Showing papers on "Dimensionality reduction published in 1975"

An Optimal Set of Discriminant Vectors

Abstract: A new method for the extraction of features in a two-class pattern recognition problem is derived. The main advantage is that the method for selecting features is based entirely upon discrimination or separability as opposed to the more common approach of fitting. The classical example of fitting is the use of the eigenvectors of the lumped covariance matrix corresponding to the largest eigenvalues. In an analogous manner, the new technique selects discriminant vectors (or features) corresponding to the largest "discrim-values." The new method is compared to some of the more popular alternative techniques via both data-dependent and mathematical examples. In addition, a recursive method for obtaining the discriminant vectors is given.

On objectives of methods of ordination

Abstract: The objectives of a number of methods of ordination are examined and a major distinction made between two approaches. The first of these has as a primary objective the efficient redescription of data, and is typified by principal components analysis. However the linear additive model implied in component analysis and the predominance of unique variance, together with lack of scale invariance suggests that other methods of dimensionality reduction might be more appropriate ecologically—either the non-metric methods of multidimensional scaling or the methods of factor analysis. The second approach, typified by Curtis and McIntosh continuum analysis, seeks to order the stands so that the resulting data matrix has a particular form, and is not directly concerned with dimensionality reduction. Continuum analysis is not the only such pathseeking method, and the objectives of several others are briefly examined. Finally the methods of Hill for seriation and the intrinsic dimensionality approach of Trunk seem to provide methods close to those required for the examination of ecological data. Concluding comments are made on problems of interpretation and the effects of sampling and description on the value of the results, especially in the light of the present tendency to employ simulated data to test the efficacy of methods of analysis.

Handwriting synthesis and classification by means of space-variant transform and Karhunen–Loève analysis

Abstract: Optical-pattern-recognition techniques are generally unable to provide an efficient approach to the classification of optical data, because of the linearity of the Fourier transform. A space-variant imaging model is proposed, whose behavior is characterized on the basis of orthonormal polynomials. The optical data are described in an orthonormal space based upon these polynomials. Proper-axis rotation and dimensionality reduction are supplied by the Karhunen–Loeve transform. The intrinsic variables then become available, allowing the clustering of the data (considered as belonging to statistical classes). This work is illustrated by examples of handwriting recognition and classification.

Divergence Analysis of Bendix Feature Extraction and Classification System

Abstract: Many investigators reporting on feature extraction algorithms expect a decrease in recognition accuracy as an inevitable consequence of information loss. A feature extraction procedure is introduced which through empirical study indicates an improvement in recognition rate beyond that of a maximum likelihood classifier while permitting computational economy as a result of dimensionality reduction. Average divergence is shown to have increased after the application of the feature extraction procedure.

A Unified Approach to Feature Selection and Learning in Unsupervised Environments

Abstract: Here the twin problems of feature selection and learning are tackled simultaneously to obtain a unified approach to the problem of pattern recognition in an unsupervised environment. This is achieved by combining a feature selection scheme based on the stochastic learning automata model with an unsupervised learning scheme such as learning with a probabilistic teacher. Test implementation of this scheme using the remotely sensed agricultural data of the Purdue laboratory for agricultural remote sensing (LARS) in a simulated unsupervised mode, has brought out the efficacy of this integrated system of feature selection and learning.

Suboptimal method of feature selection and ordering for multiclass problems

Abstract: Feature extraction remains a problem in pattern recognition, and the letter describes a method of weighting features so that the significant parameters of the input patterns are emphasised. This enables dimensionality reduction to take place without loss of information necessary to distinguish between classes.

Dimensionality reduction in multivariable stochastic systems

Abstract: The transfer function matrix of a large multi-input/multi-output linear stochastic time-invariant control system may be computationally difficult to estimate and, further, may not provide a good interpretation of the underlying structure of the system. Priestley, Rao and Tong (1073) have suggested a method, using information theoretic and statistical criteria, for reducing the dimensions of such a system, and thus, to some extent, overcoming these difficulties. The authors have undertaken a computational study of the application of this theory, illuminating the problems encountered, and demonstrating the feasibility of the method in practice.

Dimensionality reduction in multivariable stochastic systems Application to a chemical engineering plant

Abstract: The transfer function matrix of a largo multi-input/multi-output linear stochastic time-invariant control system may be computationally prohibitive to estimate and may not provide a good interpretation of the underlying structure of the system. Priestley, Rao and Tong have suggested a method, using information theoretic and statistical criteria, for reducing the dimensions of the system, and thus, to some extent, overcoming these difficulties. The feasibility of these methods has already been shown using a simulated control system : its practicality in the real situation is now demonstrated on a relatively small data set taken on a multi-input/multi-output system, a chemical engineering plant.