Compressive Sensing Based Classification in the Presence of Intra- and Inter- Signal Correlation

In this letter, we investigate the problem of classification with high dimensional data using low dimensional random projections in the presence of inter- and intra- signal correlations. Each sensor is assumed to compress its high dimensional (Gaussian) signal vector using random projections in a multi-sensor setting. In order to quantify the classification performance with compressed data, we consider the Bhattacharya distance as the performance metric. In the presence of intra-signal correlation at a given sensor, the degradation in the Bhattacharya distance with compressed data is shown to be non-linear with the compression ratio in contrast to the case when there is no intra-signal correlation. In the presence of inter-signal correlation, the degradation in the Bhattacharya distance with compressed data depends on whether or not an identical projection matrix is used to compress data at multiple sensors.