# A signal separation view of classification

arXiv: https://arxiv.org/abs/2509.24140 · HTML: https://mlsanity.com/paper/2509.24140/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 44 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Optimal approximation of piecewise smooth functions using deep ReLU neural networks](https://mlsanity.com/paper/1709.05289/) (2017)
- [Revisiting Uncertainty-based Query Strategies for Active Learning with Transformers](https://mlsanity.com/paper/2107.05687/) (2021)
- [Properly-weighted graph Laplacian for semi-supervised learning](https://mlsanity.com/paper/1810.04351/) (2018)
- [Active Learning with Neural Networks: Insights from Nonparametric Statistics](https://mlsanity.com/paper/2210.08367/) (2022)
- [Kernel based analysis of massive data](https://mlsanity.com/paper/2003.13226/) (2020)
- [Learning by Active Nonlinear Diffusion](https://mlsanity.com/paper/1905.12989/) (2019)
- [Model-Change Active Learning in Graph-Based Semi-Supervised Learning](https://mlsanity.com/paper/2110.07739/) (2021)
- [Multiscale Clustering of Hyperspectral Images Through Spectral-Spatial Diffusion Geometry](https://mlsanity.com/paper/2103.15783/) (2021)
- [Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learning](https://mlsanity.com/paper/2210.15786/) (2022)
- [Cautious Active Clustering](https://mlsanity.com/paper/2008.01245/) (2020)
- [Learning on manifolds without manifold learning](https://mlsanity.com/paper/2402.12687/) (2024)
- [A unified method for super-resolution recovery and real exponential-sum separation](https://mlsanity.com/paper/1707.09428/) (2017)
- [Super-resolution meets machine learning: approximation of measures](https://mlsanity.com/paper/1907.04895/) (2019)
- [Active Learning Classification from a Signal Separation Perspective](https://mlsanity.com/paper/2502.16425/) (2025)
- [Localized Kernel Methods for Signal Processing](https://mlsanity.com/paper/2508.04978/) (2025)

## Abstract (arXiv)

The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields both the number of classes, and a perfect classification using a minimal number of queried labels. Our approach uses localized trigonometric polynomial kernels initially developed for the point source signal separation problem in signal processing. Rather than point sources, we argue that the various classes come from different probability measures. The localized kernel technique developed for separating point sources is then shown to separate the supports of these distributions. This is done in a hierarchical manner in our MASC algorithm to accommodate touching/overlapping class boundaries. We illustrate our theory on several simulated and real life datasets, including the Salinas and Indian Pines hyperspectral datasets and a document dataset.