MULTI-LABEL CLASSIFICATION FOR DRILL-CORE HYPERSPECTRAL MINERAL MAPPING

A multi-label classification concept is introduced for the mineral mapping task in drill-core hyperspectral data analysis. As opposed to traditional classification methods, this approach has the advantage of considering the different mineral mixtures present in each pixel. For the multi-label classification, the well-known Classifier Chain method (CC) is implemented using the Random Forest (RF) algorithm as the base classifier. High-resolution mineralogical data obtained from Scanning Electron Microscopy (SEM) instrument equipped with the Mineral Liberation Analysis (MLA) software are used for generating the training data set. The drillcore hyperspectral data used in this paper cover the visible-near infrared (VNIR) and the short-wave infrared (SWIR) range of the electromagnetic spectrum. The quantitative and qualitative analysis of the obtained results shows that the multi-label classification approach provides meaningful and descriptive mineral maps and outperforms the single-label RF classification for the mineral mapping task.


INTRODUCTION
Drill-cores are cylindrical rock samples extracted by drilling from the Earth's subsurface up to hundreds of meters during the exploration campaigns. They represent unaltered samples of rocks and provide valuable information of the subsurface (Gandhi, Sarkar, 2016). Mining companies rely on extracting drill-cores to describe geological systems and target the important ore accumulations in the deposits.
The first task in the drill-core analysis is usually core logging. It consists of describing and recording mineralogical information, such as lithology or alteration patterns, by an expert on-site. By performing core logging on the cores, important regions can be identified which are then sent to laboratories for the implementation of analytical techniques. These laboratory methods include optical microscopy (Krahenbuhl et al., 2015), X-ray diffraction (XRD) (Fox et al., 2016), X-ray Fluorescence (XRF) (Nikonow, Rammlmair, 2017), Scanning Electron Microscopy (SEM) analysis integrated with the Mineral Liberation Analysis (MLA) (Fandrich et al., 2007) or with the QEMSCAN (Gottlieb et al., 2000) software, amongst others.
The mining industry is gradually integrating the use of hyperspectral sensors to complement drill-core analyses. Hyperspectral scanners provide a fast, non-destructive, and non-invasive mean to analyze the cores. Hyperspectral data are recorded in hundreds of spectral bands covering contiguous and narrow wavelengths along the electromagnetic spectrum (Kruse, 1996, van der Meer, 2004. Depending on the sensor, the data can be recorded in the visible-near infrared (VNIR, 350 -1000 nm), the short-wave infrared (SWIR, 1000 -3000 nm) or the longwave infrared (LWIR, 8000 -15000 nm). Minerals spectral responses are distinct and mainly related to the fundamental electronic and vibrational process of the molecular bonds. Also, * Corresponding author. the mineral mixtures and different grain sizes have an influence on the spectral signature (Clark, 1999). These distinct spectra helps recognizing a range of minerals.
Classic methods to analyze drill-core hyperspectral data consist of the visual comparison of the general shape and absorption features present in the spectra with a reference spectral library (Huntington et al., 2006, Mauger, Hore, 2009. Another common approach is to use an established chain of techniques available in the well-known software called ENVI (Environment for Visualizing Images. Exelis Visual Information Solutions, Boulder, Colorado). This chain includes the reduction of the dimensionality using a minimum noise fraction transformation, the selection of representative samples or endmembers using the pixel purity index and the n-Dimensional visualizer, a manual or automatic identification of the endmembers using spectral libraries and the spectral analyst, mapping the minerals and/or determining their partial abundances using spectral similarity measure (e.g., spectral angle mapper) or unmixing (e.g., linear unmixing, mixture tune matched filtering) algorithms (Littlefield, Calvin, 2014, Kruse et al., 2012, Calvin, Pace, 2016, Littlefield et al., 2012, Xu et al., 2011, Bedini et al., 2009, Kratt et al., 2010. Lately, the use and development of machine learning methods for data analysis are growing in different research fields. Machine learning techniques offer automatic approaches to discover patterns and underlying relations within large data sets. More recently, machine learning methods have been also suggested for the analysis of drill-core hyperspectral data to improve the robustness and automation of the analyses (Schneider et al., 2014, Contreras Acosta et al., 2019b, Wang et al., 2017. However, developing supervised machine learning frameworks for mineral mapping in drill-core hyperspectral data is a challenging task. This is because little prior information can be obtained in a represent-ative form to define meaningful classes and select characteristic samples for training. In (Contreras Acosta et al., 2019a), an approach where high-resolution mineralogical data, obtained from polished thin sections of some drill-core samples, are spatially re-sampled and co-registered to the corresponding hyperspectral data was proposed. The co-registered data were then used to generate the reference or ground truth data for training a supervised classification algorithm.
Based on the traditional classification concept each pixel is represented by a single instance (feature vector) and associated with a single label. Thus, the assumption is that each pixel has only one unique semantic meaning/label (Zhang, Zhou, 2014). However, although traditional classification algorithms are highly implemented and performing well, there are many learning tasks where the assumption is not completely suitable, for example in drill-core hyperspectral mineral mapping. This is because of the nature of the drill-core hyperspectral data where the pixels are usually highly mixed and it is difficult to find pure mineral spectra at the current spatial resolution of the data. Thus, pixels in drill-core hyperspectral data are expected to be labeled more meaningfully by giving multiple labels.
The multi-label classification concept was first introduced for text classification (Tsoumakas, Katakis, 2007). In multi-label classification, each pixel is associated with a set of labels Y ⊆ l, in contrast to single-label classification where a pixel is characterize by a single label l from a set of disjoint labels L (Tsoumakas, Katakis, 2007, Zhang, Zhou, 2014. In general, the available methods for multi-label classification can be grouped in two main categories: problem transformation methods and algorithm adaptation methods. The first category solves the multi-label problem by transforming it into one or more singlelabel classification problems, whereas the algorithms belonging to the second group focus on extending popular learning techniques to handle multi-label data directly (Tsoumakas, Katakis, 2007, Zhang, Zhou, 2014. The problem transformation methods try to fit data to algorithm, while the algorithm adaptation methods aim at fitting algorithm to data (Zhang, Zhou, 2014).
In this work, we introduce the use of multi-label classification to map minerals in drill-core hyperspectral data. More specifically, for the first time to map minerals, we apply a multilabel classification method, that belongs to the family of problem transformation methods, called classifier chain model (CC) (Read et al., 2009). Broadly, this method links together binary classifiers in a chain where class label predictions become features for the following classifiers (Read et al., 2019). Thus, label correlations are considered. This has more meaning in the case of drill-core hyperspectral data since pixels are highly mixed and certain mineral associations are expected. To be able to implement this method, we use high-resolution mineralogical data (i.e., SEM-MLA) to annotate the hyperspectral pixels in a small area of a drill-core. Pixels in the SEM-MLA are of 3 µm size while in the hyperspectral data pixels are of about 1.5 mm. 250000 pixels of the SEM-MLA image comprise 1 pixel at the hyperspectral spatial resolution. Multiple labels are assigned to each pixel in the SEM-MLA region based on the relative abundance of the different minerals. As a base classifier for the CC method, the well-known random forest (RF) algorithm is implemented since it has been shown to provide good results in geological applications and it can handle high-dimensional data with a limited number of training samples (Breiman, 2001).
The rest of the paper is structured as follows: section 2 describes the classifier chain method. Section 3 presents data de-scription and acquisition, experimental results, and discussions. Finally, the conclusions are drawn in Section 4.

