Hypernetwork-based approach for grid-independent functional data clustering

Anirudh Thatipelli; Ali Siahkoohi

cs.LGFeb 26, 2026

Hypernetwork-based approach for grid-independent functional data clustering

Authors: Anirudh Thatipelli, Ali Siahkoohi

Organizations: Department of Computer Science, University of Central Florida

Abstract

Functional data clustering is concerned with grouping functions that share similar structure, yet most existing methods implicitly operate on sampled grids, causing cluster assignments to depend on resolution, sampling density, or preprocessing choices rather than on the underlying functions themselves. To address this limitation, we introduce a framework that maps discretized function observations -- at arbitrary resolution and on arbitrary grids -- into a fixed-dimensional vector space via an auto-encoding architecture. The encoder is a hypernetwork that maps coordinate-value pairs to the weight space of an implicit neural representation (INR), which serves as the decoder. Because INRs represent functions with very few parameters, this design yields compact representations that are decoupled from the sampling grid, while the hypernetwork amortizes weight prediction across the dataset. Clustering is then performed in this weight space using standard algorithms, making the approach agnostic to both the discretization and the choice of clustering method. By means of synthetic and real-world experiments in high-dimensional settings, we demonstrate competitive clustering performance that is robust to changes in sampling resolution -- including generalization to resolutions not seen during training.

Figures & tables

Panel of Figure 1 — Figure 1: Overview of the proposed framework. Discretized function observations—sampled at varying resolutions and on potentially different grids (left)—are mapped by the hypernetwork encoder $H_{\bm{\theta}}$ into the weight space of a SIREN decoder (center). The per-point network $h^{(1)}$ processes each coordinate-value pair independently, mean pooling aggregates features into a fixed-dimensional vector, and the weight predictor $h^{(2)}$ outputs the SIREN weights $\bm{w}$ . The resulting weight vectors lie in a common Euclidean space regardless of the input discretization, enabling direct application of standard clustering algorithms (right). The dashed arrow denotes the reconstruction loss (equation ( 7 )) used to train the hypernetwork end-to-end. Code to reproduce the results presented in this work is available at github.com/luqigroup/hypercluster .

Figure 2: UMAP visualization of MNIST embedding. The marker shapes denote the different resolutions $r\in\{14,28,56\}$ , and the points are colored by ground-truth digit label. Digit classes form coherent clusters overlapping across resolutions, indicating that the learned representation is primarily structured by semantic identity.

Panel of Figure 3 — Figure 3: Representative MNIST samples arranged in a grid where rows correspond to discretization resolutions and columns correspond to learned clusters. Digits are clustered according to their semantic meaning, not by their discretization resolution.

Resolution	AMI $(\uparrow)$	ARI $(\uparrow)$
$14$	$0.720\pm 0.014$	$0.604\pm 0.035$
$28$	$0.724\pm 0.013$	$0.606\pm 0.034$
$56$	$0.723\pm 0.014$	$0.607\pm 0.034$
$7$	$0.578\pm 0.008$	$0.456\pm 0.034$
$112$	$0.723\pm 0.014$	$0.607\pm 0.034$

Table 1: Clustering Performance (mean

\pm

std over

5

seeds) across discretization resolutions. Trained on multi-resolution

\mathrm{R_{train}}=\{14,28,56\}

; evaluated on seen and held-out resolutions

\mathrm{R_{test}}=\{7,112\}

. ARI/AMI computed with K-Means (K=10). Stability across 14–56 and 112 indicates resolution invariance; degradation at 7 reflects severe undersampling.

Panel of Figure 4 — Figure 4: Representative Kvasir samples arranged in a grid where rows correspond to discretization resolutions and columns correspond to learned clusters. Samples are mapped to their classes, irrespective of their resolution.

Figure 5: UMAP visualization of Kvasir embeddings. Ground-truth classes are represented by different colors and markers denote different resolutions. Compared to MNIST, class separation is less pronounced due to higher intra-class variability and visual ambiguity; however, embeddings from different resolutions overlap within each semantic group, indicating minimal resolution-induced stratification.

Resolution	AMI $(\uparrow)$	ARI $(\uparrow)$
$64$	$0.479\pm 0.014$	$0.311\pm 0.010$
$128$	$0.481\pm 0.013$	$0.312\pm 0.009$
$256$	$0.481\pm 0.015$	$0.313\pm 0.010$
$32$	$0.479\pm 0.014$	$0.311\pm 0.010$
$512$	$0.481\pm 0.014$	$0.311\pm 0.010$

Table 2: Clustering Performance (mean

\pm

std over

5

seeds) across discretization resolutions. Trained on multi-resolution

\mathrm{R_{train}}=\{64,128,256\}

; evaluated on seen and held-out resolutions

\mathrm{R_{test}}=\{32,512\}

. ARI/AMI computed with K-Means (K=

8

). AMI and ARI remain stable across discretizations.

Panel of Figure 6 — Figure 6: ERing embeddings and cluster samples. Left: UMAP visualization; while class separability is less than in MNIST, embeddings do not stratify by timesteps. Right: Representative samples arranged by discretization timestep (rows) and learned cluster (columns). Class identity is preserved irrespective of discretization.

