Near-Optimal Sample Compression for Nearest Neighbors

Near-optimal sample compression for nearest neighbors

We present the first sample compression algorithm for nearest neighbors with nontrivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly optimal. Our result yields new insight into margin-based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify exis...

Positioning for Online Nearest Neighbors

Nearest-neighbors medians clustering

We propose a nonparametric cluster algorithm based on local medians. Each observation is substituted by its local median and this new observation moves toward the peaks and away from the valleys of the distribution. The process is repeated until each observation converges to a fixpoint. We obtain a partition of the sample based on the convergence points. Our algorithm determines the number of c...

Boruvka Meets Nearest Neighbors

Computing the minimum spanning tree (MST) is a common task in the pattern recognition and the computer vision fields. However, little work has been done on efficient general methods for solving the problem on large datasets where graphs are complete and edge weights are given implicitly by a distance between vertex attributes. In this work we propose a generic algorithm that extends the classic...

Iterative Nearest Neighbors

Representing data as a linear combination of a set of selected known samples is of interest for various machine learning applications such as dimensionality reduction or classification. k-Nearest Neighbors (kNN) and its variants are still among the best-known and most often used techniques. Some popular richer representations are Sparse Representation (SR) based on solving an l1-regularized lea...