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About this paper
Samet Demir, Zafer Dogan
An online Principal Component Analysis algorithm, INO-PCA, leverages a dynamically evolving parameter norm rather than explicit normalization. This approach, derived from a regularized objective, enables the norm to encode signal strength and regulate the effective learning rate, leading to superior performance characterized by exact high-dimensional dynamics and empirical outperformance over classical methods.
Key insights
- The dynamically evolving parameter norm in INO-PCA acts as an internal state variable, encoding meaningful statistical information such as signal strength (SNR) and adaptively modulating the effective learning rate.
- Theoretical analysis revealed a critical three-way relationship between the evolving norm, SNR, and an optimal instantaneous learning rate, guiding more efficient learning.
- The steady-state analysis predicted a sharp phase transition in recovery performance based on SNR, with INO-PCA achieving a lower critical threshold and higher accuracy than Oja's algorithm.
Summary by alphaXiv.
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