Recognizing Multivariate Geochemical Anomalies Related to Mineralization by Using Deep Unsupervised Graph Learning

Abstract

The spatial structure of geochemical patterns is influenced by various geological processes, one of which may be mineralization. Thus, analysis of spatial geochemical patterns facilitates understanding of regional metallogenic mechanisms and recognition of geochemical anomalies related to mineralization. Convolutional neural networks (CNNs) used in previous studies to extract spatial features require regular data (e.g., raster maps) as input. Due to the complex and diverse geological environment, geochemical samples are inevitably irregularly distributed and even partially missing in many spaces, leading to the inapplicability of CNN-based methods for geochemical anomaly identification. Also, interpolation from samples to regular grids often introduces uncertainties. To address these problems, this study innovatively transformed geochemical sampled point data into graphs and introduced graph learning to extract the geochemical patterns. Correspondingly, a novel framework of geochemical identification named GAUGE (recognition of Geochemical Anomalies Using Graph lEarning) is proposed. To assess the performance of the proposed method, this study recognized anomalies related to Au deposits in the Longyan area, the Wuyishan polymetallic metallogenic belt, China. For a set of regularly distributed samples, GAUGE achieved an accuracy similar to that of a traditional convolution autoencoder. More importantly, GAUGE achieved an area under the curve of 0.833, outperforming one-class support vector machine, isolation forest, autoencoder, and deep autoencoder network for a set of irregularly distributed samples by 10.6, 5.2, 4.8, and 2.5%, respectively. By introducing graph learning into geochemical anomaly recognition, this study provides a new perspective of extracting both spatial structure and compositional relationships of multivariate geochemical patterns, which can be applied directly to irregularly distributed samples in irregularly shaped regions without the need for interpolation. Such an improvement greatly enhances the applicability of machine learning methods in geochemical anomaly recognition, providing support for mineral resources evaluation and exploration.

Appendices

Appendix

Global Moran′s I Method for Spatial Autocorrelation

Spatial autocorrelation indicates a significant spatial distribution pattern in space through the degree of correlation between spatial objects in a region. Global Moran′s I is a common metric for quantitative representation of spatial autocorrelation (Goodchild, 1986). Its mathematical equation is:

$$I = \frac{n}{{S_{0} }}\frac{{\mathop \sum \nolimits_{i = 1}^{n} \mathop \sum \nolimits_{j = 1}^{n} w_{i,j} \left( {x_{i} - \overline{x}} \right)\left( {x_{j} - \overline{x}} \right)}}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {x_{i} - \overline{x}} \right)^{2} }}$$

(15)

where $x_{i}$, $x_{j}$ are sampling values at sampling point $i$ and $j$, respectively; $\overline{x}$ is the mean value; $w_{i,j}$ denotes weights representing the proximity relationship between sampling points $i$ and $j$. Generally, $w_{i,j}$ is related to the distance band selection, and here we calculated the spatial weights for samples only within distance K. $S_{0}$ is the sum of all elements of the spatial weight matrix ${\text{W}}$. $I$ is Global Moran’s I value, which ranges from -1 to 1. The closer it is to 1, the stronger the spatial autocorrelation is.

Activation Functions in GAT

The activation function is a function that maps inputs to outputs in neurons. It is important for deep learning models to extract and understand complex and nonlinear patterns. Sigmoid, LeakyReLU, and ReLU are used in GAUGE, and their mathematical equations are as follows:

Sigmoid (Finney, 1952):

$$Sigmoid\left( x \right) = \frac{1}{{1 + e^{ - x} }}$$

(16)

ReLU (Glorot et al., 2011):

$$Relu\left( x \right) = {\text{max}}\left( {0,x} \right)$$

(17)

LeakyReLU (Maas et al., 2013):

$$LeakyReLU\left( x \right) = {\text{max}}\left( {ax,x} \right)$$

(18)

where $x$ indicates the input of activation function. $Sigmoid\left( x \right)$, $Relu\left( x \right)$, and $LeakyReLU(x)$ are the output of the respective functions. The $a of LeakyReLU$ defaults to 0.01.