From the point of view of coupled systems developed by Stewart, Golubitsky and Pivato, lattice differential equations consist of choosing a phase space R for each point in a lattice, and a system of differential equations on each of these spaces R such that the whole system is translation invariant. The architecture of a lattice differential equation specifies the sites that are coupled to each...

For a classification problem described by the joint density P (ω,x), models of P (ω = ω′|x, x′) (the “Bayesian similarity measure”) have been shown to be an optimal similarity measure for nearest neighbor classification. This paper analyzes demonstrates several additional properties of that conditional distribution. The paper first shows that we can reconstruct, up to class labels, the class po...

Using the theory of coupled cell systems developed by Stewart, Golubitsky, Pivato and Török, we consider patterns of synchrony in four types of planar lattice dynamical systems: square lattice and hexagonal lattice differential equations with nearest neighbour coupling and with nearest and next nearest neighbour couplings. Patterns of synchrony are flow-invariant subspaces for all lattice dynam...

The accuracy of the k-nearest neighbor algorithm depends on the distance function used to measure similarity between instances. Methods have been proposed in the literature to learn a good distance function from a labelled training set. One such method is the large margin nearest neighbor classifier that learns a global Mahalanobis distance. We propose a mixture of such classifiers where a gati...

We show how to pretrain and fine-tune a multilayer neural network to learn a nonlinear transformation from the input space to a lowdimensional feature space in which K-nearest neighbour classification performs well. We also show how the non-linear transformation can be improved using unlabeled data. Our method achieves a much lower error rate than Support Vector Machines or standard backpropaga...

The nearest neighbor (NN) approach is a powerfd nonparametric technique for pattern classification tasks. In this paper, algorithms for prototype reduction, hierarchical prototype organization and fast NN search are described. To remove redundant category prototypes and to avoid redundant comparisons, the algorithms exploit geometrical information of a given prototype set which is represented a...

Molecular dynamics (MD) has been used to identify the relative distribution of dysprosium in the phosphate glass DyAl(0.30)P(3.05)O(9.62). The MD model has been compared directly with experimental data obtained from neutron diffraction to enable a detailed comparison beyond the total structure factor level. The MD simulation gives [Formula: see text] correlations at 3.80(5) and 6.40(5) Å with r...

A fast nearest neighbor algorithm for pattern classiication is proposed and tested on real data. The patterns (points in d-dimensional Euclidean space) are sorted along a space-lling curve. This way the multidi-mensional problem is compressed to the simplest case of the nearest neighbor search in one dimension.

We present results on executing point location queries in well-shaped meshes in R and R using the Jumpand-Walk paradigm. If the jump step is performed on a nearest-neighbour search structure built on the vertices of the mesh, we demonstrate that the walk step can be performed in guaranteed constant time. Constant time for the walk step holds even if the jump step starts with an approximate near...

When applied to supervised classification problems, dataset complexity determines how difficult a given dataset to classify. Since complexity is a nontrivial issue, it is typically defined by a number of measures. In this paper, we explore complexity of three gene expression datasets used for two-class cancer classification. We demonstrate that estimating the dataset complexity before performin...