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.
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering
- Applied Mathematics