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Brigitte Le Roux studies geometric data analysis, including correspondence analysis and principal component analysis. Her research account describes investigations of how principal axes change when observations, weights or the underlying Euclidean geometry are modified. This stability question asks which apparent structures survive a change in the analysis, rather than treating every fitted axis as intrinsic to the data.^[ref]

Her joint book with Henry Rouanet, Geometric Data Analysis by Brigitte Le Roux and Henry Rouanet, develops the weighted-cloud approach through correspondence analysis, Euclidean clouds and principal component analysis. It connects the linear algebra of projections with explicit choices about representation of multivariate observations.^[ref]

Geometric data analysis represents multivariate observations as weighted clouds of points, then studies their Euclidean geometry through distances, orthogonal projections and principal components. Principal component analysis applies this approach to numerical variables; correspondence analysis adapts it to a table of counts with its own weights and metric. Choosing the weights and metric is part of the analysis, since these choices decide which differences between observations count as large.^[ref]

For a column-centered data matrix with singular value decomposition $X=U\Sigma V^T$, the first $k$ principal components give coordinates $X{V}_k=U_k{\Sigma }_k$. They are the orthogonal projection onto the chosen principal directions. Rescaling one variable changes the distances and can change those directions: measurements in metres and millimetres should not receive different influence merely because the units were changed. The geometry must therefore be interpreted together with the scaling convention, rather than treating the resulting plot as an intrinsic picture of the observations.

Yen-Chi Chen works on nonparametric statistics, Causal inference, missing data and geometric analysis of data. His University of Washington research page also lists mixture models, astrostatistics and applied statistics.^[ref]

His bootstrap notes explain the distinction between the unknown population distribution and the empirical distribution used for resampling. They also discuss when a bootstrap approximation can fail, including an endpoint of a uniform distribution. This is a useful bridge between a computational recipe and the mathematical conditions needed for reliable statistical inference.^[ref]

Homepage: faculty.washington.edu/yenchic/