Evaluation of Deep Isolation Forest (DIF) Algorithm for Mineral Prospectivity Mapping of Polymetallic Deposits

Abstract

Mineral prospectivity mapping (MPM) is crucial for efficient mineral exploration, where prospective zones are identified in a cost-effective manner. This study focuses on generating prospectivity maps for hydrothermal polymetallic mineralization in the Feizabad area, in northeastern Iran, using unsupervised anomaly detection methods, i.e., isolation forest (IForest) and deep isolation forest (DIF) algorithms. As mineralization events are rare and complex, traditional approaches continue to encounter difficulties, despite advances in MPM. In this respect, unsupervised anomaly detection algorithms, which do not rely on ground truth samples, offer a suitable solution. Here, we compile geospatial datasets on the Feizabad area, which is known for its polymetallic mineralization showings. Fourteen evidence layers were created, based on the geology and mineralization characteristics of the area. Both the IForest and DIF algorithms were employed to identify areas with high mineralization potential. The DIF, which uses neural networks to handle non-linear relationships in high-dimensional data, outperformed the traditional decision tree-based IForest algorithm. The results, evaluated through a success rate curve, demonstrated that the DIF provided more accurate prospectivity maps, effectively capturing complex, non-linear relationships. This highlights the DIF algorithm’s suitability for MPM, offering significant advantages over the IForest algorithm. The present study concludes that the DIF algorithm, and similar unsupervised anomaly detection algorithms, are highly effective for MPM, making them valuable tools for both brownfield and greenfield exploration.

1. Introduction

Mineral prospectivity mapping (MPM) is an important framework in mineral exploration that is used to reduce exploration costs, minimize risk, reduce uncertainty during the exploration phases, and ultimately identify potential mineral zones [1]. MPM combines geospatial datasets with two primary approaches: knowledge-driven methods and data-driven techniques [2,3,4]. Knowledge-driven approaches focus on the metallogenic background and mineralization rules, relying on specialized knowledge within the mineral exploration field and the informed opinions of experts [5]. However, this method is often subject to a high degree of uncertainty, due to its reliance on expert opinion [1,6]. In contrast, data-driven techniques, including machine learning [7,8,9] and deep learning approaches [10,11], focus on identifying relationships between known mineral deposits and feature layers, as well as uncovering hidden relationships associated with mineralization [12]. In recent decades, various supervised machine learning methods, such as logistic regression [13], support vector machines [14,15], and random forests [13,16], as well as unsupervised algorithms, such as K-means [17,18] and IForest [13] algorithms, are increasingly being used for MPM.

Mineralization is a rare local occurrence, influenced by various geological processes [12]. In MPM, the conceptual model and attributes of the target deposit are used to extract mineralization-related features, which are then utilized to create the evidence layer [6,19]. Therefore, high values in each evidence layer have a strong relationship and significant correlation with some of the known mineral occurrences in a study area. Compared to other data points, the data from known mineral occurrences have higher values in most of the evidence layers [12]. Therefore, these evidence layers also have anomalous values associated with mineralization, which highlight significant anomalies. These anomalies represent important features related to the mineralization being sought and exhibit non-linear and complex behavior. Hence, machine learning methods based on anomaly detection can be used to identify mineralization and model its complex, hidden, and non-linear behavior. These methods can recognize patterns that are difficult to detect using conventional methods. In other words, anomaly detection algorithms are used to identify these meaningful anomalies and patterns in multi-source geospatial datasets [20].

Machine learning anomaly detection algorithms are capable of detecting anomalies and examining high-dimensional, complex, and non-linear data and hidden structures. During data mining, anomaly detection aims to identify data points that deviate significantly from the normal distribution. The main function of intelligent algorithms that are based on anomaly detection is to recognize outlier data points that differ from the rest of the dataset, according to a certain metric. These samples exhibit unusual behavior and are referred to as outliers. In the field of mineral exploration, anomaly detection has been applied in various fields, such as multi-element geochemical anomaly detection [21] and MPM studies [22]. Chen and Wu (2017) applied the one-class support vector machine (OCSVM) for gold prospectivity mapping in the Laotudingzi–Xiaosiping district, assuming that mineralization is a rare occurrence due to regional geological processes [20]. Their study showed that OCSVM models can provide valuable results in detecting anomalies in high-dimensional data, without assumptions about the underlying data distribution. Their results indicated that the OCSVM model outperformed the restricted Boltzmann machine model in terms of the ROC, AUC, and processing efficiency. The gold targets predicted by the OCSVM model and the restricted Boltzmann machine model were closely spatially related to known gold deposits and matched the regional geological characteristics of the study area. However, when applying the OCSVM model for MPM, it is crucial to properly define the parameter $v$, as it can affect the performance of the model in detecting anomalies. Moreover, the detection of geochemical anomalies associated with ore mineralization is an essential task in geochemical exploration [23]. Mineralization is a rare occurrence in the Earth’s crust and can, therefore, be considered a low probability event. To address this issue, Wang et al. (2020) used geochemical data from stream sediments and six unsupervised machine learning methods to identify geochemical anomalies associated with polymetallic Ag–Pb–Zn mineralization [24]. The results from the study suggest that the IForest algorithm is a reliable and efficient unsupervised machine learning algorithm for detecting geochemical anomalies associated with mineralization and that its integration, with appropriate dimensionality reduction techniques, can lead to more accurate detection of related anomalies. Consequently, algorithms based on unsupervised anomaly detection are widely used in geochemistry and MPM studies.

