Taiho Kanaoka

A note on the orthonormal discriminant vector method for feature extraction

Abstract We propose a new feature extraction method based on the modified “plus e -take away f” algorithm and discuss an aspect of the optimization method used in sequential feature extraction, by comparing the proposed method with the orthonormal discriminant vector (ODV) method which belongs to a class of sequential feature extraction. It is shown from experimental results that the proposed method is superior to the ODV method in terms of the error probability.

Evaluation of the branch and bound algorithm for feature selection

Abstract Narendra and Fukunaga show that the branch and bound algorithm guarantees the optimal feature subset without evaluating all possible feature subsets, if the criterion function used satisfies the ‘monotonicity’ property. In this paper, we show that the algorithm works well in terms of the recognition rate, even if the property is not satisfied.

On a theoretical comparison between the orthonormal discriminant vector method and discriminant analysis

Abstract The performance of the orthonormal discriminant vector (ODV) method is discussed in comparison with discriminant analysis. The ODV method produces the features which maximize the Fisher criterion subject to the orthonormality of features. In contrast with discriminant analysis, the ODV method has no limitation on the maximum number of features to be extracted. From a theoretical viewpoint, it is proved that the ODV method is more powerful than discriminant analysis in terms of the Fisher criterion. The theoretical conclusion is experimentally verified using two real data sets.

Evaluation of artificial neural network classifiers in small sample size situations

Small-training sample size problems in artificial neural network classifier design are discussed. A comparison of the artificial neural network (ANN) and nonparametric statistical classifiers in small sample size situations is also presented in terms of the error probability.

A searching method of the most similar string in the file of a document retrieval system

To obtain a required document from the uncertain string information inputted by the user in a document retrieval system or an electronic filing system, the string most similar to the inputted string must be searched. This paper assumes the most general case, where no constraint is imposed on the input error and discusses the efficient method of search for the string in the file which is the most similar to the inputted string. The tree structure is considered to be data structure. The string in the file corresponds to the leaf of the tree. Other vertices of the tree correspond to a string constructed from the set of strings below those vertices as a representative element. The classification of the set of strings is made based on the similarity between strings. A simulation is executed using 100 to 1000 English words as the strings in the file. The search probability of the string most similar to the input string, as well as the search efficiency based on the number of similarity calculations, are examined to evaluate the usefulness of the proposed method.

Orthogonal discriminant analysis for interactive pattern analysis

In general, a two-dimensional display is defined by two orthogonal unit vectors. In developing the display, discriminant analysis has the shortcoming that, in general, the extracted axes are not orthogonal. In order to overcome this shortcoming, the authors propose a discriminant analysis which provides an orthonormal system in the transformed space. The transformation preserves the discriminatory ability in terms of the Fisher ratio. The authors present a necessary and sufficient condition under which discriminant analysis in the original space provides an orthonormal system. Relationships between orthogonal discriminant analysis and the Karhunen-Loeve expansion in the original space are investigated.<<ETX>>

Orthogonal discriminant analysis based on a modified Fisher criterion (feature extraction)

The modified Fisher criterion takes into consideration the difference of covariance matrices. It is shown from experimental results that the proposed method is superior to the orthonormal discriminant vector and the Fehlauer-Eisenstein methods in terms of the error probability.<<ETX>>

Learning behavior of variable-structure stochastic automata in a three-person zero-sum game

The learning behavior is investigated. The game has three variable-structure stochastic automata and a random environment. In the game the players do not possess prior information concerning the payoff matrix, and at the end of every play all the players update their own strategies on the basis of the response from the random environment. Under such situations, if a payoff matrix satisfies some conditions, it can be shown that the learning behavior of the automata converges to the optimal strategies.

Use of gradated patterns in an associative neural memory for invariant pattern recognition

Distortion invariant pattern recognition is an interesting problem from the biological and technological point of view. However, it has not yet been solved by neural networks in satisfactory way. This paper investigates an associative neural network system to improve the recalling accuracy for distortion patterns. On a perception type of neural network with feedback, error back-propagation algorithm and energy function are used for a learning process and a recalling process, respectively. By using gradated patterns as learning and unknown patterns, it is shown that the recalling accuracy becomes higher than using original pattern themselves.

Homogeneous decomposition of stochastic systems

Abstract Recently, concerning the homogeneous whirl decomposition of stochastic systems, Kikuchi and Fujino (1978) have suggested a decomposition theory (for any stochastic system) using the technique of ‘state splitting’. However, their theory has the weak point that in the component stochastic system there exist several components whose transition matrices are pseudostochastic. In order to solve such a problem, this paper proposes a method to decompose any n -state ( n ⩾3) stochastic system into m ( m ⩾2) r -state (2⩽ r n ) q -neighbour (1⩽ q ⩽ m −1) component stochastic systems whose transition matrices are nonpseudostochastic.