Showing papers on "k-nearest neighbors algorithm published in 1975"

A Branch and Bound Algorithm for Computing k-Nearest Neighbors

Abstract: Computation of the k-nearest neighbors generally requires a large number of expensive distance computations. The method of branch and bound is implemented in the present algorithm to facilitate rapid calculation of the k-nearest neighbors, by eliminating the necesssity of calculating many distances. Experimental results demonstrate the efficiency of the algorithm. Typically, an average of only 61 distance computations were made to find the nearest neighbor of a test sample among 1000 design samples.

An Algorithm for Finding Nearest Neighbors

Abstract: An algorithm that finds the k nearest neighbors of a point, from a sample of size N in a d-dimensional space, with an expected number of distance calculations is described, its properties examined, and the validity of the estimate verified with simulated data.

An algorithm for a selective nearest neighbor decision rule (Corresp.)

Abstract: A procedure is introduced to approximate nearest neighbor (INN) decision boundaries. The algorithm produces a selective subset of the original data so that 1) the subset is consistent, 2) the distance between any sample and its nearest selective neighbor is less than the distance from the sample to any sample of the other class, and 3) the subset is the smallest possible.

Distribution-free exponential error bound for nearest neighbor pattern classification

Abstract: The rate of convergence of the nearest neighbor (NN) rule is investigated when independent identically distributed samples take values in a d -dimensional Euclidean space. The common distribution of the sample points need not be absolutely continuous. An upper bound consisting of two exponential terms is given for the probability of large deviations of error probability from the asymptotic error found by Cover and Hart. The asymptotically dominant first term of this bound is distribution-free, and its negative exponent goes to infinity approximately as fast as the square root of the number of preclassified samples. The second term depends on the underlying distributions, but its exponent is proportional to the sample size. The main term is explicitly given and depends very weakly on the dimension of the space.

Low-frequency approach to target identification

Abstract: This paper presents a low-frequency method for target identification, and its effectiveness is demonstrated for a large variety of objects varying in complexity from spheres and cubes to modern airplanes. The selection of an appropriate discrete set of frequencies led to a low misclassification error. A number of classification methods are examined using this discrete set of frequencies. It is shown that simple objects can be adequately classified by a linear discriminant method. For more complex targets, such as aircraft, a nearest neighbor approach is required. The introduction of phase and orthogonal polarization components further decreased misclassification error. A discussion of the tradeoff between the increased complexity and improved performance of various classification alternatives is provided.

Lattice statistics using Toeplitz matrices

Abstract: A new technique is presented for the exact calculation of both low and high density virial coefficients for lattice gases. The virial coefficients are given directly in terms of matrix products using symmetry reduced matrices as elements in a Toeplitz hypermatrix. The technique is applied to the plane−square lattice with nearest neighbor exclusion and next nearest neighbor attraction between particles. Eleven terms are given as explicit functions of the particle interaction energy in both the high and low density virial series; two variants of the basic model are also treated. For the hard core high density series, 14 virial coefficients are calculated exactly.

Ground State Spin Configurations of the Triangular Ising Net with the Nearest and Next Nearest Neighbor Interactions

Abstract: The ground states of the triangular Ising system with the nearest and next nearest neighbor interactions are obtained by the analytical way. It is pointed out that the ground state with 4×4 repeating unit cell exists besides the ground states obtained by Metcalf with the use of computer simulation.

ESR studies of the Cr3+ pair in MgO

Abstract: Next nearest neighbor Cr3+ pairs in MgO single crystals have been studied by ESR techniques. The spectra associated with the spin states S = 1 and S = 2 were observed. The appropriate spin Hamiltonian for the system is H = β H⋅g⋅S + J S1⋅S2 − j (S1⋅S2)2 + Ds{Sz2 − (1/3) S (S + 1) }, where the z axis is along 〈100〉. The axially symmetric D tensors were measured to be Ds = 0.360 cm−1 and Ds = 0.105 cm−1 for S = 1 and S = 2 states, respectively. From the study of intensity change of the resonance line as a function of temperature, the isotropic exchange coupling constant J = 83.3 cm−1 and j = 17.9 cm−1 were also determined. In addition, the temperature dependence of Ds was obtained and was attributed to thermal expansion of the crystal lattice.

k-Nearest-Neighbor Decision Rule Performance in a Speech Recognition System

Abstract: This correspondence estimates the risks of k-nearest-neighbor decision rules on classification of vocal utterances. The data are available upon request.

Effect of biquadratic exchange on two magnon states of Heisenberg ferromagnets: other neighbor exchange

Abstract: We have investigated the two magnon localized states of a one dimensional Heisenberg ferromagnet the Hamiltonian of which is made up of nearest neighbor and next nearest neighbor isotropic bilinear and biquadratic exchange terms, and a single ion anisotropy term. We have restricted our choice of parameters so that the ground state at T = 0 is the fully aligned ferromagnetic state and we have used the thermodynamic Green functions where the averages have been evaluated in the ground state so that our results are good for . We have evaluated the probabilities of finding two spin deviations a distance n apart when the system is in a localized state described by total wave vector q. We have (a) compared the effects of ferromagnetic and antiferromagnetic next nearest neighbor exchange, (b) found that localized modes can lie below or above the two free magnon band depending upon the sign and magnitude of the biquadratic exchange, (c) found that in certain cases two spin deviations appear to behave like objects ...

Relation of the thermodynamic properties of a closed chain of classical spins with arbitrary isotropic nearest-neighbor exchange to the nearest-neighbor spin-correlation functions

Abstract: Explicit relations between the energy and specific heat and the various types of nearest-neighbor two-spin-correlation functions are obtained for a closed chain of classical spins with arbitrary isotropic nearest-neighbor exchange.

Sequence-dependent properties of DNA. Optimization of empirical parameterizations

Abstract: Some physical properties of DNA can be expressed reasonably as an expansion of the interaction among base pairs. For strictly random sequences, the terms of the expansion can be rearranged in such a way that an empirical parameterization of the nearest neighbor truncation is in fact correct to all orders. A parameterization obtained from data on real native DNA's is shown to be more accurate than the term “nearest neighbor approximation” implies. When synthetic polynucleotide duplexes are used in the parameterization, the degree of its accuracy depends on the selection of duplexes. It is shown here how to optimize such a parameterization for a given set of available duplexes.

Percolation on a Cayley tree with second nearest neighbor bonds

Abstract: We derive the critical concentration for site percolation on a Cayley tree ’’decorated’’ with second nearest neighbor bonds. For a tree with connectivity K the result is ccrit =〈1+K−[(1+K)2−4K]1/2〉/2K.