A major advantage of unsupervised anomaly detection algorithms is their independence from labeled ground data, which makes them reliable for MPM in greenfield and brownfield areas [12]. Among the unsupervised anomaly detection algorithms available, the IForest algorithm is characterized by its efficiency in detecting anomalies, while maintaining low computational complexity [25,26]. IForest, a shallow ensemble learning algorithm based on decision trees, excels at identifying exploration anomalies in complex geospatial datasets [26]. It converges quickly and ensures a high level of data processing efficiency. The main function of an IForest algorithm is to identify anomalies by ensuring that they are “far” from other data points in a given feature space [27]. To detect these anomalies in a decision space, the IForest algorithm generates random split trees to isolate each data point. Then, for each tree, the number of branches required to separate each point is calculated [27]. The average of this number of branches determines the expected path length used to isolate a point of interest [27]. This expected path length is usually small for anomalies.

In contrast to other methods, the IForest algorithm does not model unit cell populations, but isolates anomaly cells directly through random partitioning. In MPM studies, the anomaly scores generated by the IForest algorithm can be used directly for the identification of anomaly cells in a raster map [28]. However, the IForest algorithm has difficulties in detecting hard anomalies in a high-dimensional and non-linearly partitionable data space, as it only performs axis-parallel isolation operations (linear partitioning) when constructing isolation trees [29,30]. Deep isolation forest (DIF) [30] is the most recent and probably most promising extension of the IForest algorithm, which was proposed to address this limitation of the original algorithm and facilitate the identification of non-linear relationships between complex features [31]. The DIF algorithm addresses this limitation by using randomly initialized neural networks to project data into random representation ensembles in which the hard anomalies can be easily isolated with axis-parallel slices, which would correspond to non-linear partitioning in the original space [30,32].

The aim of this study is to model the mineral potential of hydrothermal copper deposits and evaluate the performance of the IForest and DIF algorithms. To evaluate the effectiveness of these algorithms, we conducted a case study in the Feizabad region, an area known for its ore potential. First, 14 evidence layers were developed, based on a conceptual model of the deposit being sought. Subsequently, these algorithms were used to generate mineral potential maps. Finally, the results were evaluated using the success rate curve.

2. Geology of the Study Area

The study area, with an area of about 1154 km², is located in the northern part of the 1:100,000 scale geologic map of Feizabad in Khorasan Razavi province (Figure 1), which is located between central Iran and the Lut block [33]. The Feizabad district is located 185 km south of Mashhad. Fault movements have significantly influenced the rock facies changes in this region. The Doruneh fault, which runs through the center of the district and divides the study area into northern and southern parts, is one of the main faults in this area [34]. Volcanic and pyroclastic rocks of Tertiary age occur mainly in the northern section of this fault. In addition to intrusive rocks, sedimentary units are also present in the northern part of the region. The tuffs in this region often have a rhyolitic to rhyodacitic composition, while the lava has andesite content. Intrusive rocks from the Eocene and Oligocene periods in the form of granodiorite and diorite are mainly found in the northern part of the region [33,35]. Predominant deposit categories in the study area, near intrusive and volcanic rocks, include iron oxide–copper–gold (IOCG) deposits, epithermal bases, precious metal species, Cu veins, and porphyritic Cu–Au systems (e.g., Tanorcheh deposit) [34]. In addition to the above-mentioned mineralization, hydrothermal alteration zones have been identified, due to granodiorite and granite formations. Magma and hydrothermal fluids have caused the alteration of the rocks. The most important alteration zones in this region are iron oxide, silicified, propylitic, phyllic, and argillic zones. These alterations often occur along faults and near intrusive rocks. Faults and fractures, which direct the flow of fluid material, play a crucial role in the formation of these zones. The primary ore minerals in the main mineralized zones consist mainly of pyrite, chalcopyrite, magnetite, specularite, and gold, while the secondary minerals goethite, hematite, malachite, and azurite, are common in oxidized zones.

