Junhyung Chang and Xiaoyu Lei’s contribution to the Discussion of ‘Statistical exploration of the Manifold Hypothesis’ by Whiteley et al.
Chang 与 Lei 对《流形假设的统计探索》的讨论
We congratulate the authors on an insightful paper that spans both a general theory of manifold emergence, and methodology for exploring hidden manifold structure in high-dimensional data. In summary, assuming the result of Theorem 1 holds, the effectiveness of PCA in elucidating the geometry of the latent domain from high-dimensional data is closely related to the statistical properties of the random functions (Xj)1≤j≤p such as distinguishability and stationarity. To…