Compressed Principal Component Regression (C–PCR) Algorithm and FPGA Validation

To address the hardware and/or software implementation issues of principal component regression (PCR), we propose a novel algorithm called compressed PCR (C-PCR). C-PCR projects the input data to a lower dimensional space first, and then applies the compressed data to a significantly smaller PCR engine. We show that C-PCR can lower the computational complexity of PCR with a factor of compression ratio (CR) squared, i.e., CR
²
. Moreover, the output signal of C-PCR follows that of PCR with a small error, which increases with CR, when the projections are random. Using datasets of prerecorded brain neurochemicals, we experimentally show that C-PCR can achieve CRs as high as ~ 10. As far as hardware implementation is concerned, the experimental results show that reduction rates of 32% to 45% in different FPGA resources can be achieved using C-PCR.