3. Conceptual Model

One of the most important steps in MPM is the definition of an appropriate conceptual and descriptive model for the mineralization being sought [19]. A conceptual model includes the key characteristics and criteria of the mineralization being sought and is defined based on the characteristics of similar known mineral occurrences (KMOs). This model helps exploration geologists to select relevant criteria and identify new exploration targets in the region. In other words, important evidence layers for MPM are selected according to this descriptive model, which emphasizes the importance of defining an accurate conceptual model. Based on the studies on hydrothermal copper deposits and previous MPM research in this region, the following key features can be used to build a prospectivity model for hydrothermal copper:

• Hydrothermal copper mineralization, such as Cu–Au porphyry, in the Feizabad area shows a significant spatial correlation with intrusive rocks, such as diorite and granodiorite from the Eocene–Oligocene transition [34,36]. Therefore, the proximity to these units, which serve as a primary heat source, is an important indicator for the identification of new exploration targets in the region;

• The formation of hydrothermal deposits, such as Cu–Au mineralization, is associated with the movement of metal-rich fluids through fractures and faults [37]. These geological factors, especially their intersections, act as conduits for fluid movement. In the studied area, faults have played a crucial role in mineralization. Therefore, the proximity to fault intersections can be considered as a key factor and important layer in the MPM analysis;

• Geochemical exploration is a key method for the exploration of hydrothermal copper deposits. Previous studies conducted in the study area have demonstrated a strong association between elements such as Cu, Au, Hg, Pb, Zn, Sn, As, and Sb [6]. In addition, the results show that the geochemical maps of these elements closely match the known hydrothermal copper mineralization in the region [6]. Therefore, these eight elements were selected for this study;

• In general, hydrothermal and iron oxide alteration have been shown to be the main features of hydrothermal deposits, such as porphyry copper mineralization [38]. Alteration halos, such as potassic, phyllic, argillic, and propylitic zones, as well as iron oxide alteration, are typically found in the vicinity of hydrothermal copper deposits and have a considerable spatial extent. Therefore, ASTER remote sensing image processing was used in this study to identify areas that exhibit these alterations.

4. Materials and Methods

4.1. Data Used

MPM typically utilizes and integrates multiple types of data, including geochemical [39,40], geophysical [41,42,43], remote sensing [44,45], and geological data [37,46]. This integration enables a comprehensive assessment of the geological features and anomalies that may indicate the presence of mineral deposits.

4.1.1. Regional-Scale Geochemical Sampling

In the study region, the point data can be divided into two categories: mineralization points (known as mineral occurrences or deposits) and stream sediment geochemical data. The former was used to evaluate the prospectivity models, while the latter was applied to create geochemical evidence layers. A systematic sampling network, with a cell size of 1400 × 1400 square meters, was established within the 1:100,000 scale geological map of Feizabad to collect the samples. Stream sediments were collected from the primary drainage in each grid window. Subsequently, all the collected samples within each window were homogenized and a composite sample was assigned to the center of the window. A total of 1033 stream sediment samples were systematically collected by the Jiang Cheng company, in cooperation with the Geological Survey of Iran (GSI), from the study area, at intervals of 1400 m. These samples were analyzed in the Jiang Cheng laboratory for 28 elements, using the inductively coupled plasma–optical emission spectrometry (ICP-OES) method and, for gold (Au), through the fire assay, using appropriate preparation and coding procedures. After analyses, the data were subjected to a strict quality control (QC) process. This included checking the accuracy and precision of the results by using reference standards, repeating analyses on important samples, and performing various statistical evaluations. Once the reliability of the data was assured, it was approved by the GSI and made available to users.

The northern section of the 1:100,000 geological sheet in Feizabad consists of sedimentary units, different types of tuffs, volcanic and pyroclastic rocks of Tertiary age, and intrusive rocks of Eocene–Oligocene age. This part of the study area is, therefore, more important from a geological point of view than the southern section. The number of samples that fall into this area amounts to 587 samples. Accordingly, a total of 587 stream sediment samples were used to create the geochemical evidence layers. The distribution of the stream sediment samples collected from the study area is shown in Figure 2. Previous studies in the Feizabad region have revealed a remarkable correlation between hydrothermal copper mineralization and various elements, such as Cu, Zn, Pb, Au, Sn, Hg, As, and Sb [6,47]. As a result, basic statistical parameters for these elements were calculated and analyzed. First, histograms of the key elements were plotted (Figure 3), showing that these elements do not follow a normal distribution. This indicates a high potential for hydrothermal copper mineralization in this region [47]. In addition, the relationship between Cu and the key elements is shown in Figure 4a, and a heatmap of the correlation matrix is shown in Figure 4b, which shows that these elements correlate relatively well with each other. This confirms the results from previous studies conducted in the region.

4.1.2. Remote Sensing Data and Preprocessing

The TERRA satellite was launched in December 1999, with the ASTER sensor and four other sensors. It began taking images in March 2000. The ASTER sensor takes images with a width of 60 km and displays them as standard images of 60 × 60 km. This sensor provides high-quality images, with a high signal-to-noise ratio, and can capture stereo images to create a digital elevation model. ASTER satellite images are widely used in geological research and for the identification of hydrothermal alterations related to ore mineralization due to their excellent spatial and spectral resolution, especially in regard to shortwave infrared (SWIR) bands [38,48,49,50]. For the study, an ASTER image (00307262004065434) from the USGS website was used to identify the hydrothermal alterations associated with hydrothermal copper mineralization in the Feizabad area. The ASTER image was corrected for atmospheric influences using the IARR method (Internal Average Relative Reflectance) and the radiance data were converted into reflectance values [39].

