Variant Of Principal Component Analysis Research Articles

Some inequalities contrasting principal component and factor analyses solutions

Principal component analysis (PCA) and factor analysis (FA) are two time-honored dimension reduction methods. In this paper, some inequalities are presented to contrast the parameters’ estimates in PCA and FA. For this reason, we take advantage of the recently established matrix decomposition (MD) formulation of FA. In summary, the resulting inequalities show that (1) FA gives a better fit to a data set than PCA, (2) PCA extracts a larger amount of common “information” than FA, and (3) for each variable, its unique variance in FA is larger than its residual variance in PCA minus the one in FA. The resulting inequalities can be useful to suggest whether PCA or FA should be used for a particular data set. The answers can also be valid for the classic FA formulation not relying on the MD-FA definition, as both “types” FA provide almost equal solutions. Additionally, the inequalities give theoretical explanation of some empirically observed tendencies in PCA and FA solutions, e.g., that the absolute values of PCA loadings tend to be larger than those for FA loadings and that the unique variances in FA tend to be larger than the residual variances of PCA.

Principal Component Analysis Based on Graph Laplacian and Double Sparse Constraints for Feature Selection and Sample Clustering on Multi-View Data

Principal component analysis (PCA) is a widely used method for evaluating low-dimensional data. Some variants of PCA have been proposed to improve the interpretation of the principal components (PCs). One of the most common methods is sparse PCA which aims at finding a sparse basis to improve the interpretability over the dense basis of PCA. However, the performances of these improved methods are still far from satisfactory because the data still contain redundant PCs. In this paper, a novel method called PCA based on graph Laplacian and double sparse constraints (GDSPCA) is proposed to improve the interpretation of the PCs and consider the internal geometry of the data. In detail, GDSPCA utilizes L_2,1-norm and L₁-norm regularization terms simultaneously to enforce the matrix to be sparse by filtering redundant and irrelative PCs, where the L_2,1-norm regularization term can produce row sparsity, while the L₁-norm regularization term can enforce element sparsity. This way, we can make a better interpretation of the new PCs in low-dimensional subspace. Meanwhile, the method of GDSPCA integrates graph Laplacian into PCA to explore the geometric structure hidden in the data. A simple and effective optimization solution is provided. Extensive experiments on multi-view biological data demonstrate the feasibility and effectiveness of the proposed approach.

Unified Process Monitoring Strategy for a Facility Engaged In the Production of Multiple Portfolio of Products

The process monitoring strategies have not kept pace with the development in the production systems. Most of the multivariate statistical process monitoring methods deals with single product portfolio. The current article attempts to devise a unified monitoring strategy for monitoring of multiple products or at least different grades of the same product. A case study from an integrated steel plant producing multiple products has been deliberated to validate the monitoring strategy devised. A comparative evaluation of the unified strategy based on the multigroup variant of principal component analysis (PCA) and the individual strategy based on the conventional PCA was carried out on the basis of three parameters viz. the model fit values, fault detection and the fault diagnosis. In all the three parameters, barring some trifling differences, the unified monitoring strategy seems to replicate the individual strategies well.

Principal components of thermal regimes in mountain river networks

Abstract. Description of thermal regimes in flowing waters is key to understanding physical processes, enhancing predictive abilities, and improving bioassessments. Spatially and temporally sparse data sets, especially in logistically challenging mountain environments, have limited studies on thermal regimes, but inexpensive sensors coupled with crowd-sourced data collection efforts provide efficient means of developing large data sets for robust analyses. Here, thermal regimes are assessed using annual monitoring records compiled from several natural resource agencies in the northwestern United States that spanned a 5-year period (2011–2015) at 226 sites across several contiguous montane river networks. Regimes were summarized with 28 metrics and principal component analysis (PCA) was used to determine those metrics which best explained thermal variation on a reduced set of orthogonal axes. Four principal components (PC) accounted for 93.4 % of the variation in the temperature metrics, with the first PC (49 % of variance) associated with metrics that represented magnitude and variability and the second PC (29 % of variance) associated with metrics representing the length and intensity of the winter season. Another variant of PCA, T-mode analysis, was applied to daily temperature values and revealed two distinct phases of spatial variability – a homogeneous phase during winter when daily temperatures at all sites were <3 ∘C and a heterogeneous phase throughout the year's remainder when variation among sites was more pronounced. Phase transitions occurred in March and November, and coincided with the abatement and onset of subzero air temperatures across the study area. S-mode PCA was conducted on the same matrix of daily temperature values after transposition and indicated that two PCs accounted for 98 % of the temporal variation among sites. The first S-mode PC was responsible for 96.7 % of that variance and correlated with air temperature variation (r=0.92), whereas the second PC accounted for 1.3 % of residual variance and was correlated with discharge (r=0.84). Thermal regimes in these mountain river networks were relatively simple and responded coherently to external forcing factors, so sparse monitoring arrays and small sets of summary metrics may be adequate for their description. PCA provided a computationally efficient means of extracting key information elements from the temperature data set used here and could be applied broadly to facilitate comparisons among more diverse stream types and develop classification schemes for thermal regimes.

