In this article, we develop several novel algorithms to train classifiers that can be implemented on chip with low-power fixed-point arithmetic with extremely small word length. These algorithms are based on Linear Discriminant Analysis (LDA), Support Vector Machine (SVM), and Logistic Regression (LR), and are referred to as LDA-FP, SVM-FP, and LR-FP, respectively. They incorporate the nonidealities (i.e., rounding and overflow) associated with fixed-point arithmetic into the offline training process so that the resulting classifiers are robust to these nonidealities. Mathematically, LDA-FP, SVM-FP, and LR-FP are formulated as mixed integer programming problems that can be robustly solved by the branch-and-bound methods described in this article. Our numerical experiments demonstrate that LDA-FP, SVM-FP, and LR-FP substantially outperform the conventional approaches for the emerging biomedical applications of brain decoding.

In this paper, we propose a novel linear discriminant analysis algorithm, referred to as LDA-FP, to train on-chip classifiers that can be implemented with low-power fixed-point arithmetic with extremely small word length. LDA-FP incorporates the non-idealities (i.e., rounding and overflow) associated with fixed-point arithmetic into the training process so that the resulting classifiers are robust to these non-idealities. Mathematically, LDA-FP is formulated as a mixed integer programming problem that can be efficiently solved by a novel branch-and-bound method proposed in this paper. Our numerical experiments demonstrate that LDA-FP substantially outperforms the conventional approach for the emerging biomedical application of brain computer interface.