Globally Convergent Accelerated Proximal Alternating Maximization Method for L1-Principal Component Analysis

In this paper, we consider a ℓ
₁
-PCA problem under the large-scale data sample scenario, which has extensive applications in science and engineering. Previous algorithms for the problem either are not scalable or do not have good convergence guarantees. Our contribution is threefold. First, we develop a novel accelerated version of the proximal alternating maximization method to solve the ℓ
₁
-PCA problem. Second, by exploiting the Kurdyka-Łojasiewicz property of the problem, we show that our proposed method enjoys global convergence to a critical point, which improves upon existing convergence guarantees of other first-order methods for the ℓ
₁
-PCA problem. Third, we demonstrate via numerical experiments on both real-world and synthetic datasets that our proposed method is scalable and more efficient and accurate than other methods in the literature.