Principal Component Analysis (PCA) is an often-powerful statistical method in these kinds of studies, enabling the dimensionality of the data to be reduced while preserving their main trends [6]. In this study, PCA was applied to the geochemical dataset to identify associations between different elements and very often correctly distinguish lithological signatures [7]. The results, including eigenvalues (Figure 2), correlation matrices and biplots, were analyzed and interpreted to extract geochemically relevant conclusions [6].

Figure 2. Scree plot showing four (4) PCs with eigenvalues > 1.

The geological environments of ultramafic deposits are very often complex and could involve multiple magmatic, metasomatic, and hydrothermal processes that intersect one another [8][9]. To distinguish between them and select possible areas of economic interest, the use of multivariate statistical methods such as PCA or K-means clustering [10] is a possible way; though, thousands of data from the NGU deposit could help identify distinctive geochemical signatures, guide mineral exploration and test geological hypotheses in the shear belt. Consequently, PCA is a data analysis technique that uses a data table containing information on both individuals (samples) and quantitative variables (a percentage of the proportion of the chemical element tested in each individual sample) to condense the information. Principal component analysis aims to synthesize the structure of multivariate data by reducing the data to the components of a few, each of these principal components representing a certain percentage of the variability of the data before transformation [6]. PCA produces a summary of information by identifying similarities between variables. Variables with characteristics that come together to form a group. Links between several variables are used to identify similarities. To achieve this, PCA generates a small set of new variables (the factors: PCs) that capture the characteristics of the entire group of variables. Principal component analysis therefore produces additional variables (PC1 to PC2, PC3, PC4...) with various levels of association with the items [10].

In this study, the use of the correlation matrix plays a key role, as this technique will be used to show the relationships between different pairs of elements. But [6] warned against using standard statistical methods to find correlations and patterns with these kinds of data. Most multivariate methods, including PCA, are designed for Euclidean space rather than “simplex” space and could therefore produce erroneous results [6]. In our case Robust PCA Estimation (RPCA) in line with the recommendations of [11], the classical correlation matrix estimation is replaced by a robust estimation less sensitive to outliers as indicated in [12] with a use of “XY” graphs (bivariate diagram) to visualize and evaluate the results of the PCA study. These diagrams simultaneously visualize the importance (of different variables as vectors (arrows) and the PCA scores calculated for individual samples (dots). The length of an individual arrow is proportional to the variability of the vectors in relation to the two principal components represented, with positively correlated vectors being closer together. The proximity of sample points to specific vectors and their distance from the origin in the diagrams reflect the importance of the influence of these vectors on the sample [12]. For [6] a logarithmic transformation (= logarithms of ratios), a centered log-ratio prior to PCA is necessary, as it converts the compositional data into an unconstrained real space, thus alleviating the closure problem.

The principal component analysis conducted as part of this research used the entire sample set (10,144) of both fresh and weathered core rocks to reveal the main correlations between chemical elements, providing a better understanding of the structure of the data set. As a result, the most powerful indicators highlight the most remarkable patterns (such as a set of interconnected features common to a specific rock type) but also isolate or ignore small occurrences. Hence, the higher the correlation value reaches +1 on the scale, the stronger the correlation between the feature and the PC factor [13][10].

PCA reduced the dimensionality of the dataset, with the first three principal components (PCs) explaining 77.01% of the total variance (Table 1). The factor PC1 (46.5%) captured the mafic-felsic dichotomy, with positive loadings for Fe, Ni, Cr, and negative loadings for SiO₂ and K (Figure 3(a)). While PC2 (20.33%) highlighted carbonate and plagioclase (?) influences (Ca, Na, Mg) (Figure 3(d), Figure 3(e)) and PC3 (10.18%) associated with aluminosilicates and clay minerals (Al, Sr). Bivariate plots (e.g., PC1-PC2, PC1-PC3) visualized these relationships, revealing magmatic signatures (PC1 negative: Mg, Ti, Fe), a fluid alteration zones (PC1 positive: SiO₂, LOI, Ba) and sulfide mineralization potential (PC3 positive: Cu, Zn). An analysis of the eigenvalues and bivariate diagrams shows that the most significant contribution (46.496%) is made by factor PC1, which is composed of a robust relationship between Mg, Ti, Fe, Mn, Zn, V, Ni, Co, Cu, and Sc in a positive series. It could be aligned with a gabbro-pyroxenite axis. These are elements related to the ultramafic deposit [5].

