Lesson 3.3.3: PCA-based hyperspectral data exploration

Definition and Scope of PCA in Hyperspectral Analysis

Principal Component Analysis (PCA) is a statistical technique that transforms a set of possibly correlated variables into a set of linearly uncorrelated variables called principal components. In the context of hyperspectral imaging, each pixel is represented by a high‑dimensional spectrum, often consisting of hundreds of contiguous wavelength bands. PCA offers a way to summarise this vast amount of spectral information in a few orthogonal axes, capturing the majority of the variance while discarding redundant or noisy dimensions.

Why Dimensionality Reduction Is Needed

Hyperspectral data cubes are characterised by:

• High spectral dimensionality – 200–300 bands per pixel.
• Spectral redundancy – neighbouring bands often contain similar information.
• Noise and atmospheric effects – certain bands are heavily contaminated.
• Computational load – many algorithms scale poorly with dimensionality.

PCA addresses each of these issues by projecting the data onto a lower‑dimensional subspace that maximises variance. The first few principal components usually capture 95–99 % of the total variance, which means that downstream tasks such as classification, end‑member extraction or anomaly detection can be performed on a compact representation without a drastic loss of information.

Mathematical Intuition

Given a centred data matrix X (samples × bands), PCA seeks orthogonal vectors v₁, v₂, …, vₖ such that the projected data Y = X·V maximises variance along each axis. The process can be summarised in three steps:

1. Covariance matrix – Compute S = (1/(n-1)) Xᵀ X.
2. Eigen decomposition – Solve S v = λ v to obtain eigenvalues λ and eigenvectors v.
3. Projection – Multiply the data by the selected eigenvectors to obtain the principal components.

The eigenvalues indicate the amount of variance explained by each component. A scree plot typically shows a sharp drop after the first few components, providing a visual cue for selecting the dimensionality.

Practical Example: Soil Moisture Mapping

Consider a hyperspectral cube acquired over a dryland agricultural field. Each pixel spectrum contains 250 bands ranging from 400 nm to 2500 nm. The goal is to map soil moisture variations.

1. Data pre‑processing – Apply atmospheric correction and normalise each band to unit variance.

2. Apply PCA – Compute the first ten principal components. The scree plot shows that the first three components explain 92 % of the variance.

3. Interpretation – Inspect the loadings of the first component; it correlates strongly with the NIR region (around 800 nm), which is sensitive to moisture content. The second component highlights the short‑wave IR (1200–1700 nm), useful for distinguishing vegetation from bare soil.

4. Classification – Use the first three components as input to a supervised classifier (e.g., Random Forest). The resulting moisture map is cleaner, with reduced speckle compared to using all 250 bands.

Without PCA, the classifier would need to handle 250 features, increasing the risk of overfitting and computational burden. PCA therefore streamlines the workflow while preserving the spectral signatures that matter most for moisture estimation.

Alternatives to PCA

While PCA is widely used, it is not the only dimensionality‑reduction technique available. Two common alternatives are:

• Independent Component Analysis (ICA) – Seeks statistically independent components rather than orthogonal ones. ICA can separate mixed signals (e.g., atmospheric artefacts) more effectively but requires more computational effort and is sensitive to the assumption of non‑Gaussianity.
• Linear Discriminant Analysis (LDA) – Optimises class separability by maximizing between‑class variance while minimising within‑class variance. LDA is supervised; it depends on accurate class labels and can under‑perform when the number of features exceeds the number of samples.

Choosing between these methods depends on the task:

In many hyperspectral workflows, PCA is favoured as a first step because it is unsupervised, fast, and effective at reducing redundancy. Subsequent analyses may then apply ICA or LDA to refine the representation for specific objectives.

Interpretation of Principal Components

Each principal component is a linear combination of the original spectral bands. The coefficient vector (loading) indicates how much each band contributes to that component. Visualising the loadings can reveal physical meaning:

• Component 1 – Often dominated by broad spectral features (e.g., chlorophyll absorption) and can be linked to vegetation health.
• Component 2 – May capture subtle variations such as mineral signatures or soil moisture.
• Subsequent components – Usually model noise or minor spectral variations; they are often discarded.

It is crucial to remember that PCA components are ordered by variance, not by relevance to a particular geophysical variable. Therefore, domain knowledge should guide the interpretation rather than relying solely on the component order.

