data Analysis of Amplitude and Phase Variation](https://mlsanity.com/paper/1512.03216/) (2015)
- [Weighted Clustering Ensemble: A Review](https://mlsanity.com/paper/1910.02433/) (2019)
- [Piecewise regression mixture for simultaneous functional data clustering and optimal segmentation](https://mlsanity.com/paper/1312.6974/) (2013)
- [Simultaneous Registration and Clustering for Multi-dimensional Functional Data](https://mlsanity.com/paper/1711.04761/) (2017)
- [Online EM for Functional Data](https://mlsanity.com/paper/1604.00570/) (2016)
- [A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data](https://mlsanity.com/paper/1708.00386/) (2017)
- [Model-Based Clustering and Classification of Functional Data](https://mlsanity.com/paper/1803.00276/) (2018)
- [Clustering multivariate functional data using unsupervised binary trees](https://mlsanity.com/paper/2012.05973/) (2020)
- [Shape Analysis of Functional Data with Elastic Partial Matching](https://mlsanity.com/paper/2105.08604/) (2021)
- [Sparse Clustering of Functional Data](https://mlsanity.com/paper/1501.04755/) (2015)
- [Whole-Volume Clustering of Time Series Data from Zebrafish Brain Calcium Images via Mixture Modeling](https://mlsanity.com/paper/1611.01602/) (2016)
- [Selection of the Number of Clusters in Functional Data Analysis](https://mlsanity.com/paper/1905.00977/) (2019)
- [Functional Factorial K-means Analysis](https://mlsanity.com/paper/1311.0463/) (2013)
- [Inference on covariance operators via concentration inequalities: k-sample tests, classification, and clustering via Rademacher complexities](https://mlsanity.com/paper/1604.06310/) (2016)
- [Model-based curve registration via stochastic approximation EM algorithm](https://mlsanity.com/paper/1712.07265/) (2017)
- [A similarity measure for second order properties of non-stationary functional time series with applications to clustering and testing](https://mlsanity.com/paper/1810.08292/) (2018)
- [Multivariate Functional Data Modeling with Time-varying Clustering](https://mlsanity.com/paper/1904.11518/) (2019)
- [Clustering Brain Signals: A Robust Approach Using Functional Data Ranking](https://mlsanity.com/paper/2007.14078/) (2020)
- [Mixtures of Gaussian Processes for regression under multiple prior distributions](https://mlsanity.com/paper/2104.09185/) (2021)
- [Random cohort effects and age groups dependency structure for mortality modelling and forecasting: Mixed-effects time-series model approach](https://mlsanity.com/paper/2112.15258/) (2021)

## Built on by (most cited first, 6 of 6)

- [Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders](https://mlsanity.com/paper/2509.22969/) (2025)
- [On the Use of Relative Validity Indices for Comparing Clustering Approaches](https://mlsanity.com/paper/2404.10351/) (2024)
- [Hypernetwork-based approach for grid-independent functional data clustering](https://mlsanity.com/paper/2602.22823/) (2026)
- [Neural Operators Can Discover Functional Clusters](https://mlsanity.com/paper/2602.23528/) (2026)
- [K-Models: a Flexible and Interpretable Method for Ordinal Clustering with Application to Antigen-Antibody Interaction Profiles](https://mlsanity.com/paper/2605.14828/) (2026)
- [Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifold](https://mlsanity.com/paper/2609.30487/) (2026)

## Abstract (arXiv)

Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across various fields of sciences, including but not limited to biology, (bio)chemistry, engineering, environmental science, medical science, psychology, social science, etc. The phenomenal growth of the application of functional data clustering indicates the urgent need for a systematic approach to develop efficient clustering methods and scalable algorithmic implementations. On the other hand, there is abundant literature on the cluster analysis of time series, trajectory data, spatio-temporal data, etc., which are all related to functional data. Therefore, an overarching structure of existing functional data clustering methods will enable the cross-pollination of ideas across various research fields. We here conduct a comprehensive review of original clustering methods for functional data. We propose a systematic taxonomy that explores the connections and differences among the existing functional data clustering methods and relates them to the conventional multivariate clustering methods. The structure of the taxonomy is built on three main attributes of a functional data clustering method and therefore is more reliable than existing categorizations. The review aims to bridge the gap between the functional data analysis community and the clustering community and to generate new principles for functional data clustering.