Showing papers on "k-nearest neighbors algorithm published in 1976"

The Distance-Weighted k-Nearest-Neighbor Rule

Abstract: Among the simplest and most intuitively appealing classes of nonprobabilistic classification procedures are those that weight the evidence of nearby sample observations most heavily. More specifically, one might wish to weight the evidence of a neighbor close to an unclassified observation more heavily than the evidence of another neighbor which is at a greater distance from the unclassified observation. One such classification rule is described which makes use of a neighbor weighting function for the purpose of assigning a class to an unclassified sample. The admissibility of such a rule is also considered.

Diffraction pattern and structure of amorphous solid water at 10 and 77 °K

Abstract: X‐ray diffraction data show that there are at least two forms of amorphous solid water which differ in density and second nearest‐neighbor oxygen–oxygen distribution. (a) The lower density form, made at 77 °K, has a diffraction pattern consistent with a structure that has oxygen–oxygen nearest‐neighbor tetrahedral symmetry on average, and a nearest neighbor O–O separation of 2.76 A with small dispersion. The density of this material is estimated to be 0.94 g cm−3. While it is not possible to uniquely define the structure, the data available support the notion that its fundamental characteristic is the existence of a randomized network of hydrogen bonds with O–O–O angular distribution derived from (i.e., centered about) that of ice Ih. Comparison of neutron diffraction and x‐ray diffraction data suggests strongly that the first shell hydrogen bonds are nearly linear and that orientational correlations between water molecules are limited to nearest neighbors. (b) The higher density form, made at 10 °K, has a diffraction pattern similar to, yet distinctively different from, that of the high temperature deposit. The O–O nearest neighbor distance is the same, 2.76 A, but the dispersion in this separation is larger in the low temperature form. The diffraction pattern shows an extra peak at 3.3 A, corresponding to about 1.4 molecules, the existence of which is responsible for the estimated higher density, namely 1.1 g cm−3. The data are consistent with several models which share the feature of introducing small O–O–O angles into the structure. We discuss the relationships between our data, and inferences from the data, and the corresponding data for liquid water.

A Technique to Identify Nearest Neighbors

Abstract: A nonarithmetic procedure is described for discovering among a set of points in a d-dimensional space, the k neighbors nearest a given point, according to the Minkowski "max metric." It is shown that this procedure may be used to eliminate distance calculations when finding nearest neighbors according to any Minkowski p-metric. When used with a set of uniformly distributed sample points, the expected number of distance calculations n required by this technique is given by E[n] ? kCp,d where Cp,d is a constant determined by p and d. In the case of the Euclidean metric used in two dimensions with 1000 uniformly distributed sample points, the effective number of distance calculations required to find the nearest neighbor is approximately five.

Molecular orbital calculations of quadrupolar coupling of 11B in molecular models of glasses

Abstract: SCF–MO calculations have been made for borate glasses using B(OH)3 and BH3 as molecular models. These calculations have shown the triangular configurations to be quite stable with large energies required for out‐of‐plane distortions. Variations in the positions of nearest neighbor triangles or other neighboring charges can cause a spread in quadrupole coupling constant consistent with the experimental data. Smaller spreads in coupling can be brought about by changes in B–O bond lengths within the BO3 triangles. Gross bending of the triangles causes only very small changes in coupling.

The influence of second-nearest neighbor interactions on the thermodynamic properties of B2 phases with substitutional defects

Abstract: In order to explain some discrepancies between the theoretical predictions and the experimental data for the thermodynamic properties of substitutional B 2 phases,Chang's theoretical model is extended by including the influence of second-nearest neighbor interactions. For this purpose a new parameter η is introduced which is defined as the ratio of the interchange energies between second-nearest and first-nearest neighbors. Theoretical equations are derived for the compositional dependence of the activity and the partial molar enthalpy. Using literature data, the following phases are re-evaluated in terms of the disorder parameter α and the newly introduced parameter η: β′-AuZn, β′-AuCd, β′-AgMg, and β′-NiZn. Very good agreement is found between the theoretical curves and the experimental data for the four systems. The values of η obtained range from 0.0 for β′-NiZn to 0.5 for β′-AuZn. The inclusion of second-nearest neighbor interactions has little influence on the values of α. It is shown that the behavior of the activity curve in β′-AuZn can be explained in a physically more meaningful way by including interactions between all second-nearest neighbors rather than interactions between gold substitutional defects only, as was done byLibowitz.

