用PCA和核PCA分析航空公司利润周期，发现主成分空间聚类更稳定。
Orthogonality and Dimensionality in Airline Cluster Analysis using PCA and Kernel PCA
- 在主成分空间聚类比原始变量空间更稳定，3维主成分可复现7维结果
- 轮廓系数显示数据本质支持3个簇，非原研究宣称的6个簇
- 线性模型已足够，非线性方法无提升，适合面板数据降维聚类
本方法学研究分析了共线性、有效维度与聚类稳定性对2023年Renold等人基于1995至2020年美国航空业利润周期研究的影响。该研究使用k-means聚类、主成分分析（PCA）与系统动力学建模。我们复现了其在三个空间中的聚类实验：原始7维变量空间、3维主成分得分空间及4维主成分得分空间。结果显示六簇分类具有几何鲁棒性：3维主成分空间的k-means聚类结果与7维原始空间完全一致。为进一步检验非线性，我们在六种核函数（三类家族加线性基准）下应用核PCA，结果表明数据流形为内在线性，无明显曲率。轮廓系数分析揭示数据结构仅支持3个簇，而非6个。原始7维空间中的共线性抑制了轮廓系数信号。通过核岭回归验证，在排除新冠疫情年份后，非线性模型未带来精度提升。综上，建议在存在共线性的面板数据中，应基于主成分得分而非原始变量进行聚类。
原文摘要 · Abstract (English)
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.
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