Bounds on the Number of Measurements for Reliable Compressive Classification
This provides theoretical guarantees for compressive classification, which is incremental as it builds on existing compressive sensing frameworks.
The paper tackles the problem of classifying high-dimensional Gaussian signals from low-dimensional noisy measurements by deriving upper bounds on the number of measurements needed to achieve zero misclassification probability in low-noise regimes, showing that these bounds are sharp in simulations with synthetic and real data.
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.