Search for: All records

Understanding the mineralogy and geochemistry of the subsurface is key when assessing and exploring for mineral deposits. To achieve this goal, rapid acquisition and accurate interpretation of drill core data are essential. Hyperspectral shortwave infrared imaging is a rapid and non-destructive analytical method widely used in the minerals industry to map minerals with diagnostic features in core samples. In this paper, we present an automated method to interpret hyperspectral shortwave infrared data on drill core to decipher major felsic rock-forming minerals using supervised machine learning techniques for processing, masking, and extracting mineralogical and textural information. This study utilizes a co-registered training dataset that integrates hyperspectral data with quantitative scanning electron microscopy data instead of spectrum matching using a spectral library. Our methodology overcomes previous limitations in hyperspectral data interpretation for the full mineralogy (i.e., quartz and feldspar) caused by the need to identify spectral features of minerals; in particular, it detects the presence of minerals that are considered invisible in traditional shortwave infrared hyperspectral analysis. 

We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and machine learning problems. The algorithm maps the gradient onto a low-dimensional ran- dom subspace of dimension at each iteration, similar to coordinate descent but without restricting directional derivatives to be along the axes. Without requiring a full gradient, this mapping can be performed by computing directional deriva- tives (e.g., via forward-mode automatic differentiation). We give proofs for conver- gence in expectation under various convexity assumptions as well as probabilistic convergence results under strong-convexity. Our method provides a novel extension to the well-known Gaussian smoothing technique to descent in subspaces of dimen- sion greater than one, opening the doors to new analysis of Gaussian smoothing when more than one directional derivative is used at each iteration. We also provide a finite-dimensional variant of a special case of the Johnson–Lindenstrauss lemma. Experimentally, we show that our method compares favorably to coordinate descent, Gaussian smoothing, gradient descent and BFGS (when gradients are calculated via forward-mode automatic differentiation) on problems from the machine learning and shape optimization literature.