A computational analysis of dynamic, multi-organ inflammatory crosstalk induced by endotoxin in mice.

Bacterial lipopolysaccharide (LPS) induces an acute inflammatory response across multiple organs, primarily via Toll-like receptor 4 (TLR4). We sought to define novel aspects of the complex spatiotemporal dynamics of LPS-induced inflammation using computational modeling, with a special focus on the timing of pathological systemic spillover. An analysis of principal drivers of LPS-induced inflammation in the heart, gut, lung, liver, spleen, and kidney to assess organ-specific dynamics, as well as in the plasma (as an assessment of systemic spillover), was carried out using data on 20 protein-level inflammatory mediators measured over 0-48h in both C57BL/6 and TLR4-null mice. Using a suite of computational techniques, including a time-interval variant of Principal Component Analysis, we confirm key roles for cytokines such as tumor necrosis factor-α and interleukin-17A, define a temporal hierarchy of organ-localized inflammation, and infer the point at which organ-localized inflammation spills over systemically. Thus, by employing a systems biology approach, we obtain a novel perspective on the time- and organ-specific components in the propagation of acute systemic inflammation.

Searching for the core variables in principal components analysis

In this article, we introduce a procedure for selecting variables in principal components analysis. It is developed to identify a small subset of the original variables that best explain the principal components through nonparametric relationships. There are usually some noisy uninformative variables in a dataset, and some variables that are strongly related to one another because of their general dependence. The procedure is designed to be used following the satisfactory initial principal components analysis with all variables, and its aim is to help to interpret the underlying structures. We analyze the asymptotic behavior of the method and provide some examples.

Expression analysis of RNA sequencing data from human neural and glial cell lines depends on technical replication and normalization methods

BackgroundThe potential for astrocyte participation in central nervous system recovery is highlighted by in vitro experiments demonstrating their capacity to transdifferentiate into neurons. Understanding astrocyte plasticity could be advanced by comparing astrocytes with stem cells. RNA sequencing (RNA-seq) is ideal for comparing differences across cell types. However, this novel multi-stage process has the potential to introduce unwanted technical variation at several points in the experimental workflow. Quantitative understanding of the contribution of experimental parameters to technical variation would facilitate the design of robust RNA-Seq experiments.ResultsRNA-Seq was used to achieve biological and technical objectives. The biological aspect compared gene expression between normal human fetal-derived astrocytes and human neural stem cells cultured in identical conditions. When differential expression threshold criteria of |log2fold change| > 2 were applied to the data, no significant differences were observed. The technical component quantified variation arising from particular steps in the research pathway, and compared the ability of different normalization methods to reduce unwanted variance. To facilitate this objective, a liberal false discovery rate of 10% and a |log2fold change| > 0.5 were implemented for the differential expression threshold. Data were normalized with RPKM, TMM, and UQS methods using JMP Genomics. The contributions of key replicable experimental parameters (cell lot; library preparation; flow cell) to variance in the data were evaluated using principal variance component analysis. Our analysis showed that, although the variance for every parameter is strongly influenced by the normalization method, the largest contributor to technical variance was library preparation. The ability to detect differentially expressed genes was also affected by normalization; differences were only detected in non-normalized and TMM-normalized data.ConclusionsThe similarity in gene expression between astrocytes and neural stem cells supports the potential for astrocytic transdifferentiation into neurons, and emphasizes the need to evaluate the therapeutic potential of astrocytes for central nervous system damage. The choice of normalization method influences the contributions to experimental variance as well as the outcomes of differential expression analysis. However irrespective of normalization method, our findings illustrate that library preparation contributed the largest component of technical variance.

