When a single measurement is on the order of millions of elements, metrics which rely on statistical expectations over high-dimensional stochastic processes are nearly impossible to compute. Even when computational resources are limitless the quantity of sample data can be insufficient to form robust sample statistics required for mathematical observers. Estimating covariance/scatter matrices is a ubiquitous challenge without an obvious solution for the high dimension, low sample size (HDLSS) problem. For higher quantities of training data machine learning can offer effective classification but does not provide insight about the informative correlation structure. Mathematical observers with capabilities to convert high-dimensional, heterogeneous data into information needed for hypothesis testing, data-driven discovery, and causal inferences are sought. Linear transforms will be used to form robust estimates of HDLSS covariance. We will develop and demonstrate an inexact Manifold optimization algorithm to compute a linear transform that reduces dimensionality while preserving quadratic information. A unique challenge is posed by the biased nature of our problem on the algorithmic front as traditional stochastic methods relying on unbiased estimators are no longer feasible.