Hypernetwork-based approach for grid-independent functional data clustering

TL;DR

This work introduces a framework that maps discretized function observations into a fixed-dimensional vector space via an auto-encoding architecture and demonstrates competitive clustering performance that is robust to changes in sampling resolution -- including generalization to resolutions not seen during training.

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 (10)

• 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 \ref{['eq:loss']}) used to train the hypernetwork end-to-end. Code to reproduce the results presented in this work is available at https://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.
• 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.
• 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.