Optimality and sub-optimality of PCA I: Spiked random matrix models

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Peche showed that the spiked Wishart ensemble exhibits a sharp phase transition asymptotically: when the spike strength is above a critical threshold, it is possible to detect the presence of a spike based on the top eigenvalue, and below the threshold the top eigenvalue provides no information. Such results form the basis of our understanding of when PCA can detect a low-rank signal in the presence of noise. However, under structural assumptions on the spike, not all information is necessarily contained in the spectrum. We study the statistical limits of tests for the presence of a spike, including non-spectral tests. Our results leverage Le Cam's notion of contiguity, and include: i) For the Gaussian Wigner ensemble, we show that PCA achieves the optimal detection threshold for certain natural priors for the spike. ii) For any non-Gaussian Wigner ensemble, PCA is sub-optimal for detection. However, an efficient variant of PCA achieves the optimal threshold (for natural priors) by pre-transforming the matrix entries. iii) For the Gaussian Wishart ensemble, the PCA threshold is optimal for positive spikes (for natural priors) but this is not always the case for negative spikes.

The effect of simple imputations based on four variants of PCA methods on the quantiles of annual rainfall data.

Hydrology-related studies often require complete datasets. However, missing data is an unavoidable reality. In this regard, the imputed data could fulfill the same role as the observed ones, while they are uncertain and just estimated. The aim of this study is to compare the performance of four simple imputation variants derived from the principal component analysis (PCA) for imputing annual total rainfall series obtained from stations located in northeast Algeria. On the other hand, the study focuses on the effects on quantiles of annual rainfall data due to imputations by the former methods. The four variants are probabilistic PCA, expectation maximization PCA, regularized PCA, and singular value decomposition PCA. Annual rainfall data from 30 stations for the period ranging from 1935 to 2004 (69years) are used to generate and impute gaps for four different percentages of missing values (PMV), namely, 10, 20, 30, and 40%. Based on some well-known statistical indices, the results show that the regularized PCA and expectation maximization PCA variants perform better than the other imputation methods considered in this study and result in very good to acceptable predicted quantiles, such as the following: correlation coefficient is equal to 0.97 with 10% of percentage of missing values and 0.66 with 40%; the relative error between observed and predicted quantiles is equal to 4.74% with 10% of percentage of missing values and 3.82% with 40%.

Structure-Aware Principal Component Analysis for Single-Cell RNA-seq Data.

With the emergence of droplet-based technologies, it has now become possible to profile transcriptomes of several thousands of cells in a day. Although such a large single-cell cohort may favor the discovery of cellular heterogeneity, it also brings new challenges in the prediction of minority cell types. Identification of any minority cell type holds a special significance in knowledge discovery. In the analysis of single-cell expression data, the use of principal component analysis (PCA) is surprisingly frequent for dimension reduction. The principal directions obtained from PCA are usually dominated by the major cell types in the concerned tissue. Thus, it is very likely that using a traditional PCA may endanger the discovery of minority populations. To this end, we propose locality-sensitive PCA (LSPCA), a scalable variant of PCA equipped with structure-aware data sampling at its core. Structure-aware sampling provides PCA with a neutral spread of the data, thereby reducing the bias in its principal directions arising from the redundant samples in a data set. We benchmarked the performance of the proposed method on ten publicly available single-cell expression data sets including one very large annotated data set. Results have been compared with traditional PCA and PCA with random sampling. Clustering results on the annotated data sets also show that LSPCA can detect the minority populations with a higher accuracy.

Discrimination of brands of gasoline by using DART-MS and chemometrics

In this study, Direct Analysis in Real Time Mass Spectrometry (DART-MS) was used to analyze four different brands of gasoline collected from five local fuel service stations. Chemometric methods including analysis of variance-principal component analysis (ANOVA-PCA) and partial least squares discriminant analysis (PLS-DA) were applied to classify the gasoline samples based on brand and identify characteristic features for gasoline discrimination. To test the robustness of this method, the gasoline samples were collected once per week for eight weeks and they were analyzed by DART-MS within 24 h of collection and again two weeks after the last sample collection. Both full DART-MS spectra data and selected ion spectra data were used to construct PLS-DA models and the average classification rates of both models were 99.9 ± 0.1% for 100 independent evaluations with bootstrapped Latin partitions and were 100% for a new validation set collected two weeks later with no parametric changes. The major characteristic features corresponded to polymeric compounds in fuel additives which supported our hypothesis that proprietary additives blended in gasoline should be the marker components to distinguish gasoline with different brands. The weathered gasoline samples at different extents, i.e. 30%, 50%, 70%, and 90%, were studied and compared with un-weathered samples. The polymeric compound patterns in gasoline were found to be brand dependent and weathering extent dependent and the patterns for the weathered gasoline with different brands were still significantly different. DART-MS is demonstrated as a promising tool for the discrimination of brands of gasoline.

