# Compressive classification and the rare eclipse problem

arXiv: https://arxiv.org/abs/1404.3203 · HTML: https://mlsanity.com/paper/1404.3203/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2014.

## Built on by (most cited first, 4 of 4)

- [The Separation Capacity of Random Neural Networks](https://mlsanity.com/paper/2108.00207/) (2021)
- [Randomly Initialized One-Layer Neural Networks Make Data Linearly Separable](https://mlsanity.com/paper/2205.11716/) (2022)
- [Linearly Separable Features in Shallow Nonlinear Networks: Width Scales Polynomially with Intrinsic Data Dimension](https://mlsanity.com/paper/2501.02364/) (2025)
- [Confidence-Optimal Random Embeddings](https://mlsanity.com/paper/2104.05628/) (2021)

## Abstract (arXiv)

This paper addresses the fundamental question of when convex sets remain disjoint after random projection. We provide an analysis using ideas from high-dimensional convex geometry. For ellipsoids, we provide a bound in terms of the distance between these ellipsoids and simple functions of their polynomial coefficients. As an application, this theorem provides bounds for compressive classification of convex sets. Rather than assuming that the data to be classified is sparse, our results show that the data can be acquired via very few measurements yet will remain linearly separable. We demonstrate the feasibility of this approach in the context of hyperspectral imaging.