Hypernetwork-based approach for grid-independent functional data clustering

2026-02-26

AI Summary

This work addresses a key limitation of existing functional data clustering methods, which rely on fixed sampling grids and are thus sensitive to resolution and sampling density, often failing to capture the intrinsic structure of underlying functions. To overcome this, the authors propose a grid-agnostic clustering framework that leverages a hypernetwork to map discrete observations—sampled on arbitrary grids—into fixed-dimensional weights of an implicit neural representation (INR). This yields compact, sampling-invariant function embeddings, enabling the application of standard clustering algorithms in the resulting latent space. By uniquely integrating hypernetworks with INRs, the method generalizes effectively to arbitrary and even unseen sampling resolutions. Extensive experiments on both synthetic and real-world high-dimensional datasets demonstrate that the approach achieves robust and competitive clustering performance.

Technology Category

• Machine Learning: Clustering
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• functional data clustering
• grid dependence
• sampling resolution
• function representation
• clustering robustness

Innovation

• hypernetwork
• implicit neural representation
• grid-independent clustering
• functional data clustering
• auto-encoding architecture