Showing papers on "k-nearest neighbors algorithm published in 1984"

An exact recursion for the composite nearest‐neighbor degeneracy for a 2×N lattice space

Abstract: A set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest‐neighbor degeneracy for simple, indistinguishable particles distributed on a 2×N lattice space. The associated generating functions, as well as the expectation of the resulting statistics are also treated.

An Optimal Global Nearest Neighbor Metric

Abstract: A quadratic metric dAO (X, Y) =[(X - Y)T AO(X - Y)]? is proposed which minimizes the mean-squared error between the nearest neighbor asymptotic risk and the finite sample risk. Under linearity assumptions, a heuristic argument is given which indicates that this metric produces lower mean-squared error than the Euclidean metric. A nonparametric estimate of Ao is developed. If samples appear to come from a Gaussian mixture, an alternative, parametrically directed distance measure is suggested for nearness decisions within a limited region of space. Examples of some two-class Gaussian mixture distributions are included.

Asymptotic Normality of Nearest Neighbor Regression Function Estimates

Abstract: Let $(X, Y)$ be a random vector in the plane. We show that a smoothed N.N. estimate of the regression function $m(x) = \mathbb{E}(Y\mid X = x)$ is asymptotically normal under conditions much weaker than needed for the Nadaraya-Watson estimate. It also turns out that N.N. estimates are more efficient than kernel-type estimates if (in the mean) there are few observations in neighborhoods of $x$.

Nonparametric Data Reduction

Abstract: A nonparametric data reduction technique is proposed. Its goal is to select samples that are ``representative'' of the entire data set. The technique is iterative and is based on the use of a criterion function and nearest neighbor density estimates. Experiments are presented to demonstrate the algorithm.

Hopping transport on a randomly substituted lattice for long range and nearest neighbor interactions

Abstract: A theoretical study of hopping transport of excitations or charge carriers among particles randomly distributed on a lattice is presented. The method used is an extension of the diagrammatic technique applied by Gochanour, Andersen, and Fayer to hopping transport in a continuum. We present an exact diagrammatic analysis of the configuration averaged Green function of the Pauli master equation. We obtain a self‐consistent approximation to the Green function from which transport properties such as the mean squared displacement may be calculated for any transfer rate, any lattice type and any concentration. For a three dimensional lattice, the results are shown to be accurate in the low concentration limit and for the filled lattice, and are expected to be accurate at intermediate concentration. This is the first theory of hopping transport on a randomly substituted lattice, which is not restricted to low concentration, that can be applied in the case of a long range transfer rate. Results are presented for a Forster dipole–dipole transfer rate and for a transfer rate limited to nearest neighbors for a simple cubic lattice. The latter has a percolation threshold that is described in a qualitatively correct manner by our approximation.

Consistency for Cross-Validated Nearest Neighbor Estimates in Nonparametric Regression

Abstract: Under suitable conditions, we show that the cross-validated nearest neighbor estimates for the unknown smooth regression function in $R^p$ is asymptotically consistent.

Effect of atomic distribution on the saturation magnetization of cobalt‐chromium films

Abstract: The saturation magnetization Ms of CoCr films as a function of Cr content and atomic distribution has been modeled. For homogeneous films, two distinct cases have been calculated. The first case is a random array of atoms in an hcp lattice, while the second is an array with the condition that there be no Cr‐Cr bonds. Ms is calculated by summing up the Co atom’s contribution, counting only nearest neighbor interactions, and assuming that the Cr atom is nonmagnetic. The model assumes that the contribution of the Co atom to Ms is determined by its Cr nearest neighbors; for zero Cr nearest neighbors, the moment is maximum with the moment linearly decreasing to zero for four or more Cr neighbors. These two cases describe the range of behavior of Ms for CoCr films produced by rf diode sputtering with applied rf bias. For cold substrates with no bias, Ms is close to that predicted for the random distribution, while as the bias level is increased, Ms approaches that predicted by the no Cr‐Cr bond distribution. Fo...