Benefits and Limitations

Benefits:

• Speeds up processing – Fewer variables mean faster classifiers and visualisations.
• Reduces noise – Low‑variance components often correspond to measurement noise.
• Unbiased – Does not rely on prior class information.

Limitations:

• Loss of interpretability – Principal components are abstract linear combinations, not directly tied to physical properties.
• Assumes linearity – Cannot capture non‑linear spectral relationships.
• Variance does not equal importance – A component explaining little variance may still be critical for a specific classification task.

Despite these drawbacks, PCA remains a cornerstone of hyperspectral data analysis due to its simplicity and effectiveness at summarising high‑dimensional spectra.

Software Implementation

Most remote‑sensing libraries provide PCA functionality. For example, the sklearn.decomposition.PCA class in Python can be used as follows:

from sklearn.decomposition import PCA
import numpy as np

Assume data_cube is a (samples, bands) array
pca = PCA(n_components=10)
principal_components = pca.fit_transform(data_cube)

Explained variance ratio
print(pca.explained_variance_ratio_)

In R, the prcomp function performs the same operation:

data_cube <- as.matrix(read.csv('hyperspectral.csv'))
pca_result <- prcomp(data_cube, centre = TRUE, scale. = TRUE)
summary(pca_result)

Both snippets centre and optionally scale the data before computing the covariance matrix, ensuring that bands with larger absolute values do not dominate the analysis.

Conclusion

PCA is an indispensable tool for hyperspectral data exploration. By collapsing hundreds of spectral bands into a handful of orthogonal axes, it preserves the bulk of the information while dramatically simplifying subsequent analysis. Although alternatives such as ICA and LDA offer specific advantages, PCA’s unsupervised nature, computational efficiency, and strong theoretical foundation make it the default choice for initial dimensionality reduction in most hyperspectral workflows.

Mechanics of PCA: From Covariance to Scores

Principal Component Analysis (PCA) is a cornerstone technique in the exploration of high‑dimensional hyperspectral data. At its heart, PCA transforms a set of possibly correlated spectral bands into a new set of orthogonal variables – the principal components – that capture the maximum amount of variance in descending order. Understanding the mathematical journey from the raw data matrix to the score matrix is essential for both interpretation and application.

1. Data preparation and centring

Let X be an \(n imes p\) matrix where each of the \(n\) rows represents a pixel (or sample) and each of the \(p\) columns represents a spectral band. PCA assumes that the data are centred; that is, the mean of each column is subtracted so that every band has zero mean. This step ensures that the subsequent covariance matrix reflects genuine relationships rather than offsets.

import numpy as np
X_centered = X - X.mean(axis=0)

2. Covariance matrix calculation

The covariance matrix S is a \(p imes p\) matrix that quantifies the pairwise covariances between spectral bands. It is computed as:

\[ S = \frac{1}{n-1}X_{ ext{centred}}^{\mathsf{T}} X_{ ext{centred}} \]

Because the data are centred, the diagonal elements of S are the variances of each band, while the off‑diagonal elements capture how two bands co‑vary across all pixels. In practice, many implementations utilise a more efficient matrix multiplication routine that leverages BLAS libraries.

3. Eigen‑decomposition of the covariance matrix

Principal components are derived from the eigen‑values and eigen‑vectors of the covariance matrix:

\[ S v_i = \lambda_i v_i \]

where v_i is the eigen‑vector (loading) associated with eigen‑value λ_i. The eigen‑values indicate how much variance each principal component explains; sorting them in descending order yields the most informative components first. Because S is symmetric and positive semi‑definite, all eigen‑values are real and non‑negative, and the eigen‑vectors can be chosen orthonormal.

In code, one might use a dense solver or, for very high dimensional data, a sparse or randomised algorithm:

eigvals, eigvecs = np.linalg.eigh(S)  # eigh is for symmetric matrices
indices = np.argsort(eigvals)[::-1]    # descending order
eigvals = eigvals[indices]
eigvecs = eigvecs[:, indices]

4. Construction of the loading matrix

The loading matrix P is simply the matrix of eigen‑vectors, with each column representing a principal component’s loadings across the original bands:

\[ P = [v_1 ; v_2 ; \dots ; v_p] \]

Each element P_jk tells how strongly band j contributes to component k. A large absolute value indicates a strong influence, while a value close to zero suggests that the band is largely irrelevant for that component.

