Hypernetwork-based approach for grid-independent functional data clustering

TL;DR

This paper introduces a grid-independent functional data clustering method using hypernetworks and implicit neural representations, enabling robust clustering across various sampling resolutions and arbitrary grids.

Contribution

The authors propose a novel hypernetwork-based framework that maps discretized functions into a fixed-dimensional space for grid-independent clustering, which is robust to sampling density and resolution.

Findings

Achieves competitive clustering performance on synthetic and real data.

Demonstrates robustness to changes in sampling resolution, including unseen resolutions.

Provides a grid-agnostic approach that generalizes well across different discretizations.

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.