Related papers: Efficient Nearest-Neighbor Search for Dynamical Sy…
In this paper we present the first provable approximate nearest-neighbor (ANN) algorithms for Bregman divergences. Our first algorithm processes queries in O(log^d n) time using O(n log^d n) space and only uses general properties of the…
In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criterion. One is the distance criteria, and the other is the recall criteria.…
Querying uncertain data sets (represented as probability distributions) presents many challenges due to the large amount of data involved and the difficulties comparing uncertainty between distributions. The Earth Mover's Distance (EMD) has…
Many data-based statistical algorithms require that one find \textit{near or nearest neighbors} to a given vector among a set of points in that vector space, usually with Euclidean topology. The k-d data structure and search algorithms are…
Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let h_min(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal…
In this paper we investigate the problem of estimating the cluster tree for a density $f$ supported on or near a smooth $d$-dimensional manifold $M$ isometrically embedded in $\mathbb{R}^D$. We analyze a modified version of a $k$-nearest…
$k$-nearest neighbor classification is a popular non-parametric method because of desirable properties like automatic adaption to distributional scale changes. Unfortunately, it has thus far proved difficult to design active learning…
In the Directed Steiner Tree (DST) problem we are given an $n$-vertex directed edge-weighted graph, a root $r$, and a collection of $k$ terminal nodes. Our goal is to find a minimum-cost arborescence that contains a directed path from $r$…
Introduction. Case Based Reasoning (CBR) is an emerg- ing decision making paradigm in medical research where new cases are solved relying on previously solved similar cases. Usually, a database of solved cases is provided, and every case is…
An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. When k = 1 the complexity of the problem is polynomial. In this paper, we further find the…
Search trees on trees (STTs) generalize the fundamental binary search tree (BST) data structure: in STTs the underlying search space is an arbitrary tree, whereas in BSTs it is a path. An optimal BST of size $n$ can be computed for a given…
Nonparametric estimation of mutual information is used in a wide range of scientific problems to quantify dependence between variables. The k-nearest neighbor (knn) methods are consistent, and therefore expected to work well for large…
We consider the problem of computing a Steiner tree of minimum cost under a hop constraint which requires the depth of the tree to be at most $k$. Our main result is an exact algorithm for metrics induced by graphs with bounded treewidth…
We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest…
We propose a new finding $k$-minima algorithm and prove that its query complexity is $\mathcal{O}(\sqrt{kN})$, where $N$ is the number of data indices. Though the complexity is equivalent to that of an existing method, the proposed is…
The Reverse $k$-Nearest Neighbor (R$k$NN) query over moving objects on road networks seeks to find all moving objects that consider the specified query point as one of their $k$ nearest neighbors. In location based services, many users…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
Neural network classifiers have become the de-facto choice for current "pre-train then fine-tune" paradigms of visual classification. In this paper, we investigate k-Nearest-Neighbor (k-NN) classifiers, a classical model-free learning…
The continuous-time query model is a variant of the discrete query model in which queries can be interleaved with known operations (called "driving operations") continuously in time. Interesting algorithms have been discovered in this…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…