Embedding Principal Component Analysis for Data Reductionin Structural Health Monitoring on Low-Cost IoT Gateways

Principal component analysis (PCA) is a powerful data reductionmethod for Structural Health Monitoring. However, its computa-tional cost and data memory footprint pose a significant challengewhen PCA has to run on limited capability embedded platformsin low-cost IoT gateways. This paper presents a memory-efficientparallel implementation of the streaming History PCA algorithm.On our dataset, it achieves 10x compression factor and 59x memoryreduction with less than 0.15 dB degradation in the reconstructedsignal-to-noise ratio (RSNR) compared to standard PCA. More-over, the algorithm benefits from parallelization on multiple cores,achieving a maximum speedup of 4.8x on Samsung ARTIK 710

Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint

Fair Principal Component Analysis (PCA) is a problem setting where we aim to perform PCA while making the resulting representation fair in that the projected distributions, conditional on the sensitive attributes, match one another. However, existing approaches to fair PCA have two main problems: theoretically, there has been no statistical foundation of fair PCA in terms of learnability; practically, limited memory prevents us from using existing approaches, as they explicitly rely on full access to the entire data. On the theoretical side, we rigorously formulate fair PCA using a new notion called \emph{probably approximately fair and optimal} (PAFO) learnability. On the practical side, motivated by recent advances in streaming algorithms for addressing memory limitation, we propose a new setting called \emph{fair streaming PCA} along with a memory-efficient algorithm, fair noisy power method (FNPM). We then provide its {\it statistical} guarantee in terms of PAFO-learnability, which is the first of its kind in fair PCA literature. Lastly, we verify the efficacy and memory efficiency of our algorithm on real-world datasets.Comment: 42 pages, 5 figures, 4 tables. Accepted to the 37th Conference on Neural Information Processing Systems (NeurIPS 2023