The presence of Mg, to a lesser extent (positive), and of Ca, Na, and Ba, all negative (PC1 in Figures 3(a)-(c)) is at the origin of PC2 (20.333553%). Extraction of the elements Ca, Na, and Ba shows the presence of leaching likely due to hydrothermal fluids with the presence of carbonates. Vectors of these elements show an antithetical relationship with Al and LOI. A contribution of Mg for the formation of olivine and pyroxenes favors the development of Ni and Sc mineralization and (Ti, Fe, V) mineralization linked to magnetite rocks.

Whilst the presence of K, Si, Na, Ba (negative) to a lesser extent is linked to the PC3 factor (which represents 10.18587% of the variation) and is associated with felsic rocks and, the lower contribution of PC4 (7.146%) is associated with Si, Ka, Sr, Na and Ba, a negative series (Figure 3(c)). Principal components (PC1 to PC4) represent 84.1% of the overall variability and are the only ones for which the eigenvalues are far greater than 1.0 (Figure 2) [3][12][13]. The first two PCs represent 66.83% of the variability (46.5% and 20.33%, respectively) and illustrate a covariance of varying degrees between the group of variables. These spatially separated sequences of elements PC1-PC2-PC3-PC4 are directly apparent (Table 1).

Table 1. PCs summary and interpretations.

In Figure 3(a), PC1-PC2 biplot diagram where PC1 (Axe X) represents primary magmatic processes versus secondary process on the positive side (right), Si indicates silica enrichment due to late magmatic stages or alteration. LOI suggests

Figure 3. (a) showing primary magmatic process vs, secondary and traces elements enrichment; (b) Primary magmatic process with sulfide mineralization; (c) Contrast between magmatic and hydrothermal process; (d) Magmatic signature showing olivine, pyroxene and chromite with alteration fluid and different phases of crystallization; (e) magmatic suit with elements such as Cr, Ni, Mg, Ti with olivine, chromite, titanium magnetite. A sulfide mineralization potential zone and Ni remobilization process; (f) Late magmatic evolution, show magmatic fractionation processes and overprinting hydrothermal alteration.

secondary hydration (serpentinization), or carbonation and Ba may reflect hydrothermal fluids, indicating post-magmatic alteration. The negative side (Left) on the same Figure 3(a); Na, Ca, and Mg represent primary ultramafic mineralogy (e.g., olivine, pyroxenes) and Ti associated with ilmenite/magnetite indicating primary Fe-Ti oxides. PC2 (Axe Y), traces elements enrichment, the positive side (Top) shows Mn, Co, Cu, Zn bound to sulfide phases or late fluids, suggesting hydrothermal overprinting or sulfide mineralization. Whereas the negative side (Bottom) shows no significant variables, probably reflecting background noise. Thus, this first bivariate shows (1) a primary magmatic signature (PC1 Negative), dominated by Mg, Ca, Ti, reflecting ultramafic host rocks (olivine, pyroxenes) and Fe-Ti oxides. The low Si content corresponds to typical ultramafic compositions. (2) an alteration/secondary process (PC1 Positive), highlighted by SiO₂ and LOI, indicating serpentinization or silicification, with Ba suggesting fluid input and, (3) Traces element enrichment (PC2 Positive), high Mn, Co, Cu, Zn contents could indicate sulfide mineralization (e.g. chalcopyrite, pentlandite) or late hydrothermal remobilization.

