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Multi-Stage Methods for Cost Controlled Data Compression Using Principal Component Analysis

Author

Listed:
  • Swarnali Banerjee

    (Department of Mathematics and Statistics and Center for Data Science and Consulting, Loyola University, Chicago, IL 60660, USA)

  • Bhargab Chattopadhyay

    (School of Management & Entrepreneurship, Indian Institute of Technology Jodhpur, Jodhpur 342030, Rajasthan, India)

Abstract

Several online principal component analysis (PCA) methodologies exist for data arriving sequentially that focus only on compression risk minimization. Recent work in this realm revolves around minimizing the cost-compression risk, which takes into account compression loss and sampling costs using a two-stage PCA procedure. Even though the procedure enjoys first-order efficiency, the authors could not mathematically verify the existence of the second-order efficiency property. In this article, we minimize cost-compression risk using a modified two-stage PCA procedure, which takes into account the data compression loss as well as the sampling cost when the smallest eigenvalue of the population variance–covariance matrix or its positive lower bound is known when the data is assumed to follow a multivariate normal distribution. The modified two-stage PCA procedure is shown to possess the second-order efficiency property, among others, including the second-order risk efficiency property under some conditions. The proposed method is novel but also fast and efficient, as illustrated by extensive data analyses through simulations and real data analysis.

Suggested Citation

  • Swarnali Banerjee & Bhargab Chattopadhyay, 2025. "Multi-Stage Methods for Cost Controlled Data Compression Using Principal Component Analysis," Mathematics, MDPI, vol. 13(13), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2140-:d:1691185
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    References listed on IDEAS

    as
    1. Yata, Kazuyoshi & Aoshima, Makoto, 2013. "PCA consistency for the power spiked model in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 334-354.
    2. N. Mukhopadhyay, 1980. "A consistent and asymptotically efficient two-stage procedure to construct fixed width confidence intervals for the mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 27(1), pages 281-284, December.
    3. Kazuyoshi Yata & Makoto Aoshima, 2009. "PCA Consistency for Non-Gaussian Data in High Dimension, Low Sample Size Context," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 38(16-17), pages 2634-2652, October.
    4. Hao-Che Chen, 2014. "Visualisation of financial time series by linear principal component analysis and nonlinear principal component analysis," Papers 1410.7961, arXiv.org.
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