Performance Limits on the Classification of Kronecker-structured Models

05/07/2017
by   Ishan Jindal, et al.
0

Kronecker-structured (K-S) models recently have been proposed for the efficient representation, processing, and classification of multidimensional signals such as images and video. Because they are tailored to the multi-dimensional structure of the target images, K-S models show improved performance in compression and reconstruction over more general (union of) subspace models. In this paper, we study the classification performance of Kronecker-structured models in two asymptotic regimes. First, we study the diversity order, the slope of the error probability as the signal noise power goes to zero. We derive an exact expression for the diversity order as a function of the signal and subspace dimensions of a K-S model. Next, we study the classification capacity, the maximum rate at which the number of classes can grow as the signal dimension goes to infinity. We derive upper and lower bounds on the prelog factor of the classification capacity. Finally, we evaluate the empirical classification performance of K-S models for both the synthetic and the real world data, showing that they agree with the diversity order analysis.

READ FULL TEXT
research
06/19/2020

Information theoretic limits of learning a sparse rule

We consider generalized linear models in regimes where the number of non...
research
09/23/2021

Secrecy Capacity Bounds for Visible Light Communications With Signal-Dependent Noise

In physical-layer security, one of the most fundamental issues is the se...
research
08/12/2020

Lower-bounds on the growth of power-free languages over large alphabets

We study the growth rate of some power-free languages. For any integer k...
research
07/11/2016

Bounds on the Number of Measurements for Reliable Compressive Classification

This paper studies the classification of high-dimensional Gaussian signa...
research
10/25/2018

Tensor Matched Kronecker-Structured Subspace Detection for Missing Information

We consider the problem of detecting whether a tensor signal having many...
research
08/22/2023

On Convergence Rate of the Generalized Diversity Subsampling Method

arXiv:2206.10812v1 [stat.ME] proposes a useful algorithm, named generali...
research
06/09/2023

WindowNet: Learnable Windows for Chest X-ray Classification

Chest X-ray (CXR) images are commonly compressed to a lower resolution a...

Please sign up or login with your details

Forgot password? Click here to reset