Classification Error for a Very Large Number of Classes

Abstract: Classification error is analyzed for a situation where the number of possible classes may be on the order of a hundred or more. The error associated with classifying to a single class is shown to depend mainly on average nearest-neighbor distance between class means, noise level, and effective dimensionality of the class mean distribution and not much on other aspects of the distribution, noise correlation, or number of classes. Since single class error is large, separation of classes into groups is also explored. Group classification error has the same properties as single class error but the size of the error is moderated by the Bayes overlap between groups. Standard curves are provided to predict single class and group error. Also discussed are the effect of pattern blurring on classification error and the nearest-neighbor distance statistics throughout a distribution.

Classification Bias of the k-Nearest Neighbor Algorithm

Abstract: The k-nearest neighbor classifier has been used extensively in pattern analysis applications. This classifier can, however, have substantial bias when there is little class separation and the sample sizes are unequal. This classification bias is examined for the two-class situation and formulas presented that allows selection of values of k that yields minimum bias.

A computationally efficient approximation to the nearest neighbor interchange metric

Abstract: The nearest neighbor interchange (nni) metric is a distance measure providing a quantitative measure of dissimilarity between two unrooted binary trees with labeled leaves. The metric has a transparent definition in terms of a simple transformation of binary trees, but its use in nontrivial problems is usually prevented by the absence of a computationally efficient algorithm. Since recent attempts to discover such an algorithm continue to be unsuccessful, we address the complementary problem of designing an approximation to the nni metric. Such an approximation should be well-defined, efficient to compute, comprehensible to users, relevant to applications, and a close fit to the nni metric; the challenge, of course, is to compromise these objectives in such a way that the final design is acceptable to users with practical and theoretical orientations. We describe an approximation algorithm that appears to satisfy adequately these objectives. The algorithm requires O(n) space to compute dissimilarity between binary trees withn labeled leaves; it requires O(n logn) time for rooted trees and O(n 2 logn) time for unrooted trees. To help the user interpret the dissimilarity measures based on this algorithm, we describe empirical distributions of dissimilarities between pairs of randomly selected trees for both rooted and unrooted cases.

Kinetics of a First-Order Phase Transition: Computer Simulations and Theory

Abstract: We make a quantitative comparison between the predictions of the Becker-Doring equations and computer simulations on a model of a quenched binary A-B alloy. The atoms are confined to the vertices of a simple cubic lattice, interact through attractive nearest neighbor interactions, and move by interchanges of nearest neighbor pairs (Kawasaki dynamics). We study in particular the time evolution of the number of clusters of A atoms of each size, at four different concentrations: ρA=0.035, 0.05, 0.075, and 0.1 atoms per lattice site. The temperature is 0.59 times the critical temperature. At this temperature the equilibrium concentration of A atoms in the B-rich phase is ρ A eq =0.0145 atoms/lattice site. The coefficients entering the Becker-Doring equations are obtained by extrapolation from previously published low-density calculations, leaving the time scale as the only adjustable parameter. We find good agreement at the three lower densities. At 10% density the agreement is, as might be expected, less satisfactory but still fairly good-indicating a quite wide range of utility for the Becker-Doring equations.

Adaptive Density Flattening--A Metric Distortion Principle for Combating Bias in Nearest Neighbor Methods

Abstract: With a wide variety of approaches to density estimation, it is profitable to perturb the data so as to make 2nd order derivatives of their density vanish. An adaptive transformation to local uniformity for instance will (for unchanged variance) lower bias to a vanishing fraction of what a Rosenblatt-Parzen or nearest neighbor estimator on the raw data yields; fractional pilot sampling, a common technical device of little practical appeal, can be shown by an embedding argument to be dispensable. An upshot is that MSE can be lowered by attacking the variance directly through extra smoothing, without the usual penalty from inflated bias.

Phase transitions in a lattice gas model for coadsorption

Abstract: A lattice gas with two different sizes of interacting particles on a square lattice is studied. Two large particles are excluded from occupying a pair of nearest neighbor sites and repel if they occupy a pair of next nearest neighbor sites. A small particle on a lattice site repels both large particles and small particles which occupy nearest neighbor sites. Using reflection positivity and the Peierls argument, as many as five different types of ordered phases are proved to exist at sufficiently low temperatures. The model may be useful for the description of competitive adsorption from a gaseous mixture containing adatoms of different radii.