Characterizing the 3D structure and dynamics of chromosomes and proteins in a common contact matrix framework.

Conformational ensembles of biopolymers, whether proteins or chromosomes, can be described using contact matrices. Principal component analysis (PCA) on the contact data has been used to interrogate both protein and chromosome structures and/or dynamics. However, as these fields have developed separately, variants of PCA have emerged. Previously, a variant we hereby term Implicit-PCA (I-PCA) has been applied to chromosome contact matrices and revealed the spatial segregation of active and inactive chromatin. Separately, Explicit-PCA (E-PCA) has previously been applied to proteins and characterized their correlated structure fluctuations. Here, we swapped analysis methods (I-PCA and E-PCA), applying each to a different biopolymer type (chromosome or protein) than the one for which they were initially developed. We find that applying E-PCA to chromosome distance matrices derived from microscopy data can reveal the dominant motion (concerted fluctuation) of these chromosomes. Further, by applying E-PCA to Hi-C data across the human blood cell lineage, we isolated the aspects of chromosome structure that most strongly differentiate cell types. Conversely, when we applied I-PCA to simulation snapshots of proteins, the major component reported the consensus features of the structure, making this a promising approach for future analysis of semi-structured proteins.

On Optimal Allocation of Treatment/Condition Variance in Principal Component Analysis

The allocation of a (treatment) condition-effect on the wrong principal component (misallocation of variance) in principal component analysis (PCA) has been addressed in research on event-related potentials of the electroencephalogram. However, the correct allocation of condition-effects on PCA components might be relevant in several domains of research. The present paper investigates whether different loading patterns at each condition-level are a basis for an optimal allocation of between-condition variance on principal components. It turns out that a similar loading shape at each condition-level is a necessary condition for an optimal allocation of between-condition variance, whereas a similar loading magnitude is not necessary.

Rum classification using fingerprinting analysis of volatile fraction by headspace solid phase microextraction coupled to gas chromatography-mass spectrometry

In this study, targeted and untargeted analyses based on headspace solid phase microextraction coupled to gas chromatography-mass spectrometry (HS-SPME-GC-MS) method were developed for classifying 33 different commercial rums. Targeted analysis showed correlation of ethyl acetate and ethyl esters of carboxylic acids with aging when rums of the same brand were studied, but presented certain limitations when the comparison was carried out between different brands. To overcome these limitations, untargeted strategies based on unsupervised treatments, such as hierarchical cluster analysis (HCA) and principal component analysis (PCA), as well as supervised methods, such as linear discriminant analysis (LDA) were applied. HCA allowed distinguishing main groups (with and without additives), while the PCA method indicated 40 ions corresponding to 13 discriminant compounds as relevant chemical descriptors for the correct rum classification (PCA variance of 88%). The compounds were confirmed based on the combination of retention indexes and low and high-resolution mass spectrometry (HRMS). Using the obtained results, LDA was carried out for the analytical discrimination of the remaining rums based on manufacturing country, raw material type, distillation method, wood barrel type and aging period and 94%, 91%, 92%, 95% and 94% of rums, respectively, were correctly classified. The proposed methodology has led to a robust analytical strategy for the classification of rums as a function of different parameters depending on the rum production process.

Evaluation of batch effect elimination using quality control replicates in LC-MS metabolite profiling

Systematic variation of the instrument's response both within- and between-batches is frequently observed in untarget LC-MS metabolomics involving the analysis of a large number of samples. The so-called batch effect decreases the statistical power and has a negative impact on repeatability and reproducibility of the results. As there is no standard way of assessing or correcting LC-MS batch effects and there is no single method providing optimal results in all situations, the selection of the optimal approach is not trivial.This work explores the effectiveness of a set of tools for batch effect assessment. Qualitative tools include the monitoring of spiked internal standards, principal component analysis and hierarchical cluster analysis. Quantitative tools comprise the distribution of RSDQC values, the median Pearson correlation coefficient in QCs, the ratio of random features in QCs using the runs test, as well as multivariate tools such as the δ-statistic, Silhouette plots, Principal Variance Component Analysis and the expected technical variation in the prediction. Results show that qualitative and quantitative approaches are complementary and that by limiting the analysis to QCs the power to detect and evaluate both within and between batch effects is increased. Besides, the graphical integration of outputs from multiple quantitative tools facilitates the evaluation of batch effects and it is proposed as a straightforward way for comparing and tailoring batch effect elimination approaches.

