A novel classifier, named Nearest Linear Manifold uses a small number of prototypes to represent a class and extend their resentational capacity by using the linear manifold of the prototypes to provide more sufficient feature information for classification.

The “nearest neighbor” relation, or more generally the “k nearest neighbors” relation, defined for a set of points in a metric space, has found many uses in computational geometry and clustering analysis, yet surprisingly little is known about some of its basic properties. In this paper, we consider some natural questions that are motivated by geometric embedding problems. We derive bounds on t...

The nearest-neighbor method is perhaps the simplest of all algorithms for predicting the class of a test example. The training phase is trivial: simply store every training example, with its label. To make a prediction for a test example, first compute its distance to every training example. Then, keep the k closest training examples, where k ≥ 1 is a fixed integer. Look for the label that is m...

Collaborative Filtering (CF) Systems have been studied extensively for more than a decade to confront the “information overload” problem. Nearest-neighbor CF is based either on common user or item similarities, to form the user’s neighborhood. The effectiveness of the aforementioned approaches would be augmented, if we could combine them. In this paper, we use biclustering to disclose this dual...

Benjamini, Pemantle, and Peres constructed nearest neighbor processes which have predictability profiles that decay faster than that of the simple random walk. Häggström and Mossel found processes with even faster decaying predictability profiles. We prove that rate of decay achieved by Häggström and Mossel is optimal.