PC1-PC3 biplot at PC1 (X-axis), the dominant source of variance, probably reflects primary magmatic processes as opposed to fluid-related processes (see Figure 3(b)). Here is a positive PC1 (Right), a variable including Sr, Ca, Na and Ba. These could suggest plagioclase fractionation, carbonate alteration, or the influence of hydrothermal fluids (e.g., alkali-rich fluids or carbonatitic metasomatism). A negative PC1 (Left), variables including Al, Cr, Sc, P and REE (rare earths?). These elements reflect mafic-ultramafic minerals (e.g., spinel, pyroxene) and could indicate primary Fe-Ti-Cr magmatic assemblages or apatite enrichment. PC3 (Y Axis) captures secondary variability, potentially related to redox or trace metal signatures, showing positive PC3 (Top), a variable including Cu, Zn and Zr. Cu-Zn suggests sulfide mineralization (e.g., chalcopyrite, sphalerite), while Zr could indicate serpentinization process or mantal source (e.g., zircon) and negative PC3 (bottom) with variables including Cr and Sc (positive), associated with chromite and pyroxenes, representing residual magmatic minerals in unweathered ultramafic. In conclusion, negative PC1 values correspond to zones of main mineralization (e.g., magnetite-ilmenite-chromite), Fe-Ti-Cr mineralization. Positive PC1 values highlight fluid-affected zones, with possible remobilization of metals, a Fluid-altered zone. High Cu and Zn contents (positive PC3) could indicate Ni-Cu-EGP prospects, hence sulfide potential. High P contents could suggest the presence of apatite associated with rare earths. High Sr and Ba levels indicate fluid flow conduits, while low Al a possible leaching (e.g., serpentinization), reflecting a zone of alteration.

On PC1-PC4 biplot diagram (Figure 3(c)), the PC1 factor (X axis), a main source of variance, contrasting magmatic (negative) and hydrothermal (positive) processes, range from −0.50 to 0.35. Positive PC1 (Right) shows SiO₂, LOI, Al, K, Ba, P, Zn, fluid-dominated zones (silicic alteration, hydration, hydrothermal fluids) while negative PC1 (Left) with Ca, Ti, Cr, V, Ni, Fe, Co, Mn primary magmatic minerals (clinopyroxene, chromite, magnetite). As for PC4 (Y axis), minor but distinct variability, potentially linked to redox conditions or late weathering, ranges from 0.40 to 0.20. Positive PC4 (Top), Cu, Zn, Ba, sulfide enrichment, or oxidizing fluids (chalcopyrite, barite), while negative PC4 (Bottom), Cr, Ni, Co, reducing conditions (chromite, pentlandite). This diagram shows the potential for polymetallic mineralized zones as follows PC1 Negative + PC4 Negative, main Fe-Ti-V-Cr-Ni mineralization (magnetite, ilmenite, chromite) and PC1 Positive + PC4 Positive, hydrothermal intersections (sulfides, barite, phosphates). The presence of alteration and sulphides zones is marked by high SiO₂ + LOI values, potential zones for metal remobilization (serpentinization), and high Ba + P values, indicative of sulphides or rare-earth targets, while the potential for sulphides mineralization is marked by high Cu-Zn-Ba values (PC4 positive), indicative of potential for Cu-Ni-EGP mineralization.

For PC2-PC3 biplot diagram (Figure 3(d)), PC2 (X axis) where negative PC2 shows a magmatic signature (e.g., olivine, pyroxene, chromite) and positive PC2 indicates fluid alteration (e.g., serpentinization, carbonation). PC3 (Y axis) or negative PC3 shows elements and arrangements emanating from early crystallization products and, positive PC3 reflects late fractionation and alteration. Here the key variable groups are, (1) Primary magmatic package (PC2-Negative, PC3-Negative) shows variables such as Mg, Cr, Ni, Co with minerals such as olivine, chromite, pyroxenes, indication for cumulative zones of high mineralized potential. (2) Fluid alteration signatures (PC2-Positive) with variables such as LOI, Ba, Sr, indicating a fluid alteration signature and therefore the potential for remobilized Ni-Cu sulfides. And finally (3) Late enrichments (PC3-Positive) with elements such as Cu, Zn, P, showing potential for hydrothermal sulfide lenses or PGE. Ba/Sr peaks mark alteration fluid conduits, while a high LOI + SiO₂ indicates serpentinized shear zones.