4.1.3. Geological Data

Geological data provide essential information for the exploration of mineral deposits and for the creation of prospectivity models. Two-dimensional geological maps show basic information about different lithologic units and the distribution of faults and their intersections. This information is valuable for the creation of evidence layers [19]. A digitized map of lithological units and faults in the Feizabad area was used for this study. Analyzing the geological units and fault structures using these maps helps exploration geologists to gain a deeper understanding of the patterns associated with mineralization.

4.2. Methodological Flowchart

Figure 5 illustrates the methodological flowchart used in this study to analyze the geospatial data and generate a mineral potential model for the hydrothermal copper deposits in the Feizabad district. As a first step, geochemical, geological, and remote sensing layers were created using appropriate analytical techniques. To reduce the uncertainty and improve the accuracy of the results, we used logistic functions to convert the values into fuzzy space [6,51]. In the next step, we used intelligent algorithms, namely the IForest and DIF algorithms, to combine the geospatial data and detect anomalies. Finally, a data-driven success rate curve was used to evaluate the prospectivity models.

4.3. Logistic Function

In MPM, various evidence layers are used, considering the conceptual model of the sought mineralization. Since these layers vary in terms of their dimensions, a weighting step is necessary to normalize or rescale the unbounded exploration data for integration [1,37]. In this regard, the following logistic function was used [51]:

(1)$F_E={\displaystyle \frac{1}{1+e^{-s(E-i)}}}$

where F_E is the value of the fuzzy membership; the assigned fuzzy score, s, is the slope of the logistic function; i is the inflection point of the logistic function; and E is the weighted fuzzy evidence falling into the domain [0, 1]. Also, the values of i and s are obtained from Equations (2) and (3), respectively:

(2)$i={\displaystyle \frac{E_{max}+E_{min}}{2}}$

(3)$s={\displaystyle \frac{9.2}{E_{max}-E_{min}}}$

4.4. Isolation Forest

The IForest algorithm is a widely used shallow unsupervised anomaly detection method that builds on decision trees (isolation tree) and benefits from ensemble learning [25,52]. It builds an ensemble of isolation trees to iteratively partition the data using a random split and to isolate anomalies. An isolation tree consists of a subset of data starting at the root node and proceeding to an isolated leaf node, by recursively splitting the data into smaller subsets, until each sample is isolated [30,53] (Figure 6). This concept assumes that anomalies require fewer splits to be separated from other samples (normal samples) [54]. The major advantage of the IForest algorithm is that it can detect anomalies without modelling or profiling the data, by taking advantage of the fact that anomalies differ in regard to some features [30].

The IForest algorithm assigns an anomaly score by calculating the average path needed to isolate a sample in all isolation trees. For each sample, the path length ($h\left(x\right)$) is the number of edges traversed from the root node to the isolated leaf node. Since it is expected that abnormal samples should be easily isolated, they have a relatively shorter average path [55]. The average path length ($c\left(n\right)$) and the anomaly score ($s$) can be calculated for a given sample $x$, as follows [56]:

(4)$c\left(n\right)=2H_{(n-1)}-\left({\displaystyle \frac{2(n-1)}{n}}\right)$

(5)$s\left(x,n\right)=2^{-{\displaystyle \frac{E\left(h\left(x\right)\right)}{c\left(n\right)}}}$

where $n$ is the number of data samples used for training; $H_{\left(i\right)}$ can be calculated from $\ln \left(i\right)+0.5772156649$; $c\left(n\right)$ is used to normalize $h\left(x\right)$; and $E\left(h\left(x\right)\right)$ is the average of $h\left(x\right)$ from a set of isolation trees. The number of trees (estimators) and maximum features are the main hyperparameters of the IForest algorithm [57]. The former has a direct impact on the performance of the model, in a such a way that more trees improve the performance of the model. The latter one controls the number of features to be randomly selected and is subsequently used for splitting, during the construction of each tree.

Figure 6

A schematic image of how an isolation tree is built and separate samples using axis-parallel cuts (modified version of [58]).

[Figure omitted. See PDF]

4.5. Deep Isolation Forest

Deep isolation forest (DIF) [30] is a novel hybrid algorithm that merges casually initialized (i.e., non-optimized) deep neural networks (DNNs) and IForest to take advantage of both techniques. The general procedure of the DIF (Figure 7) is that the randomly initialized DNN projects the original data into a set of random representation spaces. Then, the classical IForest algorithm applies simple axis-parallel cuts in these newly created data spaces to identify anomalous samples [59]. The main goal of the randomly initialized DNN is to better detect hard anomalies that are not easily isolated in the original data. The randomly initialized DNN was able to expose hard anomalies in the newly created spaces, where the anomalous samples could be isolated using simple axis-parallel partitions. These axis-parallel cuts in the projected data space correspond to sophisticated and non-linear partitions in the original data space [30,32,59].