FRAMEWORK FOR THE MULTI-LABEL CLASSIFICATION
In this study, we propose to use the CC method with the RF algorithm as a base classifier to perform the multi-label classification in drill-core hyperspectral data. Once the high-resolution mineralogical data are collected by the SEM-MLA technique, they are linked to the corresponding hyperspectral data (Contreras Acosta et al., 2019a). Then, the labels for each hyperspectral pixel in the SEM-MLA region are chosen based on the frequency of the existing minerals in the SEM-MLA for the area of that pixel. For this, each hyperspectral pixel is labeled with the minerals that represent around 95% of the content in the SEM-MLA for that pixel.

The Classifier Chain (CC) method
The CC algorithm transforms the multi-label problem into a chain of binary classification problems. Binary classifiers in the chain are built upon the predictions of the preceding ones (Zhang, Zhou, 2014). This is, a chain of classifiers, C1, · · · , C |L| , where each classifier, Cj, learns and predicts the binary association of label lj ∈ L, given the feature space augmented by all prior binary relevance predictions in the chain l1, · · · , lj−1. The classification begins at C1 by determining P r(l1|x) and every subsequent classifier C2 · · · C |L| predicts P r(lj|xi, l1, · · · , lj−1). Following this method, the label information between classifiers is passed and therefore, labels correlations are taken into account (Read et al., 2009). As it is expected, the order of the chain influences the results. For more details we refer the readers to (Read et al., 2009).

Random Forest (RF)
The RF algorithm is applied as a base classifier in the CC method. In RF, a set of decision tree classifiers are trained and their individual results are combined through a voting process. This type of classifiers is the so-called ensemble learning classifiers (Breiman, 2001). Each tree gives a unit vote to the most frequent class in the input vector x and the classification label is allocated to the input vector through a majority vote: C RF = majority vote {Ĉt(x)} T 1 , where x is the input vector, Ct(x) is the class prediction of the tth tree, and T shows the total number of trees (Rodriguez-Galiano et al., 2012). Due to the different decision trees, RF is robust and it is expected to perform more accurately than an individual decision tree classifier.

EXPERIMENTAL RESULTS
In this section the data description (i.e., acquisition and preprocessing), setup employed for the experiments, and results are presented.