PC2-PC4 biplot diagram, here the PC2 (X Axis), where PC2-negative side has a primary signature of ultramafic rocks, dominated by chromium (Cr), nickel (Ni), and magnesium (Mg) (Figure 3(e)). These elements are typical of primary magmatic phases, whereas PC2 on the positive side shows elements mobile in fluids, such as barium (Ba), potassium (K), phosphorus (P), and zinc (Zn). These elements indicate hydrothermal or metasomatic processes. PC4 (Y Axis), shows PC4 negative side, early magmatic phases, marked by titanium (Ti), magnesium (Mg), and chromium (Cr). PC4-positive side of late processes, including copper (Cu), scandium (Sc), and oxygen (O₂). These elements are associated with sulfide segregation and oxide-sulfide boundaries. The analysis identified several mineralization clusters, each revealing distinct geological processes, a magmatic suite (PC2-, PC4-) has elements such as Cr, Ni, Mg, Ti, and minerals such as chromite, olivine, titaniferous magnetite. This cluster reflects primary magmatic processes and suggests a high potential for Cr-Ni-Ti mineralization. A potential sulfide mineralization (PC4+) has elements such as Cu, Sc, O₂, or Cu-Sc coupling indicates magmatic sulfide segregation. The presence of O₂ serves as an indicator for the boundary between oxidized and sulfidized phases. Fluid alteration (PC2+) is marked by elements such as Ba, K, P, Zn reflecting a carbonation process and alkaline metasomatism. These elements mark zones of nickel remobilization and hydrothermal fluid pathways. Ba/K peaks can identify fluid conduits, while phosphorus (P) can indicate potential for rare earths associated with apatite.

The PC3-PC4 biplot (Figure 3(f)) provides essential information on late magmatic evolution, hydrothermal overprinting, and metasomatic alteration. PC3 (X axis), magmatic fractionation and alteration processes, distinguishes between early and late magmatic processes. Negative PC3 values correspond to early magmatic crystallization, indicated by variables such as Ti and V, suggesting primary oxidized minerals such as titanomagnetite and vanadiferous spinels. Positive PC3 values, on the other hand, reflect late fractionation or alteration, often associated with sulfide mineralization (Cu, Zn). PC4 (Y axis), the PC4 axis highlights redox conditions and fluid interactions. Negative PC4 values correspond to reduced mineral assemblages, typical of primary magmatic conditions. Positive PC4 values indicate oxidized or fluid-rich zones, marked by elements such as Ba, Sr, and LOI, suggesting carbonate-chlorite alteration and possible nickel remobilization. Primary magmatic signatures (PC3-Negative, PC4-Negative) represent zones of primary oxidized mineralization, characterized by high Ti and V concentrations.

Sulfide potential (PC3-Positive, PC4-), magmatic sulfides (PC3+, PC4-) may appear as primary sulfide lenses, while hydrothermal overprinting (PC3+, PC4+) suggests Cu-Zn enrichment due to fluid interactions. Alteration fluids (PC4-Positive) with high Ba and Sr levels highlight fluid infiltration paths, crucial for identifying metasomatic fronts and possible Ni remobilization. The gradient between Ti-V (PC3-) and Cu-Zn (PC3+) reveals a fractionation sequence, while PC4 variations define redox boundaries.

K-Means Clustering

Cluster analysis (Figures 4-6) is a statistical technique that groups object in a population based on their similar characteristics to create clusters (groups) of individuals [7][12][14]. This type of method first creates pairs or groups, by clustering two objects or more with the most similar values of variables on the one hand. On the other, it has data for each chemical element evaluated in each participant. Though in K-means the elements are organized into groups of two or more, based on their proximity as indicated by their mean values or, could contain a single element (outliers) [3][12].