Feature Learning With Matrix Factorization Applied to Acoustic Scene Classification

In this paper, we study the usefulness of various matrix factorization methods for learning features to be used for the specific acoustic scene classification ASC problem. A common way of addressing ASC has been to engineer features capable of capturing the specificities of acoustic environments. Instead, we show that better representations of the scenes can be automatically learned from time-frequency representations using matrix factorization techniques. We mainly focus on extensions including sparse, kernel-based, convolutive and a novel supervised dictionary learning variant of principal component analysis and nonnegative matrix factorization. An experimental evaluation is performed on two of the largest ASC datasets available in order to compare and discuss the usefulness of these methods for the task. We show that the unsupervised learning methods provide better representations of acoustic scenes than the best conventional hand-crafted features on both datasets. Furthermore, the introduction of a novel nonnegative supervised matrix factorization model and deep neural networks trained on spectrograms, allow us to reach further improvements.

Maximin distance based band selection for endmember extraction in hyperspectral images using simplex growing algorithm

With the fast growing technologies in the field of remote sensing, hyperspectral image analysis has made a great breakthrough. It provides accurate and detailed information of objects in the image when compared to any other remotely sensed data. It is possible because of its high redundancy in nature. But this redundancy in hyperspectral images leads to high computational complexity in their analysis. Hence Dimensionality Reduction (DR) is a significant task in all hyperspectral image processing. DR can be achieved either by feature extraction or feature selection. Feature selection or Band selection is adopted in this paper because of no compromise in original data. Despite many algorithms that exist for band selection, this paper proposes a new concept of Maximin distance algorithm using Spectral Angle Distance (SAD) as distance measure for band selection. Virtual Dimensionality (VD) is used to provide the number of bands to be selected because it has been proved to be reliable estimate. Simplex Growing Algorithm (SGA) is deployed for endmember extraction in the experiment work. In order to evaluate the performance of the proposed band selection algorithm, the Spectral Angle Distance (SAD) and Spectral Similarity Value (SSV) are used as measures. The efficacy of our proposed algorithm has been proved from experimental results in comparison with Constrained Band Selection (CBS), Similarity Based Band Selection (SBBS), Clustering Based Band Selection (CBBS), Uniform Band Selection (UBS), Minimum Variance Principal Component Analysis (MVPCA) and Exemplar Component Analysis (ECA) and Firefly Algorithm Based Band Selection (FABBS).

105 NEAR-INFRARED SPECTROSCOPY AND AQUAPHOTOMICS ANALYSIS OF SERUM FROM MARES EXPOSED TO THE FUNGAL MYCOTOXIN ZEARALENONE

