Several types of nearest neighbor (NN) search have been proposed and studied in the context of spatial databases. The most common type is the point NN query, which retrieves the nearest neighbors of an input point. Such a query, however, is usually meaningless in highly dynamic environments where the query point or the database objects move/change over time. In this paper we study alternative f...

Nonlinear dimensionality reduction methods often rely on the nearest-neighbors graph to extract low-dimensional embeddings that reliably capture the underlying structure of high-dimensional data. Research however has shown that computing nearest neighbors of a point from a highdimensional data set generally requires time proportional to the size of the data set itself, rendering the computation...

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires k → ∞ as the sample size n → ∞) into the functional of interest, the estimators we consider fix k and perform a bias corr...

The performance of a fuzzy k-NN rule depends on the number k and a fuzzy membership-array W[I, mR], where l and m R denote the number of classes and the number of elements in the reference set X R respectively. The proposed learning procedure consists in iterative finding such k and W which minimize the error rate estimated by the 'leaving one out' method.

Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is to construct a neighborhood graph on the sample points such that clusters are “identified”: that is, the subgraph induced by points from the same cluster is connected, while subgraphs corresponding to different clusters are not connected to each other. We derive bounds ...

We propose a new approach for outlier detection, based on a new ranking measure that focuses on the question of whether a point is “important” for its nearest neighbors; using our notations low cumulative rank implies the point is central. For instance, a point centrally located in a cluster has relatively low cumulative sum of ranks because it is among the nearest neighbors of its own nearest ...

Dimensionality reduction methods are of interest in applications such as content based image and video retrieval. In large multimedia databases, it may not be practical to search through the entire database in order to retrieve the nearest neighbors of a query. Good data structures for similarity search and indexing are needed, and the existing data structures do not scale well for the high dim...

This paper presents a simple but effective density-based outlier detection approach with the local kernel density estimation (KDE). A Relative Densitybased Outlier Score (RDOS) is introduced to measure the local outlierness of objects, in which the density distribution at the location of an object is estimated with a local KDE method based on extended nearest neighbors of the object. Instead of...