Optimal subset selection for distributed local principal component analysis

Given that distributed PCA methods may sometimes produce large local approximation error, we propose a novel distributed PCA method, called distributed local PCA, to reduce the error by dimensionality reduction with an optimal subset selection criterion. The advantages of our optimal subset selection for the DLCPA include enhanced accuracy through precise covariance estimation, efficiency in handling large data sets, scalability in managing variable-exceeding-node scenarios, robustness against outliers, flexibility in parameter selection, and adaptability across data distributions. The involved low-dimensional covariance sub-estimators are obtained by computing their local principal components in distributed manner, and the one-step average covariance estimator is computed. Besides, mean squared error (MSE) is selected to measure the performance of the proposed method, and an optimal sub-estimator from the optimal criterion is obtained as having the minimum MSE value among all covariance sub-estimators. It is shown that the proposed method can not only improve the estimation accuracies in both simulated and real data experiments, but also greatly save computing time, which has a good promotion value in tackling big data problems.