Dimensionality Reduction

An unsupervised linear transformation that projects data onto orthogonal axes (principal components) ranked by explained variance.

• Mechanism: Computes eigenvectors of the covariance matrix.
• Output: Uncorrelated features ordered by information content.
• Radiomics Use: Reduces hundreds of texture features to a handful of components capturing >95% variance.
• Limitation: Assumes linear relationships; components lack direct biological interpretability.

A supervised projection that maximizes class separability rather than total variance.

• Mechanism: Finds axes that maximize the ratio of between-class variance to within-class variance.
• Key Distinction: Unlike PCA, LDA explicitly uses outcome labels (e.g., malignant vs. benign).
• Radiomics Use: Identifying the feature subspace that best separates tumor subtypes.
• Constraint: Requires more samples than features; assumes normally distributed classes with equal covariance.

A non-linear technique for visualizing high-dimensional data in 2D or 3D space by preserving local neighborhood structure.

• Mechanism: Converts pairwise Euclidean distances into conditional probabilities representing similarity; minimizes KL divergence between high-D and low-D distributions.
• Key Parameter: Perplexity controls the balance between local and global structure.
• Radiomics Use: Exploratory visualization of patient clusters based on radiomic profiles.
• Warning: Non-deterministic; unsuitable as a preprocessing step for downstream classifiers.

A manifold learning technique that preserves both local and global data structure with superior speed and scalability compared to t-SNE.

• Mechanism: Constructs a fuzzy topological representation of the data using simplicial sets, then optimizes a low-dimensional embedding via cross-entropy.
• Advantages: Deterministic results; preserves more global structure; scales to millions of data points.
• Radiomics Use: Identifying continuous trajectories of tumor heterogeneity across a patient cohort.
• Key Parameters: Number of neighbors and minimum distance between embedded points.

An embedded method that performs automatic feature selection during model training by applying an L1 penalty to regression coefficients.

• Mechanism: The L1 norm forces irrelevant feature coefficients to exactly zero, effectively removing them from the model.
• Radiomics Use: Building a sparse radiomic signature where only a small subset of stable, predictive features are retained.
• Advantage: Simultaneously performs dimensionality reduction and model fitting.
• Tuning: The regularization strength (lambda) is typically selected via cross-validation to maximize predictive performance.

A non-linear neural network approach where a bottleneck layer learns a compressed representation of the input radiomic features.

• Architecture: An encoder compresses the input; a decoder reconstructs it. The latent bottleneck vector becomes the reduced feature set.
• Radiomics Use: Learning complex, non-linear interactions between texture and shape features that linear methods miss.
• Variants: Variational Autoencoders (VAEs) enforce a continuous, smooth latent space suitable for generative tasks.
• Consideration: Requires substantial data for training; latent dimensions are not directly interpretable.

An unsupervised linear transformation that converts correlated radiomic features into a set of linearly uncorrelated principal components. The first component captures the maximum variance, with each subsequent component capturing the remaining variance orthogonally. In radiomics, PCA reduces thousands of texture features to a handful of components while preserving the underlying data structure, directly mitigating the curse of dimensionality.

A stability-based reduction strategy that identifies and retains only radiomic features demonstrating high test-retest reproducibility and low inter-observer variability. Features with an intraclass correlation coefficient (ICC) below a threshold (often < 0.75) are discarded before model training. This ensures the final biomarker is resilient to scanner noise and segmentation differences, not just statistically significant in a single cohort.

The computational process of removing unwanted technical variability from radiomic features caused by differences in scanner manufacturers, acquisition protocols, or reconstruction kernels. Without harmonization, batch effects can dominate biological signal, rendering multicenter models useless. This preprocessing step is critical before any dimensionality reduction to ensure retained features reflect true biology rather than scanner artifacts.

A statistical batch-effect correction method originally developed for genomics and adapted to radiomics. ComBat estimates and removes additive and multiplicative scanner effects while preserving biological covariates of interest. When applied before PCA or feature selection, it standardizes feature distributions across imaging centers, enabling robust multicenter radiomic signature development without discarding informative features.

A phenomenon where the number of features (p) far exceeds the number of samples (n), causing models to overfit and distance metrics to become meaningless. In radiomics, extracting thousands of features from a few hundred patients creates this exact scenario. Dimensionality reduction is not optional—it is mathematically required to build generalizable predictive models in the p >> n regime.

The extraction and analysis of temporal changes in radiomic features across treatment timepoints. Rather than reducing dimensions on a single scan, delta-radiomics computes feature deltas and then applies reduction techniques to identify which texture changes predict response. This captures dynamic tumor heterogeneity that static features miss, adding a temporal dimension to the dimensionality reduction challenge.