We study the fundamental problem of clustering $n$ points into $K$ groups drawn from a mixture of isotropic Gaussians in $\mathbb{R}^d$. Specifically, we investigate the requisite minimal distance $Δ$ between mean vectors to partially recover the underlying partition. While the minimax-optimal threshold for $Δ$ is well-established, a significant gap exists between this information-theoretic limit and the performance of known polynomial-time procedures. Although this gap was recently characterized in the high-dimensional regime ($n \leq dK$), it remains largely unexplored in the moderate-dimensional regime ($n \geq dK$). In this manuscript, we address this regime by establishing a new low-degree polynomial lower bound for the moderate-dimensional case when $d \geq K$. We show that while the difficulty of clustering for $n \leq dK$ is primarily driven by dimension reduction and spectral methods, the moderate-dimensional regime involves more delicate phenomena leading to a "non-parametric rate". We provide a novel non-spectral algorithm matching this rate, shedding new light on the computational limits of the clustering problem in moderate dimension.

Models (SDMs) predict species across space from spatially explicit features.

Deep learning algorithms have recently gained significant attention due to their impressive performance.

The learner's goal is to identify the optimal arm

We also propose a loss function adapted to the severe class imbalance. We show that our model outperforms state-of-the-art alternatives on UA V point clouds.

When the optimality gap is negligible, we propose another algorithm that outperforms our first algorithm, highlighting the subtlety of this dueling bandit problem.