5. Production of Continuous Evidence Layers

5.1. Geochemical Evidence Layers

The identified targets serve as promising locations that should be further investigated in later phases of the exploration efforts. During MPM, various geospatial features, such as geochemical data, are of great importance [6]. Geochemical studies, which are essential for understanding the distribution and behavior of elements associated with mineralization, play a crucial role in MPM, especially at the regional scale [40]. Exploration geochemistry focuses on the analysis of trace elements that tend to be associated with primary mineralization, with an emphasis on the identification of “primary halos” and “secondary halos” that form as a result of natural dispersion of trace elements [60]. These halos are usually found in the vicinity of mineralization and must be accurately identified for effective exploration. The study of secondary halos and their correlation with mineralization locations is a critical aspect of identifying new exploration targets. When analyzing stream sediment geochemical data on a regional scale, the separation of geochemical anomalies associated with mineralization and the creation of geochemical anomaly maps are essential components of MPM [61]. The geochemical anomaly layer is a critical component for the successful identification of areas with mineralization potential, especially for hydrothermal copper deposits.

Various techniques and concepts have been developed to determine geochemical anomalies and create layers of evidence for MPM on a regional scale [40,61,62]. These methods primarily focus on investigating the behavior and geochemical information of elements that show a positive association with mineralization [40,47]. In other words, the evidence layers are created according to the conceptual model of the mineralization being sought. During MPM with anomaly detection algorithms, it is important to use evidence layers that are suitable and have a high correlation with the targeted mineralization [12]. In other words, when using unsupervised anomaly detection methods, the layers will be better created based on the conceptual model of the target mineralization. Therefore, the information on eight geochemical elements was used in this study, according to the conceptual model (see Section 3) of the sought mineralization, and the values of these layers were transformed into 0 and 1 spaces using the logistic function. Figure 8 shows the resulting layers.

5.2. Proximity to the Hydrothermal Alteration Zones

Effective modeling of the mineralization potential of hydrothermal copper deposits requires the provision of various footprints, including the geological features associated with hydrothermal alteration related to mineralization. In this context, remote sensing data, such as satellite imagery, plays a crucial role in accurately mapping the surface distribution of these hydrothermal alterations, including argillic, phyllic, propylitic, and iron oxide types, which are fundamental to accurate geological assessments [48,63,64]. In this study, hydrothermal alteration zones associated with copper mineralization in the Feizabad district were identified using ASTER imagery. The Band Ratio [64] and Spectral Angle Mapper (SAM) [65] methods were then used to process the ASTER image, in order to precisely identify and delineate the hydrothermal alteration zones. Band ratios of 4/2, 5/6, 7/6, and 8/9 were used for specific mapping of iron oxide minerals, argillic, phyllic, and propylitic alteration zones. The SAM method was applied to selected endmember minerals, such as kaolinite, muscovite, and chlorite. The spectral absorption features of the endmember minerals in the SWIR bands of the ASTER image were used as the spectral range for the detection of argillic, phyllic, and propylitic alteration zones. Kaolinite in bands 5 and 6 (2.145 to 2.225 μm) was used to map the argillic zone, muscovite in bands 6 and 7 (2.185 to 2.285 μm) was used to identify the phyllic zone, and chlorite in bands 8 and 9 (2.295 to 2.430 μm) was used to delineate the propylitic zone. Threshold values were then determined using statistical methods (mean + 2 standard deviations) and all the regions that showed alteration zones were superimposed on a single band. Figure 9 illustrates the spatial distribution map of these hydrothermal alteration zones and their spatial relationships to known mineral occurrences, intrusive rocks, and faults.

Given the strong correlation between the identified alteration zones and the geological evidence, hydrothermal alteration is considered a key indicator for the exploration of hydrothermal copper deposits. After delineating these alteration zones, four distance-based evidence layers were created, as shown in Figure 10. These evidence layers significantly improve the modeling of the potential of hydrothermal copper deposits, as they provide important spatial data on hydrothermal alteration and, thus, improve the accuracy of the exploration efforts.

5.3. Proximity to Intrusive Rocks

Hydrothermal copper deposits, such as Cu–Au porphyry deposits and Cu veins, as well as other hydrothermal systems, often occur in close association with intrusive rocks, such as granite, granodiorite, and diorite from the Eocene–Oligocene period in the study area [34,35,36]. These intrusive rocks have played a critical role in the formation of mineral deposits in the Feizabad region, so proximity to these rocks significantly increases the likelihood of discovering hydrothermal copper deposits [34]. Consequently, exploration efforts in areas close to these intrusive rocks are more promising than in areas further away. To develop a relevant evidence layer associated with intrusive rocks, the intrusive units were first digitized using ArcMap 10.8. A layer was then created for the proximity to the intrusive rocks. Subsequently, the values of this layer were transformed into a fuzzy space using a logistic function to improve the precision and interpretability and reduce the uncertainty in the MPM analysis. Figure 11 illustrates the constructed evidence layer and shows a strong spatial correlation between the known mineral occurrences and these layers. Therefore, this map can be used as a reliable and fundamental layer in mapping the mineral prospectivity of hydrothermal copper deposits.

