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arXiv · 2609.23468

Exact Sign Recovery for PCA Connectivity Analysis in Mixture Models

Kohei Kawamoto
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Abstract

We study exact sign recovery for the PCA connectivity construction of Ding and He (2004), based on the first K-1 principal components. For any fixed number of components with affinely independent means, we derive the oracle signal projection explicitly. Under anisotropic sub-Gaussian noise and random component sizes, a rowwise eigenspace bound yields a sufficient condition, governed by the weakest signal direction, for recovering all connectivity signs without requiring a bounded condition number of the nonzero signal spectrum. Under isotropic Gaussian noise with a fixed mean shape, we obtain an asymptotically sharp cutoff, with an explicit formula when the mixing proportions are equal and the means form a regular simplex.

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Kohei Kawamoto. 2026-09-20. Exact Sign Recovery for PCA Connectivity Analysis in Mixture Models. https://arxiv.org/abs/2609.23468

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