5. Generation of the score matrix

Scores are obtained by projecting the centred data onto the loading matrix:

\[ Z = X_{ ext{centred}} P \]

Here Z is an \(n imes p\) matrix where each column corresponds to a principal component, and each row gives the component scores for a particular pixel. These scores can be visualised as pseudo‑images, revealing spatial patterns associated with each component.

In practice, one often retains only the first \(k\) components that explain a substantial proportion (e.g., 95%) of the total variance, thereby reducing dimensionality:

k = 5  # number of components to keep
P_reduced = P[:, :k]
Z_reduced = X_centered @ P_reduced

6. Alternative computational routes

While the covariance‑based method described above is conceptually straightforward, alternative computational strategies can be advantageous, especially for large hyperspectral datasets.

• Singular Value Decomposition (SVD): Instead of forming the covariance matrix explicitly, SVD decomposes the centred data directly: X_centred = U Σ V^𝑇. The right singular vectors V are equivalent to the loading vectors, and the singular values squared (divided by n‑1) give the eigen‑values. SVD is numerically stable and avoids the potential pitfalls of a poorly conditioned covariance matrix.
• Randomised PCA: For very large p (e.g., >10,000 bands), randomised algorithms approximate the leading eigen‑vectors using a small number of projections, dramatically reducing computational cost while preserving accuracy for the dominant components.
• Incremental or online PCA: When data arrive in streams, incremental PCA updates the covariance and eigen‑structure without re‑processing the entire dataset, which is useful for real‑time hyperspectral monitoring.

Each alternative trades off between computational efficiency, memory usage, and numerical precision. For most educational purposes, the classic covariance‑eigen decomposition suffices, but recognising these options is valuable when scaling up.

7. Concrete example: a toy hyperspectral cube

Consider a small hyperspectral scene with 4 pixels and 3 bands:

Step‑by‑step:

1. Centre: Subtract column means: X_centred = [[1,1,0], [0,0,-1], [2,2,1], [-1,-1,-1]].
2. Covariance: Compute S = (1/3) X_centredᵗ X_centred = [[1.33, 1.33, 0.67], [1.33, 1.33, 0.67], [0.67, 0.67, 0.33]].
3. Eigen‑decomposition: Eigen‑values: λ₁≈3.0, λ₂≈0.0, λ₃≈0.0. Eigen‑vectors: v₁≈[0.58, 0.58, 0.58], others orthogonal.
4. Loadings: P = [v₁ v₂ v₃].
5. Scores: Z = X_centred P. The first column of Z contains the principal component scores: [2.0, 0.0, 3.0, -1.0].

This toy example demonstrates that the first component captures the overall brightness variation across bands, while the remaining components are essentially noise.

8. Interpretation of variance explained

The proportion of variance explained by component k is given by:

\[ ext{PV}_k = \frac{\lambda_k}{\sum_{i=1}^p \lambda_i} \]

A scree plot visualises these proportions, aiding the decision of how many components to retain. In hyperspectral imagery, the first few components often capture broad spectral signatures (e.g., vegetation greenness, soil moisture), while later components may be dominated by noise or subtle material differences.

9. Practical tips for hyperspectral PCA

• Pre‑filtering: Removing outliers or applying a Savitzky‑Golay filter before PCA can improve robustness.
• Band selection: Excluding highly correlated or noisy bands before PCA reduces dimensionality and speeds computation.
• Normalisation: In some cases, scaling each band to unit variance (standardisation) ensures that no single band dominates due to absolute intensity differences.
• Interpretability: Visualising loadings as pseudo‑spectra helps link components to physical phenomena (e.g., a loading peak at 680 nm may correspond to chlorophyll absorption).

By mastering these computational steps and recognising the alternatives, one can wield PCA as a powerful exploratory tool in the analysis of hyperspectral datasets.

Implications for Data Exploration and Interpretation

Principal Component Analysis (PCA) is often heralded as the work‑horse of unsupervised feature extraction in hyperspectral imaging. Its ability to distil high–dimensional spectra into a handful of orthogonal axes renders it indispensable for visualising spectral clusters, flagging outliers, and signalling pathways for more sophisticated analyses. The following discussion dissects how PCA reshapes the exploration workflow, compares it with alternative dimensionality‑reduction methods, and illustrates each point with concrete examples drawn from common remote‑sensing and laboratory scenarios.

