Principal Component Analysis

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Principal Component Analysis

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High-Dimensional Data

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Dimensionality Reduction

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Intrinsic Dimensionality

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Low-Dimensional Structure

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279 papers

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Orthogonality and Dimensionality in Airline Cluster Analysis using PCA and Kernel PCA
Jun 6, 2026Andreas SchlapbachPrincipal Component Analysis Cluster Structure
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Easy, robust approximate message passing for planted spike models
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Riemannian Stochastic Optimization for Sufficient Dimension Reduction
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Log-Ratio Propagation on the Simplex: A Theory of Cellwise Contamination for Compositional Data
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Few-Shot Resampling for Scalable Statistically-Sound Data Mining
May 29, 2026Leonardo Pellegrina, Fabio VandinData Mining Resampling
ScaleMAP: Preserving Local Density and Neighborhood Structure in Low-Dimensional Embeddings
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Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions
May 28, 2026Jingda Wu, Changxiao CaiLow-Dimensional Structure Score-Based Diffusion Model
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May 26, 2026Tomoki Koike, Prakash Mohan, Marc T. Henry de Frahan +2Dimensionality Reduction Shallow Water Equations
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May 26, 2026Sai-Aakash Ramesh, Archit Sood, Andrew Corbett +1Dimensionality Reduction Distributional Learning
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Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offs
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Optimal Representation Size: High-Dimensional Analysis of Pretraining and Linear Probing
May 19, 2026Valentina Njaradi, Clémentine Dominé, Rachel Swanson +2Model Pretraining Unlabeled Data
Robust Subspace-Constrained Quadratic Models for Low-Dimensional Structure Learning
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Optimal Reconstruction from Linear Queries
May 19, 2026Yuval Filmus, Shay Moran, Elizaveta NesterovaReconstruction Error Optimal Sample Complexity

Jun 6, 2026 · cs.LGJ/K move · Enter open · S save

Orthogonality and Dimensionality in Airline Cluster Analysis using PCA and Kernel PCA

Andreas Schlapbach

Swiss Federal Railways (SBB), Switzerland

This methodological study analyzes the effects of collinearity, effective dimensionality, and cluster stability in a 2023 study of US airline profit cycles from 1995 to 2020 by Renold et al., which uses k-means clustering, principal component analysis, and system dynamic modelling.We replicate their clustering experiment in three spaces -- the original 7-dim. raw-variable space, a 3-dim. PC score space, and a 4-dim. PC score space using their dataset. We show that the six-cluster taxonomy is geometrically robust: k-means in 3-PC space produces bit-for-bit identical cluster assignments relative to 7D raw space. As a nonlinearity check we apply kernel PCA under six kernels spanning three families plus a linear baseline. The kernels confirm an intrinsically linear manifold with no detectable curvature. The silhouette criterion reveals that the dataset structurally supports only three clusters, not six. Collinearity in the raw 7D space suppresses the silhouette signal. A kernel ridge regression check confirms no nonlinear accuracy gain over linear ridge once the COVID19 year is excluded. Together, these results argue for clustering on PC scores rather than raw variables in collinearity-prone panel data.

Principal Component Analysis Cluster Structure Image Clustering K-Means Kernel Method Flight Performance Orthogonality

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