Functional Data for Cluster Analysis

Lists of open-access functional datasets from different fields of application. We only collect data that can be used for cluster analysis. The main objective is to facilitate comparing with existing clustering methods (for functional data) and evaluating new clustering methods. A recent comprehensive review of clustering methods for functional data is available here. Our team is actively developing functional data clustering methods tailored to various data types and application domains. The software tools we have developed can be accessed here.

For datasets that need further processing on the linked data, a copy of them can be found in the Data folder. (This ongoing project is a bit slow, due to other commitments of the contributor.)

One-dimensional Functional Data

Name	Available at	Field	Task	Size	Length	Missing Value
ARC_Mobile	Publisher	Health	Clustering	125	30/40	Yes
ArrowHead	UEA & UCR Time Series Classification Repository	Computer Vision	Classification	211	251	No
BirdChicken	UEA & UCR Time Series Classification Repository	Computer Vision	Classification	40	512	No
BTH_PM25	Publisher	Environment	Clustering	73	48	Yes
China_PM25	Publisher	Environment	Clustering	338	731	Yes
DiatomSizeReduction	UEA & UCR Time Series Classification Repository	Bioinformatics	Classification	322	345	No
ECG200	UEA & UCR Time Series Classification Repository	ECG	Classification	200	96	No
FaceFour	UEA & UCR Time Series Classification Repository	Computer Vision	Classification	112	350	No
Flour	R (cfda)	Food	Classification	115	241	No
Fungi	UEA & UCR ...	Bioinformatics	Classification	204	201	No
GunPoint	UEA & UCR Time Series Classification Repository	Motion	Classification	200	150	No
Meat	UEA & UCR Time Series Classification Repository	Food	Classification	120	448	No
Plane	UEA & UCR ...	Shape	Classification	210	144	No
Phoneme	e-Book (ElemStatLearn)	Speech	Classification	4K+	256	No
Strawberry	UEA & UCR Time Series Classification Repository	Food	Classification	983	235	No
Symbols	UEA & UCR Time Series Classification Repository	Computer Vision	Classification	1K+	398	No
Tecator	CMU StatLib	Food	Classification	240	100	No

Multi-dimensional Functional Data

Name	Available at	Field	Task	Size	Length	Dimension
BasicMotions	UEA & UCR Time Series Classification Repository	Motion	Classification	80	100	6
Blink	UEA & UCR ...	EEG	Classification	950	510	4
ECG_Arrhythmia	Publisher	ECG	Classification	10K+	5000	12
EEG_Full	UCI Machine Learning Repository	EEG	Classification	122	256	64
Epilepsy	UEA & UCR ...	Motion	Classification	275	207	3
ERing	UEA & UCR ...	Gesture	Classification	300	65	4
EyesOpenShut	UEA & UCR ...	EEG	Classification	98	128	14
FingerMovements	UEA & UCR ...	EEG	Classification	416	50	28
Japanese_Vowels	UCI Machine Learning Repository	Speech	Classification	640	29	12
UWaveGestureLibrary	UEA & UCR ...	Gesture	Classification	4K+	315	3

Manifold-valued Functional Data

We provided a Python generator for manifold-valued functional data. It can simulate five families of trajectories:

• Hypersphere (unit sphere trajectories)
• Hyperbolic (Poincaré ball model)
• Swiss roll (Swiss-roll curves, up to 3D)
• Lorenz (chaotic attractor, up to 3D)
• Pendulum (simple pendulum dynamics, up to 3D)

Each dataset is a collection of multi-dimensional functions that evolve along a specified manifold or dynamical system. The generator script lives in the Data/Manifold/ directory as manifold_valued_data_generator.py. You can import it or run it directly. This generator was used in our NeurIPS work to evaluate FAEclust.

Outputs & Shapes

• X.shape = (n_samples, n_features, n_steps): multivariate time series laid out as [sample, feature, time].
• y.shape = (n_samples,): integer labels (0 … n_clusters-1) for cluster/dynamics identity.

Key Parameters

• n_samples: number of time series (functions) to generate.
• n_features: dimensionality per time step (e.g., 2D, 3D coordinates).
• n_steps: length (number of time points) in each trajectory.
• n_clusters: number of distinct clusters/dynamics per dataset.
• base_noise (optional): small perturbations; useful for realism.
• seed (optional): random seed for reproducibility.

To change the size of a dataset (e.g., more functions), edit the corresponding tuple in specs - no other code changes needed.