In this study the clustering analysis used is K-means, which aims to group samples to minimize variation within groups and maximize variation between groups; this method has been successfully applied to lithogeochemical data individuals [7][12][14]. It is then possible to calculate the various statistical parameters for each group, including the average chemical composition of each. Determining the average chemical composition of the cluster enables a theoretical petrological name to be assigned to the cluster (lithogeochemical determination) and compared with the petrographic determination in the field supported by [5] & [15] in their respective studies.

But there is a limitation in using K-means clusters as it tends to form groups of similar size (in Euclidean space), whereas this can cause problems for raw, untransformed data, where variables often differ by several orders of magnitude in terms of absolute abundance, meaning it works best for spherically distributed data [16]. Principal components are best suited to the K-means cluster, as they are both centered and scaled [12][13]; and use the Kaiser-Guttmann rule which states that the eigenvalue must be greater than 1.0 (Figure 2) for conventionally scaled data for the number of principal components selected for inclusion in K-means clustering [13].

1)K-means=6

An analysis of the results (Figures 6(a)-(f)) by clustering shows, a) a PC1 representing a major geochemical gradient, probably reflecting the compositional continuity (Junction) between ultramafic and mafic. Strong contributions from Mg, Ca and Sr suggest that this PC captures mafic-ultramafic mineralogy. b) PC2 shows strong associations with Al, P, K and Ba, potentially representing secondary alteration processes or felsic contamination components. c) PC3 correlates with transition metals (Ni, Co, Mn, Zn) and SiO₂, possibly reflecting sulfide mineralization or serpentinization processes. d) PC4 is associated with trace elements such as Ti, Sc, V, and some transition metals, possibly representing accessory mineral phases [12].

An association of notable elements indicating a mafic-ultramafic signature with elements such as Mg, Ca, Sr, Na clustering in the PC1-PC2 space. Alteration indicators Al, K, Ba, LOI (loss on ignition) show similar behavior. Sulfide-related elements Ni, Co, Zn, Mn often cluster together, and the SiO₂ component appears as a distinct vector in several graphs. The K-means clustering plot shows the sum of squares (variance) as a function of the number of clusters (K). Key Observations are, a) The “elbow” method suggests an optimal K where the variance reduction begins to flatten (Figure 4). The graph shows a reduction in variance up to at least K = 6, (but the exact optimal K is unclear here. b) For an ultramafic deposit, one would expect natural clusters corresponding to different ultramafic lithologies (dunite, harzburgites, lherzolite), alteration zones (serpentinized vs. fresh) and mineralized zones (sulfide-bearing vs. sterile). c) The high initial variance (approx. 2500) suggests considerable geochemical heterogeneity in the dataset [3].

A geological interpretation for the NGU ultramafic deposit shows a) The PC1 gradient probably represents the primary magmatic differentiation trend, from the most depleted (Mg-rich) to the least depleted compositions. b) PC2 may represent secondary processes such as serpentinization (contributing Al, K, Ba) or other fluid-related alteration. c) Transition metal associations (Ni, Co, etc.) in PC3 and PC4 could indicate sulfide mineralization, common in ultramafic systems, while d) SiO₂ behavior (SiO₂ mobility) suggests that it does not simply follow the primary magmatic trend, but could reflect secondary silicification [5].

In this study with an average K = 6 it is clear that further study is essential and, a) determine the optimum K so a clearer plot of intra-cluster variance as a function of K would help identify the true “elbow” point for cluster number selection. b) Validate clusters geologically by comparing statistical clusters with geological mapping to ensure they have petrological significance. c) Examine element ratios

Figure 4. Graphic showing high initial variance and optimal K. The K-means clustering plot shows the sum of squares (variance) as a function of the number of clusters (K).

Figure 5. Pie chart showing clustering K = 4. Red: unweathered ultramafic lithology (Mg-Fe-rich, low SiO₂). Orange colored: Fe-Ti mineralized zones (enriched in Ti, Fe, Cr, V). Green: hydrothermal altered domains (carbonate/serpentine-rich?). Blue: transitional or mixed lithologies (e.g., silicified ultramafic).

