Showing papers on "k-nearest neighbors algorithm published in 1971"

A Direct Method of Nonparametric Measurement Selection

Abstract: A direct method of measurement selection is proposed to determine the best subset of d measurements out of a set of D total measurements. The measurement subset evaluation procedure directly employs a nonparametric estimate of the probability of error given a finite design sample set. A suboptimum measurement subset search procedure is employed to reduce the number of subsets to be evaluated. Teh primary advantage of the approach is the direct but nonparametric evaluation of measurement subsets, for the M class problem.

Estimation of Density from a Sample of Joint Point and Nearest-Neighbor Distances

Abstract: Distances are measured from sample points to the nearest member of a population, from that member to its nearest neighbor, and from that neighbor to its nearest neighbor. The point-to-nearest member is used to obtain an estimate of density, which is characteristically unbiased if the population is random, but biased if the population is uniformly or contagiously distributed. The bias is corrected by an exponential function of the sum of the point distances divided by the sum of either the nearest- or second-nearest-neighbor distances. The distances also provide an index of departure from randomness.

The minimum distance approach to classification

Abstract: The work to advance the state-of-the-art of miminum distance classification is reportd. This is accomplished through a combination of theoretical and comprehensive experimental investigations based on multispectral scanner data. A survey of the literature for suitable distance measures was conducted and the results of this survey are presented. It is shown that minimum distance classification, using density estimators and Kullback-Leibler numbers as the distance measure, is equivalent to a form of maximum likelihood sample classification. It is also shown that for the parametric case, minimum distance classification is equivalent to nearest neighbor classification in the parameter space.

Random Walks with Nonnearest Neighbor Transitions. I. Analytic 1‐D Theory for Next‐Nearest Neighbor and Exponentially Distributed Steps

Abstract: We present here exact analytic results for random walks on one‐dimensional lattices with nonnearest neighbor transitions. After deriving the generating function for such lattices with and without boundaries, we have calculated a number of moment properties (mean first passage times to absorption, mean recurrence times and their dispersion, mean excursion from the origin, etc.) for random walks with next‐nearest neighbor transitions and for random walks with exponentially distributed step length. In the latter case, variation of one of the parameters permits us to cover the whole range of step lengths from nearest neighbor transitions to steps of any finite length l. Since we have obtained explicit expressions for the generating function for these walks, any additional desired moment properties can readily be calculated. Among the interesting results of this study are: (1) The moment results for random walks with next‐nearest neighbor transitions differ from the analogous nearest neighbor results at most by a factor of O(1); (2) the one‐dimensional moment results for walks with arbitrary step length differ from the analogous one‐dimensional results for walks with nearest neighbor transitions by several orders of magnitude; (3) the mean time to absorption for a random walker with equal probabilities for steps of arbitrary length in one dimension agrees to within a factor of O(1) with the mean time for absorption for a random walker with nearest neighbor steps in three dimensions; (4) the mean time to absorption for a random walker with equal probabilities for steps of arbitrary lengths is independent of the dimensionality of the lattice.

Two-Magnon Bound States in a Linear Heisenberg Chain with Nearest and Next Nearest Neighbor Interactions

Abstract: The bound state problems associated with two magnons in a linear chain of spin 1/2 with nearest and next nearest neighbor exchange integrals, J and α J , respectively, are studied. The Hamiltonian is rewritten in terms of the Fermi operators in place of spin operators, and an integral equation to determine the bound state energies is obtained. In the cases when the total wave number K of two magnons is π or π/2, analytical solutions are easily obtained. A part of the present results disagrees with Majumdar's ones. Computer studies on the bound states are performed for a finite chain composed of spins up to twenty. They are consistent with the analytical results.

EPR Study of LiGa5O8: Cr3+

Abstract: An EPR study has been undertaken of Cr3+ in LiGa5O8. The site symmetry is rhombic and the system can be described by the spin Hamiltonian, H=gβH·S+D [Sz2− 1 3S (S+1)]+E (Sx2− S y2), where D=0.331±0.002 cm−1, E=0.018±0.002 cm−1, and the average g value, assumed isotropic, is 1.980±0.005. The axes of the spin Hamiltonian are tilted slightly from the expected crystallographic directions. The arrangement of Li+ and Ga3+ ions in next‐to‐nearest neighbor positions results in a large electrostatic field of odd parity at the site of the chromium ion.

Exact Nearest‐Neighbor Statistics for Two‐Dimensional Rectangular Lattices

Abstract: Expressions are developed which describe exactly the ensemble average of the number of nearest, next‐nearest, and third‐nearest‐neighbor pairs per particle, when indistinguishable particles are arranged on a two‐dimensional rectangular lattice

K-Nearest Neighbor Rules.

Abstract: : The k - Nearest Neighbor Rule is one specific example of a statistical decision rule. The report deals with a specific modification of this rule. The topics included are the distribution of risk of any sample - based decision rule in terms of the training set sample size, rule structure and underlying probability densities, evaluation of a k - nearest neighbor rule, the metric used in non parametric decision rules. (Author)

Evidence for long-range repulsive atomic interactions in metals from bond energy calculations

Abstract: The first and second nearest neighbor bond energies are calculated for a variety of liquid metals from heat of vaporization, density, and surface tension data using a simple pair-wise interaction model of cohesive forces. The first nearest neighbor interaction is found to be attractive, while the second nearest neighbor interaction is repulsive. This longer range repulsive interaction is not surprising, in view of the Friedel oscillations known to exist in the potential function for ion-ion interactions in a metal. It is suggested that γ-plot calculations for solid metals take this repulsion into account.