5.4. Proximity to the Intersection of Faults

Extensive research has emphasized the critical role of structural anomalies in enhancing permeability and facilitating the formation of mineral deposits, especially metal deposits [37,66]. Consequently, it can be assumed that most metallic mineralization occurs in close proximity to these structural features. Thus, hydrothermal copper deposits have unique and direct spatial and genetic relationships with faults [37]. Faulting plays an important role in the formation of these deposits and can significantly influence the distribution of alterations. Structural discontinuities, such as faults, are widely recognized as the main indicator of the presence of hydrothermal copper deposits. Mineral-bearing magmatic and hydrothermal fluids are transported through the rock via faults and fractures, especially at their intersections [37]. These intersections are considered optimal locations for hydrothermal mineralization due to their increased permeability. In the Feizabad area, the distance of fault intersections has been identified as a key structural factor controlling hydrothermal mineralization. In this study, a map of the proximity to fault intersections was first created (Figure 12). This map was then weighted using a logistic function. The resulting map was then used to model the mineralization potential of hydrothermal copper deposits.

6. Results and Analysis

6.1. Optimization of Unsupervised Anomaly Detection Algorithms

Hyperparameter tuning is of paramount importance for the performance of machine learning and deep learning algorithms, including the IForest and DIF algorithms. The optimal selection of these parameters depends on the specific characteristics of the dataset used. For example, the IForest algorithm includes crucial parameters, such as the maximum number of features and the number of trees. Consequently, these hyperparameters have been optimized in this research. Similarly, the DIF algorithm includes parameters such as the number of trees and the number of ensemble representations, which were carefully optimized to enhance the algorithm’s performance.

The identification of suitable parameters usually requires the use of ground truth samples. In general, the optimal parameters are determined by constructing an ROC curve and evaluating the AUC, based on these samples [21]. The accuracy of the ROC curve depends on both the positive and negative ground truth samples. However, in MPM studies, especially at the regional scale, negative samples may not be available. In such scenarios, negative samples are selected based on various constraints [67]. However, this selection is inherently random, making the process a major challenge and a significant source of uncertainty in MPM [68].

The Feizabad area has extensive known mineral deposits. Therefore, an evaluation technique commonly used in MPM, called the success rate curve, was utilized to select the optimal hyperparameters for the IForest and DIF algorithm. This curve is not based on labeled negative samples and, thus, minimizes uncertainty. Therefore, different models with various parameter settings were developed in this study and the success rate curve was plotted for each model. Among all the models, two models were identified as the most effective. In this context, we systematically investigated the optimal hyperparameters for the two adopted algorithms. These include the number of trees (set to 1000) and the maximum features (set to 14) for the IForest algorithm and the number of representations (set to 5) and the number of trees (set to 100) for the DIF algorithm. The IForest and DIF models are implemented using Sklearn 1.0.2 [69] and PyOD 2.0.2 [70], respectively, in a Python 3.8 environment.

6.2. Integration of Continuous Evidence Layers

6.2.1. IForest Prospectivity Model

The Feizabad region is characterized by the presence of granodiorite and diorite intrusive rocks, which have favored the development of hydrothermal alteration zones and associated hydrothermal copper mineralization. The favorable tectonic environment in the region favors the formation of such mineralization, which is often manifested by the enrichment of elements, such as Cu, Sb, As, Au, Zn, Pb, and other trace elements. To identify potential zones for hydrothermal copper deposits, we first created 14 evidence layers (Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12) based on the mineralization characteristics and the conceptual model. Recognizing that footprints associated with mineralization are a rare event with a low probability of occurrence, we applied machine learning algorithms specifically designed for anomaly detection. Among these algorithms, the IForest algorithm was selected due to its effectiveness in detecting such anomalies. We applied an IForest algorithm to map the mineral prospectivity for hydrothermal copper in northeastern Iran.

A comparative analysis between the resulting prospectivity model (Figure 13) and the geological map (Figure 1) shows that the areas with the highest probability of mineralization, characterized by high prospectivity values, correspond closely with faulted andesite and associated intrusive rocks. In addition, these anomalous zones show a strong correlation with highly faulted tuffs. The correlation between known mineral occurrences and areas of high prospectivity confirms the reliability of the prospectivity model created with the IForest algorithm. The results underline the effectiveness of the IForest method in delineating prospective zones for hydrothermal copper mineralization. However, it is important to point out that the IForest algorithm has limitations in certain regions, particularly in the northern and central areas, and underperforms in recognizing some known mineral occurrences. This shortcoming may be due to the difficulty encountered by the algorithm in capturing the complex and non-linear geological patterns prevalent in these areas. Consequently, more advanced techniques, such as the DIF algorithm, need to be used to improve the accuracy of prospectivity mapping.

