Two important optimization problems in the analysis of geometric data sets are clustering and sketching. Here, clustering refers to the problem of partitioning some input metric measure space into k clusters, minimizing some objective function f . Sketching, on the other hand, is the problem of approximating some metric measure space by a smaller one supported on a set of k points. Specifically...

Feature subset selection presents a common challenge for the applications where data with tens or hundreds of features are available. Existing feature selection algorithms are mainly designed for dealing with numerical or categorical attributes. However, data usually comes with a mixed format in real-world applications. In this paper, we generalize Pawlak’s rough set model into d neighborhood r...

Sample weighting and variations in neighborhood or data-dependent distance metric definitions are three principal directions considered for improving k-NN classification technique. Recently, manifold-based distance metrics attracted considerable interest and computationally less demanding approximations are developed. However, a careful comparison of these alternative approaches is missing. In ...

In data stream applications, data arrive continuously and can only be scanned once as the query processor has very limited memory (relative to the size of the stream) to work with. Hence, queries on data streams do not have access to the entire data set and query answers are typically approximate. While there have been many studies on the k Nearest Neighbors (kNN) problem in conventional multid...

In this paper we evaluate the performance of the highest probability SVM nearest neighbor (HP-SVM-NN) classifier, which combines the ideas of the SVM and k-NN classifiers, on the task of spam filtering. To classify a sample, the HP-SVM-NN classifier does the following: for each k in a predefined set {k1, ..., kN} it trains an SVM model on k nearest labeled samples, uses this model to classify t...

The nearest neighbour (NN) rule is widely used in pattern recognition tasks due to its simplicity and its good behaviour. Many fast NN search algorithms have been developed during last years. However, in some classification tasks an exact NN search is too slow, and a way to quicken the search is required. To face these tasks it is possible to use approximate NN search, which usually increases e...

The nearest neighbor classifier (NNC) is a popular non-parametric classifier. It is a simple classifier with no design phase and shows good performance. Important factors affecting the efficiency and performance of NNC are (i) memory required to store the training set, (ii) classification time required to search the nearest neighbor of a given test pattern, and (iii) due to the curse of dimensi...

This paper presents the nearest neighbor value (NNV) algorithm for high resolution (H.R.) image interpolation. The difference between the proposed algorithm and conventional nearest neighbor algorithm is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. In other words, the proposed concept selects one pixel, among four direct...

The approximation of nearest neighbor interaction (NNI) is widely used in short-time spin dynamics with dipole-dipole interactions (DDI) when the intensity spin-spin $\sim 1/r^3$, where $r$ a distance between those spins. However, NNI can not approximate long time evolution such systems. We consider system 1/r^{\alpha}$, $\alpha\ge 3$, and find low boundary $\alpha_c$ applicability to an arbitr...