Resolution	AMI $(\uparrow)$	ARI $(\uparrow)$
$33$	$0.564\pm 0.041$	$0.408\pm 0.049$
$65$	$0.559\pm 0.042$	$0.404\pm 0.051$
$130$	$0.559\pm 0.042$	$0.403\pm 0.049$
$16$	$0.558\pm 0.049$	$0.404\pm 0.056$
$260$	$0.556\pm 0.044$	$0.402\pm 0.051$

Table 3: Clustering Performance (mean

\pm

std over

5

seeds) across discretization timesteps. Trained on multi-resolution

\mathrm{R_{train}}=\{33,65,130\}

; evaluated on seen and held-out resolutions

\mathrm{R_{test}}=\{16,260\}

. ARI/AMI computed with K-Means (K=

6

). AMI and ARI remain unaffected across different discretizations.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 7 — Figure 7: Representative members from four learned clusters on MNIST. The learned embeddings maintain class separation and avoid resolution-level stratification.

Figure 8: Training and validation loss curves for MNIST.

Resolution	KMeans(AMI) $(\uparrow)$	KMeans(ARI) $(\uparrow)$	GMM(AMI) $(\uparrow)$	GMM(ARI) $(\uparrow)$
$14$	$0.713$	$0.586$	$0.703$	$0.589$
$28$	$0.717$	$0.589$	$0.702$	$0.590$
$56$	$0.750$	$0.674$	$0.706$	$0.597$
$7$	$0.593$	$0.525$	$0.414$	$0.149$
$112$	$0.716$	$0.590$	$0.701$	$0.589$

Appendix

Table 4: Clustering algorithm comparison on MNIST. Trained on

\mathrm{R_{train}}=\{14,28,56\}

; evaluated on seen and held-out resolutions

\mathrm{R_{test}}=\{7,112\}

K=10

for both

K

-means and GMM.

Figure 9: Training and validation loss curves for the Kvasir dataset.

Resolution	KMeans(AMI) $(\uparrow)$	KMeans(ARI) $(\uparrow)$	GMM(AMI) $(\uparrow)$	GMM(ARI) $(\uparrow)$
$64$	$0.492$	$0.311$	$0.467$	$0.320$
$128$	$0.493$	$0.314$	$0.472$	$0.295$
$256$	$0.499$	$0.320$	$0.472$	$0.295$
$32$	$0.493$	$0.313$	$0.474$	$0.299$
$512$	$0.494$	$0.313$	$0.472$	$0.295$

Appendix

Table 5: Clustering algorithm comparison on Kvasir. Trained on

\mathrm{R_{train}}=\{64,128,256\}

; evaluated on seen and held-out resolutions

\mathrm{R_{test}}=\{32,512\}

K=8

for both

K

-means and GMM.

Figure 10: Training loss curve for the ERing dataset.

Resolution	KMeans(AMI) $(\uparrow)$	KMeans (ARI) $(\uparrow)$	GMM (AMI) $(\uparrow)$	GMM (ARI) $(\uparrow)$
$33$	$0.564$	$0.439$	$0.567$	$0.373$
$65$	$0.556$	$0.432$	$0.553$	$0.365$
$130$	$0.553$	$0.428$	$0.553$	$0.365$
$16$	$0.553$	$0.424$	$0.584$	$0.388$
$260$	$0.553$	$0.166$	$0.552$	$0.363$

Appendix

Table 6: Clustering algorithm comparison on ERing. Trained on

\mathrm{R_{train}}=\{33,65,130\}

; evaluated on seen and held-out resolutions

\mathrm{R_{test}}=\{16,260\}

K=6

for both

K

-means and GMM.

	MNIST	Kvasir	ERing
SIREN hidden width	5	32	5
SIREN layers	4	4	4
$d_{z}$ (SIREN params)	81	2,307	94
Batch size	128	64	16
Epochs	500	100	100
$\omega_{0}$	30	30	30

Appendix

Table 7: Per-dataset hyperparameter settings.

Clustering

Clustering groups data points by shared structure, developing methods to discover, validate, and interpret groups across diverse data and constraints.

See all 345 papers

funOCLUST: Clustering Functional Data with Outliers
Jul 31, 2025Katharine M. Clark, Paul D. McNicholasFunctional Data Analysis Clustering
Department of Mathematics & Statistics, Trent University, Ontario, Canada. · Department of Mathematics & Statistics, McMaster University, Ontario, Canada.
Neural Operators Can Discover Functional Clusters
Feb 26, 2026Yicen Li, Jose Antonio Lara Benitez, Ruiyang Hong +3Clustering Unsupervised Clustering
McMaster University and the Vector Institute, Main St., Hamilton, L8S 4L8, Ontario, Canada · Rice University, Main St., Houston, 77005, Texas, United States
Functional Autoencoders for Amplitude-Phase Representation Learning
Sep 28, 2026Peida Wu, Xinyang Xiong, Pengcheng ZengFunctional Data Analysis Representation Learning
School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA, USA · Institute of Mathematical Sciences, ShanghaiTech University, Shanghai, China

Jul 31, 2025J/K move · Enter open · S save

funOCLUST: Clustering Functional Data with Outliers

Katharine M. Clark, Paul D. McNicholas

Department of Mathematics & Statistics, Trent University, Ontario, Canada. · Department of Mathematics & Statistics, McMaster University, Ontario, Canada.

Functional Data Analysis Clustering Unsupervised Clustering

Open paper AskPDF arXiv

Functional data present unique challenges for clustering due to their infinite-dimensional nature and potential sensitivity to outliers. An extension of the OCLUST algorithm to the functional setting is proposed to address these issues. The approach leverages the OCLUST framework, creating a robust method to cluster curves and trim outliers. The methodology is evaluated on both simulated and real-world functional datasets, demonstrating strong performance in clustering and outlier identification.

Abstract

Clustering

Explore similar work

funOCLUST: Clustering Functional Data with Outliers

Neural Operators Can Discover Functional Clusters

Functional Autoencoders for Amplitude-Phase Representation Learning