6.2.2. Deep Isolation Forest Prospectivity Model

Anomalies within evidence layers frequently demonstrate a strong spatial correlation with the mineralization sought, despite exhibiting intricate and non-linear behavior. To effectively identify such anomalies, advanced anomaly detection algorithms, such as the DIF algorithm, can be utilized. In this research, the DIF algorithm, an extension of the classic IForest algorithm, was employed to generate a prospectivity map of the Feizabad region (Figure 14). In certain cases, this algorithm has surpassed the classical IForest algorithm in accurately identifying hidden and intricate anomalies. For instance, it has exhibited enhanced performance in detecting known mineral occurrences in the central and northern parts of the region, where the classical IForest algorithm encountered limitations. This highlights the capacity of strong and optimized intelligent algorithms to model non-linear and complex geological behaviors, thereby identifying areas that are challenging to detect using the basic IForest algorithm.

A success rate curve was applied to evaluate and validate the prospectivity models created using the IForest and DIF methods. This curve is one of the most powerful and widely recognized tools for evaluating the predictive capabilities of a model and provides a measure of its accuracy. The assessment analyzes the spatial correlation between known mineral occurrences and the classifications produced by each model [12,71]. Success rate curves are particularly effective in comparing the performance of different prospectivity models for mineral occurrences. From an MPM perspective, appropriate prospectivity models should predict a larger number of known mineral occurrences over a smaller area. Accordingly, the assessment method must facilitate the correlation between different map classes and known mineral occurrences. To achieve this, the map was first classified and then a success rate curve was created to evaluate the accuracy of the classification. This curve shows the spatial correspondence between the favorable area and the location of known mineral occurrences. To plot the success rate curve, different threshold values are determined from the MPM values in the predictive model. Then the proportion of predicted mineral occurrences is compared with the proportion in the favorable area [2].

As shown in Figure 15, the success rate curves for both the IForest and DIF models exceed the gauge line, indicating that both predictive models have successfully established a positive relationship with known mineral occurrences. The curve associated with the prospectivity model derived from the DIF method performs better, compared to the IForest model. This demonstrates that the DIF method is better able to identify non-linear and complex anomalies associated with mineralization and highlights its effectiveness in mapping prospectivity.

7. Discussion

Unsupervised anomaly detection algorithms provide a reliable method for identifying zones of high mineralization potential during MPM, especially in greenfields where labeled data is unavailable [20]. These algorithms do not suffer from the challenges associated with data-driven supervised MPM methods, which arise from the inherent characteristics of geospatial datasets and the rarity of mineralization [12]. Unsupervised techniques can work without a ground truth sample, in contrast to data-driven supervised methods, which can be hampered by the rarity of mineralization events and rely largely on well-defined training datasets. The reliability of the prospectivity models produced is increased and the uncertainty associated with the model results is greatly reduced by this independence from labeled data.

The application of these algorithms is a suitable option for creating mineral potential models and increasing the success rate in determining exploration targets. These algorithms do not require negative ground truth samples, which significantly reduces the uncertainty in prospectivity modelling. In this study, we applied unsupervised anomaly detection algorithms that are capable of processing complicated exploration datasets with high dimensions. The Feizabad region is a suitable location for hydrothermal copper mineralization, due to its geological and tectonic conditions. This area was selected as a case study. Initially, 14 evidence layers were created, based on the mineralization characteristics (Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12).

Mineralization is a local geological event with a low probability of occurrence, making it an anomaly. For MPM studies, geospatial datasets are generated based on the mineralization features sought in the study area. As high values in certain evidence layers typically correlate with some known mineral occurrences, anomaly detection techniques are especially well suited to this type of study. The case study demonstrates that the IForest and DIF methods can be utilized to map areas with high potential for mineralization. Both methods exhibited good performance in identifying promising areas. However, the DIF method outperformed the IForest algorithm, which may be attributed to its ability to expose and recognize hard anomalies associated with mineralization.

The ability of the DIF method to identify known mineral occurrences that the basic IForest prospectivity model could not detect demonstrates its superiority over the IForest algorithm. This difference draws attention to one of the main advantages of the DIF algorithm, namely due to its neural network-based architecture, it can handle high-dimensional data and process the complex and non-linear features that often characterize mineralization patterns. The IForest algorithm may struggle to deal with the complexity of geological data and may miss important anomalies, despite being simpler and more computationally intensive.

Although both methods can detect potential areas of mineralization, each of them has limitations. The IForest algorithm might struggle to model complex, non-linear behavior when the dataset is highly intricate, leading to the loss of promising areas. This means that the technique may not fully capture the complexity of the data, especially in areas where the footprints of mineralization are weak. Conversely, the DIF approach has its own difficulties, mostly related to the optimization of the hyperparameters, even though it is better at handling complicated datasets. Extensive experimentation is required to determine the best settings for the hyperparameters, which can have a large impact on how accurate the prospectivity models are.

Even though unsupervised techniques, such as IForest and DIF, do not require labeled datasets, the quality level and applicability of the input evidence layers are still very important. These algorithms only work under the assumption that the evidence layers they use are reliable markers for mineralization. Even the most advanced algorithms will not be able to produce useful and accurate prospectivity maps if the input data is of poor quality or does not accurately reflect the mineralization processes. Consequently, careful layer selection and evidence preparation are crucial workflows.

