CuBAS Improves Data Sampling for Supervised Classification

The quality of a training dataset is as crucial as its size for effective machine learning, yet many sampling methods overlook the inherent geometric structure of the data distribution. This research presents CuBAS (Curvature-Based Adaptive Sampling), a novel information-geometric framework for intelligently selecting data in supervised classification tasks. CuBAS operates on the principle that a labeled dataset can be viewed as a statistical manifold. Within this manifold, local curvature, estimated using the ratio of second to first-order observed Fisher information, accurately reflects the geometric complexity of the data. By constructing a k-nearest-neighbor graph, a closed-form curvature score is derived for each data point. This curvature signal allows CuBAS to partition the data into low-curvature regions (smooth, homogeneous clusters) and high-curvature regions (decision boundaries that are highly informative for classification). By strategically selecting data points from both types of regions, CuBAS builds compact yet maximally informative training subsets. Empirical evaluations across over 60 benchmark datasets demonstrate that CuBAS consistently and significantly outperforms random sampling and uncertainty-based baselines, regardless of labeling budget or classifier architecture. It is also computationally efficient, scaling linearly with the number of k-NN graph edges.