Aquaphotomics is a branch of near-infrared (NIR) spectroscopy in which bond vibrations from organic molecules and water create unique spectral absorbance patterns to profile complex aqueous mixtures. Aquaphotomics has been shown to detect virus infected soybean plants from extracts, classify probiotic bacteria, and detect contamination of aquatic ecosystems. We have used aquaphotomics to characterise serum profiles from horses in various phases of the reproductive cycle such as oestrus and diestrus. Because serum is a complex solution of biomolecules, various modes of serum processing (e.g. large protein removal for proteomics or mass spectrometry) may provide different NIR spectral profiles for quantitative analysis of specific compounds or their effects. Zearalenone is a fungal mycotoxin that may have estrogenic potential in mares and is found in feedstuffs. The objectives of this study were to (1) establish NIR spectral profiles of serum and protein-precipitated serum (PPS) collected at peak oestrus from mares; (2) determine if NIR profiles correlate and quantify E2 concentrations in serum or PPS; and (3) determine if NIR can detect differences in serum chemistry of zearalenone-treated mares. Mares were fed zearalenone daily at low (2 mg, 2 mares, 5 cycles) and high (8 mg, 1 mare, 3 cycles) concentrations, plus control (0 mg, 1 mare, 3 cycles). Oestrus cycles were monitored by ultrasound and serum hormone analysis. Serum collected at peak oestrus had E2 values determined by radioimmunoassay (range 0.02–16.87 pg mL−1). Protein precipitated serum had high and medium MW proteins removed with acetonitrile. NIR spectra, collected in triplicate with a 1 mm quartz cuvette and ASD FieldSpec®3 (Boulder, CO, USA), were pre-treated with a Savitsky-Golay 1st derivative for inspection of spectral features, principal component analysis, and partial least-squares regression (PLS) to investigate spectral correlations to E2 concentrations and zearalenone treatment effects. The NIR profiles contrasting serum and PPS at oestrus had distinct spectral features differing significantly at 1320, 1491, 1536, and 1566 nm in the NIR water spectrum, and principal component-1 accounted for 97% of principal component analysis variance in spectra from serum compared to PPS. In the PLS cross-validation linear fit regression model, NIR predicted E2 concentrations (validated by RIA) from serum (slope = 0.89, SECV = 1.92, R2 = 0.81, 3 factors), and from PPS (slope = 0.61; SECV = 1.84, R2 = 0.76, 4 factors). Spectral predictions were poorest at the low E2 threshold, E2 = 0.02 pg mL−1. The PLS model validation metrics of zearalenone dose-dependent effects were also evident in serum (slope = 0.88, SECV = 1.26, R2 = 0.86) and in PPS (slope = 0.67, SECV = 1.96, R2 = 0.66). Correlations of quantitative values of E2 and zearalenone were both better for spectra taken of serum compared to PPS. In summary, NIR spectral profiles of serum chemistry may be able to map E2 hormone levels during reproductive cycling, and these spectra may also have correlations that reflect exposure of mares to estrogenic toxins such as zearalenone. Research was supported by USDA-ARS Biophotonics grant #58-6402-3-018.

Geochemical investigation of stream sediments from the nlonako area; littoral, Cameroon: implications for Au, Ag, Cu, Pb and Zn mineralization potentials

Nlonako area belongs to Cameroon Volcanic Line. To determine the mineralization potentials of the area, stream sediment survey and geochemistry were carried out. The results show weak anomalies in Gold and Silver with threshold values of 0.001 and 0.073 respectively. Copper, Lead and Zinc have some relatively high values which are 690ppm, 182ppm and 378ppm with mean values statistically calculated to be 73.90, 46.51 and 198.58 respectively. The data analyzed using multivariate statistical methods yielded 5 factors from Principal Component Analysis (PCA). These five factors are; Factor 1 (Ce, La, Nb, Y), Factor 2 (W, Mo, Sr, As, Cd, Ni), Factor 3 (Pb, Sn, Zn, Sb), Factor 4 (Au, Ag, Cu) and Factor 5 (Cr, Co, Bi). These factors point mostly to a possible sulphide mineralization. Gold shows high correlation with Ag and Cu while Y correlates more highly and positively with Ce and La. There is a relatively high input of the light rare-earth elements which form the highest factor (34.363%) of the total PCA variance and possibly points to a granitic source rock. The existence of mafic–ultramafic igneous rocks in the study area underlies high correlations between Cr and Co and other factors gotten from PCA.

Geographically Weighted Principal Components Analysis to assess diffuse pollution sources of soil heavy metal: Application to rough mountain areas in Northwest Spain

Heavy metal pollution can result in the degradation of the soil, air and water bodies' quality affecting the health of all living organism. We analyze the spatial distribution of the concentrations of soil heavy metal and relationship with natural or anthropogenic origin. The analysis was performed in Principality of Asturias (mountain region of NW of Spain), where soil heavy metal pollution has become a severe problem. First, a standard Principal Components Analysis (PCA) was performed over a population of 334 soil samples to identify the sources of fourteen heavy metal and metalloids (Ag, As, Ba, Hg, Cd, Co, Cr, Cu, Mn, Mo, Ni, Pb, Sb, Zn). Due to the high geological heterogeneity of the territory, the PCA analysis was improved using a variant of PCA known as Geographically Weighted Principal Components Analysis (GWPCA). The first six principal components in a standard PCA account for about 57% of soil heavy metal variability but when GWPCA is performed this figure increases to >80% in some areas. We conclude that GWPC1 corresponds to a geogenetic component with changing winning variables adapted to the geological characteristics of the territory (lithology and mining), while GWPC2 corresponds to a factor related to atmospheric pollution including heavy metal released from vegetation cover via wildfires.