Our research validates the use of unsupervised anomaly detection methods during MPM, especially in areas where data limitations may make typical supervised approaches impractical. In particular, the DIF algorithm has potential due to its sophisticated management of complicated and non-linear interactions, giving it a major advantage over simpler techniques such as the IForest algorithm. The limitations of these methods must be carefully considered before using them in practice, especially with regard to the quality of the input data and the adjustment of the hyperparameters. Subsequent studies should focus on improving these approaches, possibly by developing more automated hyperparameter optimization procedures and by investigating strategies to improve the comprehensibility of the models.

8. Conclusions

The application of unsupervised anomaly detection techniques, including Isolation Forest (IForest) and Deep Isolation Forest (DIF), has proven effective in mineral prospectivity mapping (MPM) for polymetallic deposits. By using high-dimensional geospatial datasets without requiring labeled data, these algorithms overcome many challenges as-sociated with traditional supervised methods, particularly in regions with limited positive samples and complex mineralization styles. Both IForest and DIF successfully identified areas of high mineralization potential in the Feizabad area. However, DIF outperformed IForest, particularly in regions where geo-logical patterns are more intricate and non-linear. Its ability to use neural networks to model these complexities enabled better detection of mineralization zones that IForest missed. The success rate curves further validated the superior performance of DIF, making it a more effective tool for mapping potential mineral deposits. The integration of proximity to hydrothermal alteration zones, intrusive rocks, and fault intersections significantly enhanced the accuracy of the models. Remote sensing da-ta, such as ASTER imagery, provided valuable input for identifying alteration zones like argillic, phyllic, and propylitic areas, all of which played critical roles in defining high-potential mineral zones. Additionally, proximity to fault intersections and intrusive rocks provided key evidence layers that further refined the prospectivity models. Despite the superior performance of DIF, careful attention to hyperparameter optimi-zation remains essential for maximizing the accuracy of these models. While DIF shows promise for both greenfield and brownfield exploration, its success depends heavily on the quality of input data and the proper tuning of algorithm parameters.

In conclusion, unsupervised algorithms like DIF offer a flexible, scalable, and accurate approach to MPM, especially in complex geological environments. These methods can be adapted to various deposit types and exploration scenarios, making them invaluable tools for the discovery of new mineral resources.

Author Contributions

Conceptualization, M.S., S.M.B.G., S.A.A.S.M., Z.H.; methodology, M.S., S.M.B.G., S.A.A.S.M.; software, M.S., S.M.B.G., S.A.A.S.M., Z.H.; validation, M.S., S.M.B.G., S.A.A.S.M., A.M.; formal analysis, M.S., S.M.B.G.; investigation, M.S., S.M.B.G.; resources, M.S., S.M.B.G., S.A.A.S.M.; data curation, M.S., S.M.B.G., S.A.A.S.M., A.B.P., Z.H.; writing original draft preparation, M.S., S.M.B.G., S.A.A.S.M., Z.H.; writing review and editing, M.S., S.M.B.G., S.A.A.S.M., A.B.P., N.E.H., S.R., H.R., B.Z., Z.H.; visualization, M.S., S.M.B.G., S.A.A.S.M., A.B.P.; supervision, M.S., S.M.B.G., S.A.A.S.M., A.B.P., A.M.; project administration, M.S., S.M.B.G., S.A.A.S.M., A.B.P., Z.H., A.M. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data are contained within the article.

Acknowledgments

We would like to thank the Department of Mining Engineering, Amirkabir University of Technology (Tehran Polytechnic University). The Institute of Oceanography and Environment (INOS), the Universiti Malaysia Terengganu (UMT), and the Universiti Sains Malaysia (USM) are also thanked for their assistance in editing, rewriting, revising, and re-organizing the manuscript.

Conflicts of Interest

The authors declare that there are no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures

Figure 1. Simplified geological map of Feizabad region [33].

Figure 2. The distribution of the collected stream sediment samples in the study area.

Figure 3. Histograms for the key elements linked to hydrothermal copper mineralization.

Figure 4. (a) The relationship between Cu and the key elements. (b) A correlation matrix heatmap for the key elements related to the hydrothermal copper mineralization.

Figure 5. The workflow applied in this study to generate prospectivity models.

Figure 7. The workflow of DIF algorithm [30].

Figure 8. The geochemical evidence layers linked to the hydrothermal copper mineralization in the Feizabad district.

Figure 9. The distribution map of hydrothermal alterations and their spatial relationships with known mineral occurrences, intrusive rocks, and faults.

Figure 10. The evidence layers related to the proximity maps of (a) the argillic alteration zone; (b) the phyllic alteration zone; (c) the propylitic alteration zone; and (d) the iron oxide alteration zone.

Figure 11. Proximity to the intrusive rocks in the Feizabad region.

Figure 12. Proximity to the intersection of faults in the study area.

Figure 13. The IForest prospectivity model of the Feizabad region.

Figure 14. The DIF prospectivity model of the Feizabad region.

Figure 15. Success rate curves for the IForest and DIF prospectivity models.

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