This paper presents a new algorithm to answer k -nearest neighbor queries called the Fractal k -Nearest Neighbor (k NNF ()). This algorithm takes advantage of the fractal dimension of the dataset under scan to estimate a suitable radius to shrinks a query that retrieves the k -nearest neighbors of a query object. k -NN() algorithms starts searching for elements at any distance from the query ce...

Data generated by current computing systems is rapidly increasing as they become more interconnected as part of the Internet of Things (IoT). The growing amount of generated data, such as multimedia, needs to be accelerated using efficient massive parallel processors. Associative memories, in tandem with processing elements, in the form of look-up tables, can reduce energy consumption by elimin...

In the practice of molecular evolution, different phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [24] or from different genes [15, 16, 17, 18, 14]. Comparing these trees to find their similarities (e.g. agreement or consensus) and dissimilarities, i.e. distance, is thus an important issue in computational molecular b...

The relationships between the generalized directional derivative of the distance function and the existence of nearest points as well as some geometry properties in Banach spaces are studied. It is proved in the present paper that the condition that for each closed subset G of X and x ∈ X \ G, the Clarke, Michel-Penot, Dini or modified Dini directional derivative of the distance function is 1 o...

Few studies empirically estimate the effects of metropolitan growth on nonmetropolitan communities at a national scale. This paper estimates the growth effects of 276 MSAs on population in 1,988 nonmetropolitan communities in the United States from 2000 to 2007. We estimate the distance for growth spillovers from MSAs to nonmetropolitan communities and test the assumption that a single MSA infl...

The k-Nearest Neighbor is one of the simplest Machine Learning algorithms. Besides its simplicity, k-Nearest Neighbor is a widely used technique, being successfully applied in a large number of domains. In k-Nearest Neighbor, a database is searched for the most similar elements to a given query element, with similarity defined by a distance function. In this work, we are most interested in the ...

Nearest neighbor (NN) classification assumes locally constant class conditional probabilities, and suffers from bias in high dimensions with a small sample set. In this paper, we propose a novel cam weighted distance to ameliorate the curse of dimensionality. Different from the existing neighborhood-based methods which only analyze a small space emanating from the query sample, the proposed nea...

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications. First, the characterization yields a singular value formula for determining the nearest pencil whose eigenvalues lie in a...