A statistical framework for dimensionality reduction implementation in FPGAs

Dimensionality reduction or feature extraction has been widely used in applications that require a set of data to be represented by a small set of variables. A linear projection is often chosen due to its computational attractiveness. The calculation of the linear basis that best explains the data is usually addressed using the Karhunen-Loeve transform (KLT). Moreover, for applications where real-time performance and flexibility to accommodate new data are required, the linear projection is implemented in FPGAs due to their fine-grain parallelism and reconfigurability properties. Currently, the optimization of such a design in terms of area usage is considered as a separate problem to the basis calculation. In this paper, we propose a novel approach that couples the calculation of the linear projection basis and the area optimization problems under a probabilistic Bayesian framework. The power of the proposed framework is based on the flexibility to insert information regarding the implementation requirements of the linear basis by assigning a proper prior distribution. Results using real-life examples demonstrate the effectiveness of our approach