Showing papers on "Dimensionality reduction published in 1980"
TL;DR: Monte Carlo results presented here further confirm the relatively good performance of non-parametric Bayes theorem type algorithms compared to parametric (linear and quadratic) algorithms and point out certain procedures which should be used in the selection of the density estimation windows for non- Parametric algorithms to improve their performance.
55 citations
TL;DR: It is emphasized that the interactive pattern recognition system ISPAHAN is well suited to find optimal decision functions based on mappings, and two families of new mapping algorithms are defined.
28 citations
9 citations
01 Jan 1980
TL;DR: A new construction of spherepackings using codes is given, which covers the construction of Leech and Sloane and three new alternatives of a construction, which leads to the Leech lattice are given.
Abstract: A new construction of spherepackings using codes is given, which covers the construction of Leech and Sloane [3]. The dense packings of Sloane [10] are also obtained here, but without the use of complex numbers. Several new records on the packing desity in high dimensions are given. In the second part of this paper three new alternatives of a construction, which leads to the Leech lattice . 24 i ~n lR , are g ven.
2 citations
TL;DR: The dual of a convex network problem is constructed and the dimension of the problem is reduced from that of the arc set of the underlying network to that ofthe node set, so that the dual program is unconstrained.
Abstract: A convex network problem is a mathematical program where the objective function is convex and the constraint set is a network with flow conservation at each node. Further there are upper and lower bounds associated with each edge. In this paper, we construct the dual of such a program and hence reduce the dimension of the problem from that of the arc set of the underlying network to that of the node set. Further the dual program is unconstrained. Generally this reduction is significant and in one particular case, the dimension is reduced to unity and hence trivially solvable. The mathematical machinery is provided by the duality theory of generalized geometric programming.
TL;DR: A method is developed for choosing the dimensionality of the patterns using the axes of the feature space as the eigenvectors of matrices of the form R 2 −1 R 1 where R 1 and R 2 are real symmetric matrices.
Abstract: This paper considers the problem of selection of dimensionality and sample size for feature extraction in pattern recognition. In general, the axes of the feature space are selected as the eigenvectors of matrices of the form R 2 −1 R 1 where R 1 and R 2 are real symmetric matrices. Expressions are derived for obtaining the changes in the eigenvalues and eigenvectors when there are changes of first order of smallness in the matrices R 1 and R 2. Based on this theory, a method is developed for choosing the dimensionality of the patterns. Also expressions are derived for the selection of sample size for estimating the eigenvectors, for two gaussian distributed pattern classes with equal means, unequal covariance matrices and with unequal means and equal covariance matrices.