Optimal Sample Acquisition for Optimally Weighted PCA From Heterogeneous Quality Sources

Modern high-dimensional datasets are often formed by acquiring samples from multiple sources having heterogeneous quality, i.e., some sources are noisier than others. Collecting data in this manner raises the following natural question: what is the best way to collect the data (i.e., how many samples should be acquired from each source) given constraints (e.g., on time or energy)? In general, the answer depends on what analysis is to be performed. In this paper, we study the foundational signal processing task of estimating underlying low-dimensional principal components. Since the resulting dataset will be high-dimensional and will have heteroscedastic noise, we focus on the recently proposed optimally weighted PCA, which is designed specifically for this setting. We develop an efficient method for designing sample acquisitions that optimize the asymptotic performance of optimally weighted PCA given resource constraints, and we illustrate the proposed method through various case studies.