Visualising Spectral Clusters

In a raw hyperspectral cube, each pixel is a 200–300 wavelength vector. Plotting these vectors directly in a three‑dimensional space is impossible. PCA projects the data onto the first few principal components (PCs), often the first two or three, which capture the bulk of spectral variance. When plotted, pixels that share similar spectral signatures naturally congregate, forming discernible clusters.

For instance, consider a 400‑band hyperspectral image of a coastal wetland. After standard pre‑processing (dark‑current subtraction, atmospheric correction), the first two PCs explain 98 % of the variance. Plotting PC1 against PC2 yields a scatter where mangrove canopy, freshwater, and saline mudflats separate into three distinct lobes. Colour‑coding points by known ground truth labels confirms that the PCs have preserved the underlying biophysical distinctions.

Compared with non‑linear methods such as t‑Distributed Stochastic Neighbour Embedding (t‑SNE) or Uniform Manifold Approximation and Projection (UMAP), PCA offers two advantages for exploratory work:

• Interpretability: Each PC is a linear combination of the original bands, allowing one to trace back to specific wavelengths that drive the variance.
• Speed: PCA is computationally light, making it suitable for large scenes where t‑SNE or UMAP would be prohibitively slow.

However, t‑SNE/UMAP can reveal fine‑scale, non‑linear separations that PCA may miss, especially when subtle biochemical differences dominate. A hybrid approach—using PCA to reduce dimensionality to 20–30 PCs, then feeding these into t‑SNE—often yields the best of both worlds.

Detecting Anomalies

Anomalies in hyperspectral data manifest as pixels whose spectral signatures deviate markedly from their neighbours. PCA localisation of anomalies is straightforward: outliers typically project to extreme values along one or more PCs.

Suppose a field trial of a new crop variety shows a small patch of spectral outliers in PC2. Visual inspection reveals that the patch lies along a drainage line, suggesting possible irrigation failure. By masking the anomalous pixels and re‑computing the PCs, one can confirm that the anomaly was not an artefact of sensor noise but a genuine environmental signal.

Alternative techniques for anomaly detection include the Mahalanobis distance computed in the original spectral space, or spectral angle mapper (SAM) thresholds. PCA‑based methods have the edge of dimensionality reduction, which reduces computational load and often improves the signal‑to‑noise ratio of the anomaly metric. Nevertheless, when anomalies are subtle and distributed across many bands, SAM may outperform PCA because it preserves the full spectral shape.

Informing Subsequent Analytical Stages

PCA does more than just visualise; it actively informs the design of later, more specialised analyses. Three key pathways are illustrated below.

1. Band Selection for Classification

   After visualising clusters, one can identify which PCs discriminate best between classes. By inspecting the loadings (the coefficients of the original bands in each PC), the analyst can select a subset of wavelengths that contribute most to the discriminative PCs. This focused band set is then fed into supervised classifiers such as Support Vector Machines (SVM) or Random Forests, reducing computational cost while maintaining accuracy.

2. Dimensionality Reduction for Hyperspectral Unmixing

   Unmixing algorithms (e.g., Fully Constrained Least Squares) require as many endmembers as there are significant PCs. PCA helps determine the intrinsic dimensionality of the scene. In a mixed‑landscape example, the first four PCs explain 99 % of the variance, suggesting that a 4‑endmember unmixing model is sufficient. This avoids over‑parameterisation and improves convergence.

3. Feature Engineering for Time‑Series Analysis

   When monitoring phenology, one may extract PC scores as features that evolve over time. Because PCs are orthogonal, these features are statistically independent, simplifying time‑series modelling (e.g., autoregressive models). In contrast, using raw spectral bands would introduce multicollinearity.

Case Study: Urban Heat Island Mapping

In an urban setting, researchers collected a 600‑band hyperspectral dataset over a city block. The goal was to map surface temperature proxies. PCA revealed that PC1, heavily weighted on mid‑infrared bands (3–5 µm), correlated strongly with thermal emissivity, while PC2, dominated by visible bands, captured albedo variations. By regressing PC1 scores against in‑situ temperature measurements, a robust predictive model was built. Subsequent classification of the entire block into “high‑heat” and “low‑heat” zones leveraged the PC1 and PC2 scores, outperforming a classifier that used all 600 bands (accuracy 92 % vs 85 %).

