Beyond Explained Variance: A Cautionary Tale of PCA
We address shortcomings of principal component analysis (PCA) for visualizing high-dimensional data lying on a nonlinear low-dimensional manifold via two-dimensional scatterplots, focusing on a fossil teeth dataset from the early mammalian insectivore Kuehneotherium. While the PCA scatterplot reported by Jolliffe and Cadima (Philosophical Transactions of the Royal Society A, 2016) shows clustering in the region where PC2 < 0, our analysis based on t-SNE and persistent homology (PH) reveals a ring-like structure with no evident clustering and intrinsic dimensionality equal to one. We further propose a generative probabilistic-geometric model in which the data are sampled uniformly from a u...
| Authors | Gionni Marchetti |
|---|---|
| Primary category | cond-mat.stat-mech |
| Published | 13 May 2026 |
| Last updated at source | 17 May 2026 |
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