ArticleIEEE transactions on information theory2021
How to reduce dimension with PCA and random projections?
Article in IEEE transactions on information theory, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers, 1 of them a synthesis that pooled it.
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Who cites it
5 citing papers in PubMed, 1 synthesis or guideline pooled it.
- Insights into Parkinson's Disease-Related Freezing of Gait Detection and Prediction Approaches: A Meta Analysis.Sensors (Basel, Switzerland) · 2024Pooled it
- Dimension Reduction for Large-Scale Federated Data: Statistical Rate and Asymptotic Inference.Journal of the American Statistical Association · 2026Article
- Robust angle-based transfer learning in high dimensions.Journal of the Royal Statistical Society. Series B, Statistical methodology · 2025Article
- Sharp-SSL: Selective High-Dimensional Axis-Aligned Random Projections for Semi-Supervised Learning.Journal of the American Statistical Association · 2025Article
- High-fidelity and high-speed wavefront shaping by leveraging complex media.Science advances · 2024Article
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Authors and funding
4 authors.
Funding
Abstract
In our "big data" age, the size and complexity of data is steadily increasing. Methods for dimension reduction are ever more popular and useful. Two distinct types of dimension reduction are "data-oblivious" methods such as random projections and sketching, and "data-aware" methods such as principal component analysis (PCA). Both have their strengths, such as speed for random projections, and data-adaptivity for PCA. In this work, we study how to combine them to get the best of both. We study "sketch and solve" methods that take a random projection (or sketch) first, and compute PCA after. We compute the performance of several popular sketching methods (random iid projections, random sampling, subsampled Hadamard transform, CountSketch, etc) in a general "signal-plus-noise" (or spiked) data model. Compared to well-known works, our results (1) give asymptotically exact results, and (2) apply when the signal components are only slightly above the noise, but the projection dimension is non-negligible. We also study stronger signals allowing more general covariance structures. We find that (a) signal strength decreases under projection in a delicate way depending on the structure of the data and the sketching method, (b) orthogonal projections are slightly more accurate, (c) randomization does not hurt too much, due to concentration of measure, (d) CountSketch can be somewhat improved by a normalization method. Our results have implications for statistical learning and data analysis. We also illustrate that the results are highly accurate in simulations and in analyzing empirical data.
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Registered trials
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