AdaOja: Adaptive Learning Rates for Streaming PCA

Amelia Henriksen; Rachel Ward

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arXiv · 1905.12115

AdaOja: Adaptive Learning Rates for Streaming PCA

Amelia Henriksen·Rachel Ward

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Abstract

Oja's algorithm has been the cornerstone of streaming methods in Principal Component Analysis (PCA) since it was first proposed in 1982. However, Oja's algorithm does not have a standardized choice of learning rate (step size) that both performs well in practice and truly conforms to the online streaming setting. In this paper, we propose a new learning rate scheme for Oja's method called AdaOja. This new algorithm requires only a single pass over the data and does not depend on knowing properties of the data set a priori. AdaOja is a novel variation of the Adagrad algorithm to Oja's algorithm in the single eigenvector case and extended to the multiple eigenvector case. We demonstrate for dense synthetic data, sparse real-world data and dense real-world data that AdaOja outperforms common learning rate choices for Oja's method. We also show that AdaOja performs comparably to state-of-the-art algorithms (History PCA and Streaming Power Method) in the same streaming PCA setting.

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BibTeX RIS

Amelia Henriksen, Rachel Ward. 2019-05-28. AdaOja: Adaptive Learning Rates for Streaming PCA. https://arxiv.org/abs/1905.12115

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