We establish several combinatorial bounds on the complexity (number of vertices and edges) of the complement of the union (also known as the common exterior) of k convex polygons in the plane, with a total of n edges. We show: 1. The maximum complexity of the entire common exterior is (nn(k) + k 2). 1 2. The maximum complexity of a single cell of the common exterior is (nn(k)). 3. The complexit...

The k-nearest neighbors (k-NN) classification rule is still an essential tool for computer vision applications, such as scene recognition. However, k-NN still features some major drawbacks, which mainly reside in the uniform voting among the nearest prototypes in the feature space. In this paper, we propose a new method that is able to learn the “relevance” of prototypes, thus classifying test ...

Advances in geo-sensing technology have led to an unprecedented spread of location-aware devices. In turn, this has resulted into a plethora of location-based services in which huge amounts of spatial data need to be efficiently consumed by spatial query processors. For a spatial query processor to properly choose among the various query processing strategies, the cost of the spatial operators ...

Given an initial rectangular range or k nearest neighbor (k-nn) query (using the L1 metric), we consider the problems of incrementally extending the query by increasing the size of the range, or by increasing k, and reporting the new points incorporated by each extension. Although both problems may be solved trivially by repeatedly applying a traditional range query or L1 k-nn algorithm, such s...

The nearest neighbour (NN) and k-nearest neighbour (k-NN) classification rules have been widely used in Pattern Recognition due to its simplicity and good behaviour. Exhaustive nearest neighbour search may become unpractical when facing large training sets, high dimensional data or expensive dissimilarity measures (distances). During the last years a lot of fast NN search algorithms have been d...

Nearest neighbour (NN) searches and k nearest neighbour (k-NN) searches are widely used in pattern recognition and image retrieval. An NN (k-NN) search finds the closest object (closest k objects) to a query object. Although the definition of the distance between objects depends on applications, its computation is generally complicated and time-consuming. It is therefore important to reduce the...

A probabilistic k-nn (PKnn) method was introduced in [13] under the Bayesian point of view. This work showed that posterior inference over the parameter k can be performed in a relatively straightforward manner using Markov Chain Monte Carlo (MCMC) methods. This method was extended by Everson and Fieldsen [14] to deal with metric learning. In this work we propose two different dissimilarities f...

The k-nearest neighbour (k-NN) technique, due to its interpretable nature, is a simple and very intuitively appealing method to address classification problems. However, choosing an appropriate distance function for k-NN can be challenging and an inferior choice can make the classifier highly vulnerable to noise in the data. In this paper, we propose a new method for determining a good distance...