Related papers: Randomized partition trees for exact nearest neigh…
KNN has the reputation to be the word simplest but efficient supervised learning algorithm used for either classification or regression. KNN prediction efficiency highly depends on the size of its training data but when this training data…
We consider the problem of finding high dimensional approximate nearest neighbors. Suppose there are d independent rare features, each having its own independent statistics. A point x will have x_{i}=0 denote the absence of feature i, and…
In an earlier paper we introduced a special kind of k-width junction tree, called k-th order t-cherry junction tree in order to approximate a joint probability distribution. The approximation is the best if the Kullback-Leibler divergence…
Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable…
We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…
Within a mathematically rigorous model, we analyse the curse of dimensionality for deterministic exact similarity search in the context of popular indexing schemes: metric trees. The datasets $X$ are sampled randomly from a domain $\Omega$,…
Developing increasingly efficient and accurate algorithms for approximate nearest neighbor search is a paramount goal in modern information retrieval. A primary approach to addressing this question is clustering, which involves partitioning…
We propose a novel application of coded computing to the problem of the nearest neighbor estimation using MatDot Codes [Fahim. et.al. 2017], that are known to be optimal for matrix multiplication in terms of recovery threshold under storage…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
The approximate nearest neighbor problem ($\epsilon$-ANN) in high dimensional Euclidean space has been mainly addressed by Locality Sensitive Hashing (LSH), which has polynomial dependence in the dimension, sublinear query time, but…
$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
This paper proposes a spatial k-nearest neighbor method for nonparametric prediction of real-valued spatial data and supervised classification for categorical spatial data. The proposed method is based on a double nearest neighbor rule…
This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies…
K-Nearest Neighbours (k-NN) is a popular classification and regression algorithm, yet one of its main limitations is the difficulty in choosing the number of neighbours. We present a Bayesian algorithm to compute the posterior probability…
k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…
Hash codes are a very efficient data representation needed to be able to cope with the ever growing amounts of data. We introduce a random forest semantic hashing scheme with information-theoretic code aggregation, showing for the first…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts.…