We introduce a new nearest neighbor search algorithm. The algorithm builds a nearest neighbor graph in an offline phase and when queried with a new point, performs hill-climbing starting from a randomly sampled node of the graph. We provide theoretical guarantees for the accuracy and the computational complexity and empirically show the effectiveness of this algorithm.

Algorithms that use point-cloud models make heavy use of the neighborhoods of the points. These neighborhoods are used to compute the surface normals for each point, mollification, and noise removal. All of these primitive operations require the seemingly repetitive process of finding the k nearest neighbors (kNNs) of each point. These algorithms are primarily designed to run in main memory. Ho...

Data mining is frequently obstructed by privacy concerns. In many cases, data is shared with third party for the mining purpose. However, sharing of data for analysis is not possible due to prevailing privacy laws and/or policies. Privacy preserving data mining techniques have been developed to address this issue by providing mechanisms to mine the data while guaranteing certain levels of priva...

We study the energy per particle of a one-dimensional ferromagnetic/anti-ferromagnetic frustrated spin chain with nearest and next-to-nearest interactions close to the helimagnet/ferromagnet transition point as the number of particles diverges. We rigorously prove the emergence of chiral ground states and we compute, by performing the Γ-limits of proper renormalizations and scalings, the energy...

The metric learning problem is concerned with learning a distance function tuned to a particular task, and has been shown to be useful when used in conjunction with nearest-neighbor methods and other techniques that rely on distances or similarities. This survey presents an overview of existing research in metric learning, including recent progress on scaling to high-dimensional feature spaces ...

The k-nearest neighbour (kNN) problem appears in many different fields of computer science, such as computer animation and robotics. In crowd simulation, kNN queries are typically used by a collision-avoidance method to prevent unnecessary computations. Many different methods for finding these neighbours exist, but it is unclear which will work best in crowd simulations, an application which is...