Lithological Mapping via Random Forests: Information Entropy as a Proxy for Inaccuracy

Abstract

Machine Learning Algorithms (MLA) can be an effective means of lithological classification. The Random ForestsTM (RF) supervised classification approach allows prediction of lithology from disparate geophysical, geochemical and remote sensing data. In this study, we examine the relationship between prediction accuracy and information entropy (H). Data were processed in accordance with industry best practice and input selection was optimised using RF. Using a training set containing 1.4% of available pixels, we produced a classified lithology map with an overall accuracy of 76% with regards to mapped geology. In addition, we produced a class membership probability for each pixel, a precursor to defining the ultimate class designation at each pixel. H was calculated at each pixel from output class membership probabilities; and in this context provides a measure of the state of disorder for each. H was normalised with 0–1 representing the minimum to maximum possible H for each pixel.

H equal to 1 at a pixel represents an equal probability of all candidate classes occurring, whereas H equal to 0 describes a 100% probability of single class occurring. In this study, we demonstrate that there is a significant difference in the distribution of H between correctly and incorrectly classified pixels. The median H of incorrectly classified samples occurs above the 75% percentile of H for correctly classified samples. Conversely, both the mean and median H for correctly classified pixels occurs below the 25% percentile level for incorrectly classified samples.

This information can be used to determine the well-defined transition range in H, above which classification is likely to be inaccurate. Using this approach, a geoscientist can produce a lithological map, a quantifiable measure of uncertainty and a quantifiable transition range above which they are likely to encounter incorrect classification, avoiding wasted expense in targeting based on an incorrect model.