A Closed-Form Adaptive-Landmark Kernel for Certified Point-Cloud and Graph Classification
We introduce PALACE (Persistence Adaptive-Landmark Analytic Classification Engine), the data-adaptive companion to PLACE, paying a small cross-validation tier on three knobs (budget, radii, bandwidth; $\leq 5$ choices each). A cover-theoretic core (Lebesgue-number criterion on the landmark cover) yields four closed-form guarantees. (i) A structural lower distortion bound $λ(τ;ν)$ on $\mathcal{D}_n$ under cross-diagram non-interference, with a $(D/L)^2$ budget reduction over the uniform grid when diagrams concentrate. (ii) Equal weights $w_k = K^{-1/2}$ maximizing $λ$, and farthest-point-sampling positions $2$-approximating the optimal $k$-center covering radius; both derived from training...
| Authors | Sushovan Majhi, Atish Mitra, Žiga Virk et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 May 2026 |
| Last updated at source | 5 May 2026 |
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