On Attractive Interaction between f Electrons in Valence Fluctuating Systems

Abstract: The mutual interaction between f electrons by one-phonon exchange is investigated with a simplified model including the characteristic feature of valence fluctuating compounds; the local dilation of lattice couples with the local density of f electrons. When an angle made by f site-ligand (or f site)- f site is smaller than π/2, one-phonon exchange results in an attractive interaction between neighboring f electrons. The following cases are typical examples where an attractive interaction can exist; a pair of f electrons at the next nearest neighbor sitesin the bcc lattice and a pair at the nearest neighbor sites in the fcc lattece. The proposed mechanism of attractive interaction is consistent with the observations that CeCu 2 Si 2 and UBe 13 are superconductors, while CeAl 3 and CeCu 6 are not.

Lattice dynamics and crystal stability of bromine

Abstract: The lattice dynamics and crystal stability of bromine have been studied using an interaction potential which includes atom–atom and Coulombic terms. It was found that in addition to high order electrostatic terms, a specific interaction of the form −D/r8 between nearest neighbor atoms, which is identified as an induced dipole‐induced quadrupole term, is needed to stabilize the observed orthorhombic structure and to give a good fit with other static and dynamical observables.

Finite element computation on nearest neighbor connected machines

Abstract: Research aimed at faster, more cost effective parallel machines and algorithms for improving designer productivity with finite element computations is discussed. A set of 8 boards, containing 4 nearest neighbor connected arrays of commercially available floating point chips and substantial memory, are inserted into a commercially available machine. One-tenth Mflop (64 bit operation) processors provide an 89% efficiency when solving the equations arising in a finite element problem for a single variable regular grid of size 40 by 40 by 40. This is approximately 15 to 20 times faster than a much more expensive machine such as a VAX 11/780 used in double precision. The efficiency falls off as faster or more processors are envisaged because communication times become dominant. A novel successive overrelaxation algorithm which uses cyclic reduction in order to permit data transfer and computation to overlap in time is proposed.

Dependence of the phase-diagram on the coupling parameters in water-lattice models

Abstract: This paper reports specific results obtained with the two previously proposed lattice models of water as based on the cluster variation method. The hydrogen-bonded lattice gas with next nearest neighbor repulsion has a Hamiltonian with three coupling parameters. We map out the region in the coupling parameter space which gives a phase diagram that has the same topology as the phase diagram of water. We first discuss, using the simple model, how one diagram evolves into a seemingly different topology and explain how the first order terminal points disappear in the metastable region. We then use the extended model, which contains two extra degrees of freedom, to describe four phase diagrams that show some of the desired features we want in a water potential. The final choice is made, using a potential labelled 9, which shows all desired features in a qualitative way. This potential has a critical point at T c = 0.807 E p , and a triple point at T 3 = 0.971 E p , where E p is the nearest neighbor attractive energy in the absence of the H-bonding. The density-temperature and the pressure-density projection of the potential are given. The relative number of hydrogen-bonded pairs at constant pressure is given. A discussion is given about the limitations of the model.

Contour Processing Algorithm For Hexagonally Sampled Images

Abstract: This paper describes a contour tracking algorithm for images which have been hexagonally sampled. Both formal and informal descriptions of the procedure as well as performance statistics are included.IntroductionMachine vision systems utilize image processing and understanding algorithms in which the image data isstored in a two dimensional array. Furthermore, this data is usually rectangularly sampled. This type ofsampling operation is described byf(xl,x2) = fa(x1T1,x2T2) (1) where T1 and T2 are the horizontal and vertical sampling intervals, and xl and x2 are the row -column coordinates in image space. The advantages (and disadvantages) of rectangular sampling rather than other types of two dimensionalsampling are usually not considered. This adherence to the rectangular standard is inappropriate and inef-ficient for some tasks. For example, it has been shownithat hexagonal sampling is the optimal samplingscheme for signals which are band limited over a circular region of the Fourier plane. In fact, no othersampling scheme permits a lower sampling density. Another feature of hexagonal sampling is that it resolvesthe nearest neighbor question. As shown in figure 1, the eight neighbors of a pixel are not of equal distance