Ground State Spin Configurations of the Triangular Ising Net with the First, Second and Third Nearest Neighbor Interactions

Abstract: The ground states of the triangular Ising system with the first, second and tlurrl nc:trest neighbor interactions, whose interaction constants are denoted by ] 1 , J, and ] 3 , in the absence of an external magnetic field are obtained by the analytical way. It is shown that in the coordinate space of (J1, J2, J,), a total of seven ground states are found and many >otates are degenerated on the boundary planes between domains of those ground stales. Spm configurations of the ground states are shown and the phase diagram of the ground states h g1Yen.

On Finding K Nearest Neighbors in the Plane

Abstract: : The nearest neighbor problem arises in several applications such as density estimation, pattern classification and information retrieval. The problem is to find, among a set of points (or feature vectors), the one which is most similar or closest to a given test point according to some dissimilarity or distance measure. One straightforward way of solving it is to compute the 'distances' between each point of the set and the test point and then search for the point P with minimum distance. The k-nearest neighbor problem to be considered here is a variant of the classical nearest neighbor problem.

Feature Selection and Classification

Abstract: The classification process involves much less computational effort than the foregoing subprocesses which locate the candidate nodule in the lung fields of the radiograph and find its boundary. One can readily specify features to distinguish the different candidate nodule categories as simple functions of the nodule boundary, and great care has been taken to optimize this boundary. For this reason no exotic classification process was required and we used a nearest neighbor classification procedure due to Cover and Hart (1967).

Pressure induced phase transitions of mercury chalcogenides

Abstract: The nearest neighbor dependence of the pressure induced polymorphic phase transitions of mercury chalcogenides have been analyzed. An ionic and a metallic model were used to compute the lattice energies of both low and high pressure phases and the transition pressures of the HgSexTe1−x alloys. It was found that, contrary to the alkali halides, the transition pressure increases experimentally as well as indicated by theoretical calculations with increasing nearest neighbor distance. This is interpreted with the different behavior of the nearest neighbor distances related to the phase transitions. In the case of the alkali halides, although the dimensions of the unit cell decrease in going from the low to the high pressure phase, the nearest neighbor distances increase. However, in the case of the mercury chalcogenides, the trend concerning the unit cell is the same as in the case of the alkali halides, nevertheless the nearest neighbor distances decrease as a result of the pressure induced phase transition...

Variational localized-site cluster expansions. II. Trees and near trees.

Abstract: Cluster expanded wavefunctions involving localized‐site states and only pair excitations between nearest neighbor sites are considered. In the case that the bonds connecting these nearest neighbor sites form a tree graph (without rings), exact matrix element formulas are obtained in terms of the inverse of a modified type of topological matrix associated with this tree graph. The treatment of some near‐tree cases, without any touching rings, is also discussed.

ESR studies of nearest neighbor Cr3+ pairs in MgO

Abstract: Nearest neighbor Cr3+ pairs in MgO have been studied by ESR techniques. The spectrum associated with the S=2 spin state was observed. The appropriate spin Hamiltonian for the system is H=βH⋅g⋅S + Ds{S2z−1/3 S (S+1) }, where the z axis is along 〈110〉. The axially symmetric D tensor was measured to be 0.182±0.009 cm−1, 0.206±0.009 cm−1, and 0.231±0.009 cm−1 for the S=2 spin state. In addition, the temperature dependence of Ds was obtained and was attributed to thermal expansion of the crystal lattice.

