# Bounds on the Number of Measurements for Reliable Compressive Classification

arXiv: https://arxiv.org/abs/1607.02801 · HTML: https://mlsanity.com/paper/1607.02801/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2016.

## Built on by (most cited first, 3 of 3)

- [Feature Selection for Network Intrusion Detection](https://mlsanity.com/paper/2411.11603/) (2024)
- [Statistical optimality conditions for compressive ensembles](https://mlsanity.com/paper/2106.01092/) (2021)
- [Compressive Mahalanobis Metric Learning Adapts to Intrinsic Dimension](https://mlsanity.com/paper/2309.05751/) (2023)

## Abstract (arXiv)

This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the probability of misclassification to zero in the low-noise regime, both for random measurements and designed ones. Such bounds reveal two important operational regimes that are a function of the characteristics of the source: i) when the number of classes is less than or equal to the dimension of the space spanned by signals in each class, reliable classification is possible in the low-noise regime by using a one-vs-all measurement design; ii) when the dimension of the spaces spanned by signals in each class is lower than the number of classes, reliable classification is guaranteed in the low-noise regime by using a simple random measurement design. Simulation results both with synthetic and real data show that our analysis is sharp, in the sense that it is able to gauge the number of measurements required to drive the misclassification probability to zero in the low-noise regime.