Data description
For the acquisition of the drill-core hyperspectral data an unpolished half of a drill-core sample was used (see the RGB image of the Drill-core sample in Fig. 1). The acquisition was performed with a SisuRock drill-core scanner equipped with an AisaFenix VNIR-SWIR hyperspectral sensor. This sensor acquires data that encompass the 380-2500 nm range of the electromagnetic spectrum. The spectral resolution is 3.5 nm in the VNIR and 12 nm in the SWIR with a total of 450 bands. The size of the drill-core hyperspectral image is 33 × 189 pixels where each pixel covers an area of 1.5 × 1.5 mm 2 . In the preprocessing stage of the data, radiometric and geometric corrections were carried out to correct the sensor-shift and the effect of lenses, respectively. For this, the toolbox presented in (Jakob et al., 2017) was used.
For the training set, high-resolution mineralogical data were acquired from a carbon-coated polished thin section of about 30 µm thickness from an specific region of the drill-core sample using the SEM instrument with the MLA software. The region where the thin section was taken is represented by the red rectangle in the RGB image of the drill-core shown in Fig. 1 (see Thin section in Fig. 1). In general, the SEM-MLA analysis consists of defining mineral grains using the back-scatter electron signal received off the sample and defining the mineral phases with X-ray measurements on a closely-space grid. Pixels in the resultant SEM-MLA image are of 3 µm size (see SEM-MLA image in Fig. 1). 250000 pixels of the SEM-MLA image comprise 1 pixel at the hyperspectral spatial resolution.

Experimental setup
As explained in Section 2, labels for the re-sampled SEM-MLA pixels were chosen based on the frequency of the minerals for that region in the SEM-MLA image. For this, a threshold of around 95% of the content, in the SEM-MLA, was considered to avoid minerals with very low frequency. 22 minerals are identified by the SEM-MLA analysis (see legend of the SEM-MLA image in Fig. 1). However, in the VNIR-SWIR range of the electromagnetic spectrum not all of these minerals have diagnostic absorption features. For example, minerals like Px (piroxene), Qz (quartz), and Py (pyrite) are represented similarly as flat spectra in this range. For this reason, the minerals without representative diagnostic absorption features in the VNIR-SWIR range were grouped as OMs (other minerals).
For a complete qualitative analysis, a typical multi-class RF algorithm was also used to train a model and then, on a later stage, predict a unique label for each pixel in the entire drill-core hyperspectral image. To train the RF classifier, the SEM-MLA image was also considered, however, for each re-sampled pixel a unique label was given (i,e., the most frequent mineral). For all these implementations, 500 decision trees were used and the number of prediction variables was set equal to the number of input bands.

Multi-label classification results
To implement the multi-label classification algorithm, the order of the chain was set based on the frequency of the minerals in the SEM-MLA image. This is because the nature of the SEM-MLA data that gives the quantity of the minerals, therefore, we can conclude that this is the most relevant order. The reference data used to train the CC are shown in Fig.  2. As can be observed, Wmca (white mica), Bt (biotite), Chl (chlorite), Amp (amphiboles), Gp (gypsum), and OMs are the most dominant minerals present in the re-sampled SEM-MLA. Fig. 3 shows the results of the multi-label classification. Wmca and Gp are mostly present in the veins and alteration halos, whereas the matrix is mainly composed of OMs with Chl, Bt,

Classes
Accuracies ( and less amount of Wmca and Amp (amphiboles). By comparing these maps with the high-resolution mineralogical image (SEM-MLA image in Fig. 1), a similar mineralogical distribution can be observed. The SEM-MLA image shows that the matrix in the sample is dominantly composed of Pl (plagioclase) partly altered to Wmca, Chl, and Bt. The veins are of two types: Qz and Wmca veins, and Gp, Wmca, and scarce Py veins. Minerals such as Qz, Pl, and Py are not mapped individually due to the lack of diagnostic absorption features in the VNIR-SWIR, but have been included in the OMs class. Moreover, the mineral map obtained from the classic multi-class RF classification (shown in Fig. 4) highlights the advantages and capabilities of the multi-label approach for the mineral mapping task. This is because of the nature of drill-core hyperspectral data which is having mixed pixels, and when considering one single label per pixel the mapping is generalized. Thus, performing a multi-label classification on drill-core hyperspectral data presents an advantage for mapping the different minerals present in the pixels of the sample.

CONCLUSION
In this paper, we introduce the use of multi-label classification for drill-core hyperspectral mineral mapping. For this, the CC method together with RF is used. This method links together RF binary classifiers in a chain. This means that each class label is predicted by one classifier and the resultant predictions are included in the feature space for the following classifier. For generating the training set, we used SEM-MLA data, which provides high-resolution mineralogical analysis. From the analysis of the results, we have seen that the multi-label classification approach provides more descriptive and meaningful results than a typical RF classification where the mapping is less detailed.
As part of our future work, we will implement other advance multi-label classification algorithms and compare the performance on larger drill-core hyperspectral datasets for the mineral mapping task.  The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIII-B3-2020, 2020 XXIV ISPRS Congress (2020 edition)  The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIII-B3-2020, 2020 XXIV ISPRS Congress (2020 edition)