Properties of the linear Heisenberg chain with nearest and next-nearest neighbor interactions☆

Abstract: The spectrum and properties of finite chain linear spin- 1 2 Heisenberg models with nearest and next-nearest neighbor interactions have been computed. Closed cyclic chains of up to 12 sites and open linear chains of up to 10 sites have been investigated for a range of ratios of nearest and next-nearest neighbor interactions. Internal energies, specific heats, entropies and susceptibilities all are extrapolated to give accurate infinite chain estimates of these properties.

Generation of low tehmperature series for Ising models with nearest and next nearest neighbor interactions

Abstract: We have generalized the code method of Sykes et al. and applied it to the Ising model with nearest and next nearest neighbor interactions. On the bcc lattice, we have obtained the first seven low temperature polynomials for arbitrary sign of the interactions. Special cases of this model are the Ising ferromagnet and the Ising antiferromagnet with next nearest neighbor ferromagnetic interactions. The latter system exhibits a tricritical point which we plan to study using our low temperature data and high temperature series to be obtained in the future.

Linear Classical Spin Chain with Nearest, Next-Nearest Neighbor and Spin-Lattice Interactions

Abstract: The spin-Peierls transition in the onedimensional, s= 1/2 antiferromagnetic Heisenberg chain with nearest neighbor interactions was investigated by Pytte1' and is recently observed in TTFCuS4 (CF 3) 4 • 2' In 1-D, s= 1/2 antiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interactions the spin-Peierls transition appears in the Hartree-Fock approximation. When the nearest and next-nearest neighbor exchange constants make the energy of the spin wave negative,3' ferromagnetic chains have also the spinPeierls transitions. The spin-phonon coupling effectively causes the alternating of part of the exchange interaction. This causes the change of the phase diagram of the Heisenberg chain. One of the most interesting aspects of the spin-Peierls transition is the spin arrangement in dimerized states. The aim of this paper is to investigate the properties of the ground state of linear classical spin chain with nearest and next-nearest neighbor interactions and spin-lattice interactions. We consider the following Hamiltonian:

Binary mixture with nearest and next nearest neighbor interaction on a one‐dimensional lattice

Abstract: A mixture of two kinds of molecules on a one‐dimensional lattice with free ends is considered. The energy term is assumed to consist of interactions of nearest neighbors and next nearest neighbors and interaction with the uniform external field. The partition function is evaluated by determining the degeneracies.

Charge transfer in electrostatically coupled chains: Effects of the nearest neighbor Coulomb correlations

Abstract: The effects of the nearest neighbor Coulomb correlations on the character of the charge transfer between donor and acceptor molecular chains are investigated. We use a modified Hubbard model for the individual donor and acceptor chains. In this model the intramolecular Coulomb interactions are taken to be infinitely large, and the transfer integrals are considered to be infinitely small. All the intermolecular interactions except those between the nearest neighbors along the chains are treated within the mean field approximation. The free energy of this model can be calculated for an arbitrary strength of the nearest neighbor interaction and results are given for the temperature dependences of the charge transfer and the zero field paramagnetic spin susceptibility.

Excition transport in impure molecular crystals. II. Local defect scattering

Abstract: We derive an exact formula for the exciton propagator in a linear, nearest neighbor coupled molecular crystal containing a single arbitrary local imperfection. This imperfection modifies both the molecular energy (diagonal scattering) as well as the energy transfer between the imperfection site and its nearest neighbors (off‐diagonal scattering). It may be an impurity molecule, a locally misaligned molecule or a local lattice compression. This calculation provides an exact extension of earlier work on single site scattering and of perturbation theory of diagonal and off‐diagonal scattering. For special values of the scattering parameters we also present simplified formulas for the propagator. In all cases however, even in the general exact case, the results are reduced to practical forms, requiring only a simple integration for numerical applications.

Determination of nearest neighbor degeneracy on a one‐dimensional lattice

Abstract: A general method is proposed for the determination of the degeneracy of nearest neighbor pairs on a one‐dimensional lattice. Explicit results are given for the special cases involving two and three kinds of molecules.