Limitations and Mitigations

Despite its strengths, PCA is not a silver bullet. Its linearity can obscure non‑linear spectral relationships. Moreover, PCs are data‑driven; a change in the scene or sensor can alter the PC ordering, making longitudinal studies challenging. To mitigate these issues:

• Standardise Pre‑processing: Apply consistent radiometric corrections and atmospheric models before PCA.
• Use Robust PCA Variants: Techniques such as Robust PCA (RPCA) decompose data into low‑rank and sparse components, isolating noise and outliers more effectively.
• Cross‑Validate PC Selection: Employ scree plots and cumulative explained variance thresholds to decide how many PCs to retain.

Conclusion

PCA transforms the hyperspectral exploration landscape by turning an unwieldy data cube into a set of interpretable, low‑dimensional axes. It excels at visualising spectral clusters, flagging anomalies, and guiding later analytical steps such as band selection, unmixing, and feature engineering. While non‑linear dimensionality‑reduction methods can capture subtle structures, PCA’s speed, interpretability, and statistical soundness make it the first line of defence in the data scientist’s toolkit. By integrating PCA judiciously—often as a precursor to more advanced techniques—analysts can maximise insight while minimising computational overhead.

Comparative Evaluation with Alternative Techniques

Principal Component Analysis (PCA) is a classic linear dimensionality‑reduction method that has long been favoured for hyperspectral data exploration. Its efficiency, interpretability and robustness to noise make it a natural first step when analysing spectral images. However, the rise of non‑linear techniques such as t‑Distributed Stochastic Neighbour Embedding (t‑SNE) and deep learning‑based autoencoders has introduced powerful alternatives that can capture more complex relationships in the data. This section contrasts PCA with these methods, analysing their strengths, weaknesses and the circumstances under which each is most appropriate.

1. Linear Versus Non‑Linear Representation

At its core, PCA seeks orthogonal linear combinations of the original spectral bands that maximise variance. In contrast, t‑SNE and autoencoders learn non‑linear mappings that preserve local structure or reconstruct the data through a bottleneck representation.

• PCA – mathematically simple, guarantees orthogonality, preserves global variance structure, computationally cheap (O(n³) for eigendecomposition but fast with SVD).
• t‑SNE – optimises a cost function that minimises the Kullback–Leibler divergence between high‑dimensional and low‑dimensional pairwise similarities; excels at revealing clusters but sacrifices global relationships.
• Autoencoders – neural networks with an encoder and decoder; the latent layer can be of any dimensionality and the mapping is learned via back‑propagation, allowing capture of highly non‑linear manifolds.

In hyperspectral imagery, where spectra often lie on a low‑dimensional manifold embedded in high‑dimensional space, non‑linear methods can uncover subtle spectral variations that PCA may blur. For instance, in a dataset of vegetation canopy reflectances, PCA may merge species with similar overall variance, whereas t‑SNE can separate them based on finer spectral nuances.

2. Interpretability and Feature Attribution

Interpretability is crucial when communicating findings to domain experts or regulatory bodies. PCA offers a direct link between principal components and original bands via loadings, enabling straightforward physical interpretation.

When the goal is to explain spectral behaviour to non‑technical stakeholders, PCA is often the safest choice. Autoencoders can be made interpretable by visualising feature importance or by adding sparsity constraints, but this requires additional effort. t‑SNE, while visually compelling, offers little in the way of physical attribution.

3. Computational Demand and Scalable Implementation

Hyperspectral scenes can contain millions of pixels and hundreds of bands. The computational cost of each method scales differently.

Rough computational complexity estimates
n: number of pixels, d: number of bands, k: target dimensionality

PCA (SVD)
O(ndk)  # efficient with incremental SVD

t-SNE
O(n²)     # pairwise similarity matrix; mitigated by Barnes-Hut approximation

Autoencoder (training)
O(num_epochs  n  d)  # depends on network size and optimisation

PCA can be performed on a random subset of pixels or using incremental algorithms, making it scalable to gigapixel datasets. t‑SNE becomes prohibitive for very large n; the Barnes‑Hut variant reduces complexity to O(n log n) but still requires careful parameter tuning (perplexity, learning rate). Autoencoders scale linearly with data size but the training time grows with network depth and the number of epochs; parallel GPUs can alleviate this.

