Optimal L1-principal component analysis on reconfigurable hardware
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An accomplished alternative to L 2 principal components in the case of outlying data and useful for dimensionality reduction, L 1 principal components play an increasingly important role in many scientific and engineering applications. The high computational complexity of optimal L 1 principal components pose a challenge for efficient signal processing and data analysis systems for time bounded applications. The state of art optimal L 1 principal component algorithm for any given real value data matrix X ∈ R D × N , dimensionality K has complexity of O (2 N K ). In this work we introduce a smart exhaustive-search algorithm for optimal L 1 principal component calculation with complexity of O (2 N -1 + K - 1/ K ). As FPGAs are becoming more powerful it presents a flexible and low-cost alternative for the implementation of high performance signal processing algorithms like the optimal L 1 principal components calculator algorithm. Here we have implemented the first ever high-performance optimal L 1 principal components calculator for a real-valued data, using the smart exhaustive-search (SE) algorithm. This thesis aims to present a FPGA design with improved efficiency over Matlab based solution. The proposed architecture demonstrates dimensional dependent acceleration ranges from 2.1X to 60X for matrices of arbitrary size with upper bound constraints of 16 × 16.