(for ultramafic systems), such as Mg/Si, Mg/(Fe + Mg) or Ni/MgO could provide clearer clustering. d) Perform spatial analysis by mapping cluster assignments to see if they correspond to spatial patterns in the deposit [12].

Figure 6. Biplots clustering showing samples color-coded using K-means clustering: K = 6 (a)-(f) and K = 4 (a, b, c, d, reference to pie chart presentation).

2)K-means=4

In this analysis, PC1 (major lithological control) reflects the primary composition of ultramafic rocks (Mg, Ca, Na), typical of magmatic cumulates such as dunites. Its negative correlation with Al and K underlines its opposition to weathering processes. PC2 captures the effects of serpentinization and metasomatic fluids (Al, K, Ba), revealing rock-fluid interactions, while PC3 and PC4 isolate key elements such as Ni, Co, and Ti, associated with sulfides and accessory minerals, respectively. The presence of SiO₂ in PC3 suggests zones of silicification, potentially linked to hydrothermal circulation. The correlation between Ni and Co in PC3 could indicate remobilized sulfide mineralization [17]. Optimal cluster validation shows significant variance reduction up to K = 4 with diminishing returns beyond 4 clusters, justifying the selection and/or the four (4) clusters solution illustrated on the curve and supported by the pie chart (Figure 5). The clustering results and the choice of K = 4 clusters are justified by optimal variance reduction. Each cluster corresponds to a distinct geological facies (Figures 6(a)-(d)):

a) Cluster 1 (4930 samples), unweathered ultramafic lithology (Mg-Fe-rich, low SiO₂).

b) Cluster 2 (3285 samples), Fe-Ti mineralized zones (enriched in Ti, Fe, Cr, V).

c) Cluster 3 (480 samples), hydrothermal altered domains (carbonate/serpentine-rich?).

d) Cluster 4 (1435 samples), transitional or mixed lithologies (e.g., silicified ultramafic).

- Outlier values (14 samples), exotic lithologies (e.g., pegmatitic veins).

Cluster 1 involves fresh, unaltered rocks; Clusters 2 and 4 are priority targets for Fe-Ti ore and associated alteration halos, while Cluster 3 represents alteration gradients (talc-carbonate serpentinization) [5]. Though optimal clustering (K = 4) grouped samples into fresh ultramafic Rocks with high Mg-Fe, low SiO₂, a Fe-Ti mineralized zones (3285 samples) enriched in Ti, Fe, Cr, V and hydrothermally altered domains (480 samples) with carbonate and serpentine-rich and, lastly a transitional lithologies (1435 samples) with mixed compositions. The K = 4 choice is consistent with geological facies grouped from samples but also aligned with the PCA geological process finding (Table 1) and, PC1 to PC4 explaining 84.14% of total variance observed. PC1 to PC4 eigenvalues are > 1 [13], whereas the remaining PCs (PC5, PC6…) are below (<) 5% each, hence does not match [18] position, suggesting retaining components presenting > 5% variance each for geological explanation.

This study demonstrates that the deposit follows a model of at least two phases of magmatic fractionation with hydrothermal overprinting. The results of K-means and PCA analyses demonstrate:

1) The dominance of Fe-Ti oxides (Clusters 1 and 4, PC1-PC3), Ni-Cr in the high PC1 zones.

2) The presence of accessory sulfides (Cluster 3, PC1-PC3).

3) The influence of hydrothermal processes (PC2-PC4).

The Ba-Sr pair (PC2) could indicate fluid-enriched zones, similar to Kiruna-type deposits [41]. PC2 could guide the exploration of areas with metallotect potential (fluid corridors).

Priority targets could be Clusters 1 & 4, which are Fe-Ti rich zones, a priority for oxide exploration and exploitation. While cluster 3 may have potential in this huge shear zone (60 km long) for Cu-Zn sulfides, similar to Fe-Ti-P type deposits [38]. But Ni-Co rich clusters should be prioritized for sulfide analyses.