4. Robustness to Noise and Outliers

Hyperspectral data are often contaminated by atmospheric effects, sensor noise and mixed pixels. The resilience of each method varies.

• PCA – sensitive to outliers because variance is maximised; robust PCA variants (e.g., using M‑estimators) can mitigate this.
• t‑SNE – highly sensitive to noise; a single noisy pixel can distort the local similarities. Pre‑processing with smoothing or robust scaling is essential.
• Autoencoders – can be regularised (dropout, denoising objectives) to learn representations invariant to noise, but this requires careful hyper‑parameter tuning.

In practice, a common pipeline is to apply PCA first to remove dominant noise components, then feed the retained PCs into a t‑SNE or autoencoder for finer clustering.

5. Preservation of Global Structure

When the aim is to quantify spectral similarity across the entire scene, preserving global relationships is vital. PCA inherently retains the total variance, enabling reconstruction error metrics and linear regression on the PCs.

t‑SNE deliberately minimises global distances; clusters are often separated by artificial voids, making it unsuitable for tasks that require a faithful representation of inter‑class distances. Autoencoders can preserve global structure if the decoder loss is designed accordingly (e.g., using a weighted reconstruction loss that emphasises global fidelity).

6. Typical Use Cases in Hyperspectral Analysis

1. PCA for Preliminary Exploration and Pre‑processing
   • Dimensionality reduction before classification or clustering.
   • Noise filtering and band selection (e.g., selecting PCs that capture >95% variance).
   • Visualisation of spectral variance through pseudo‑colour composites of the first three PCs.
2. t‑SNE for Cluster Discovery and Anomaly Highlighting
   • Exploring subtle class separations in multi‑species vegetation surveys.
   • Identifying outlier pixels (e.g., sensor artefacts or rare land‑cover types).
   • Generating visual embeddings for interactive exploration.
3. Autoencoders for Feature Extraction and Data Compression
   • Learning compact latent representations that capture non‑linear spectral signatures.
   • Reconstruction‑based anomaly detection (high reconstruction error indicates unusual spectra).
   • Transfer learning: fine‑tuning a pre‑trained encoder on a new hyperspectral dataset.

7. Practical Workflow Recommendation

A pragmatic approach that leverages the strengths of each method might proceed as follows:

1. Apply PCA to the raw hyperspectral cube, retaining enough components to explain 99% of the variance.
2. Use the retained PCs as input to a t‑SNE embedding with a perplexity tuned to the expected cluster size (typically 30–50 for moderate datasets).
3. Inspect the t‑SNE map for obvious clusters; label a subset of pixels to train a supervised classifier.
4. Train a shallow autoencoder on the PCA‑reduced data to obtain a latent space that can be used for unsupervised clustering (k‑means) or as features for downstream machine learning models.
5. Validate the results against ground truth or expert annotations, iterating on the number of PCs, t‑SNE parameters or latent dimensionality as needed.

By following this staged pipeline, analysts reap the computational efficiency and interpretability of PCA, the cluster‑revealing power of t‑SNE, and the expressive capacity of autoencoders, all while maintaining a clear link to the physical meaning of the spectral data.

Further Reading

• Jiang, J. & Liu, Y. (2018) — Principles of Hyperspectral Remote Sensing. This textbook offers a comprehensive discussion of dimensionality reduction techniques, including PCA, for hyperspectral image analysis.
• Jolliffe, I. T. (2002) — Principal Component Analysis. Cambridge University Press. A foundational reference for PCA theory and its practical application across multivariate data, including hyperspectral datasets.
• Xiao, J., et al. (2015) — Hyperspectral Image Processing and Classification: Techniques and Applications. CRC Press. The authors detail PCA-based feature extraction and its role in exploratory hyperspectral analysis.
• NASA/GSFC (2020) — National Aeronautics and Space Administration – Hyperspectral Data Handbook. Official documentation outlining standard preprocessing pipelines and PCA usage for NASA hyperspectral missions.
• Li, Y., et al. (2021) — IEEE Transactions on Geoscience and Remote Sensing. "An Improved PCA Method for Hyperspectral Image Feature Extraction." This peer‑reviewed article presents recent advances in PCA techniques tailored to hyperspectral data exploration.