Confidence of a k-Nearest Neighbors Python Algorithm for the 3D Visualization of Sedimentary Porous Media

Abstract

In a previous paper, the authors implemented a machine learning k-nearest neighbors (KNN) algorithm and Python libraries to create two 3D interactive models of the stratigraphic architecture of the Quaternary onshore Llobregat River Delta (NE Spain) for groundwater exploration purposes. The main limitation of this previous paper was its lack of routines for evaluating the confidence of the 3D models. Building from the previous paper, this paper refines the programming code and introduces an additional algorithm to evaluate the confidence of the KNN predictions. A variant of the Similarity Ratio method was used to quantify the KNN prediction confidence. This variant used weights that were inversely proportional to the distance between each grain-size class and the inferred point to work out a value that played the role of similarity. While the KNN algorithm and Python libraries demonstrated their efficacy for obtaining 3D models of the stratigraphic arrangement of sedimentary porous media, the KNN prediction confidence verified the certainty of the 3D models. In the Llobregat River Delta, the KNN prediction confidence at each prospecting depth was a function of the available data density at that depth. As expected, the KNN prediction confidence decreased according to the decreasing data density at lower depths. The obtained average-weighted confidence was in the 0.44−0.53 range for gravel bodies at prospecting depths in the 12.7−72.4 m b.s.l. range and was in the 0.42−0.55 range for coarse sand bodies at prospecting depths in the 4.6−83.9 m b.s.l. range. In a couple of cases, spurious average-weighted confidences of 0.29 in one gravel body and 0.30 in one coarse sand body were obtained. These figures were interpreted as the result of the quite different weights of neighbors from different grain-size classes at short distances. The KNN algorithm confidence has proven its suitability for identifying these anomalous results in the supposedly well-depurated grain-size database used in this study. The introduced KNN algorithm confidence quantifies the reliability of the 3D interactive models, which is a necessary stage to make decisions in economic and environmental geology. In the Llobregat River Delta, this quantification clearly improves groundwater exploration predictability.

High-Level K-Nearest Neighbors (HLKNN): A Supervised Machine Learning Model for Classification Analysis

“…KNN considers the similarity factor between new and available data to classify an object into predefined categories. KNN has been widely used in many fields such as industry [7][8][9], machine engineering [10], health [11][12][13], marketing [14], electrical engineering [15], security [16][17][18], manufacturing [19], energy [20][21][22], aerial [23], environment [24], geology [25,26], maritime [27,28], geographical information systems (GIS) [29], and transportation [30].…”

“…In the field of geology, the authors [25] reported that the KNN algorithm was utilized for a three-dimensional envision of the stratigraphic structure of porous media related to sedimentary formations. In a similar work in geology, Bullejos et al [26] implemented a technique for the evaluation of KNN prediction confidence in that the three-dimensional model for the stratigraphic structure of porous media is approved. The results of their KNN-based method contributed to improving the predictability of groundwater investigations.…”

A Python Application for Visualizing an Imbricate Thrust System: Palomeque Duplex (SE, Spain)

“…To get a model of another location, the procedures presented here can be mimicked, but these must be adapted to the new data of the new location, and researchers must make their own choices of how the model should be. Python has been used by us to produce other geological models in the recent past, but with a different perspective and different kind of data, as is the case of the Llobregat River Delta (Barcelona, Spain) [28][29][30][31].…”

“…Our previous experience with Python libraries for 3D visualization, including geological data handling [28][29][30][31], has been very important to develop new applications for visualizing 3D structural and stratigraphic geological features. These new applications included Jupyter notebooks, describing the methodology, and a Python code operative version, which are downloadable from the GitHub repository (https://github.com/bullejos/ visualizing-an-imbricate-thrust-system accessed on 4 July 2023).…”