The subspace methods of classification are decision-theoretic pattern recognition methods in which each class is represented in terms of a linear subspace of the Euclidean pattern or feature space. In most reported su...
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The subspace methods of classification are decision-theoretic pattern recognition methods in which each class is represented in terms of a linear subspace of the Euclidean pattern or feature space. In most reported subspace methods, a priori criteria have been applied to improve either the class representation or the discriminatory power of the subspaces. Recently, construction of the class subspaces by learning has been suggested by Kohonen, resulting in an improved classification accuracy. A variant of the original learning rule is analyzed and results are given on its application to the classification of phonemes in automatic speech recognition.
A recursive method for finding a hyperplane separating two given finite sets X1 and X2 in Euclidean space En is presented. It is unknown a priori if these two sets are linearly separable. According to the proposed met...
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A recursive method for finding a hyperplane separating two given finite sets X1 and X2 in Euclidean space En is presented. It is unknown a priori if these two sets are linearly separable. According to the proposed method, a certain sequence (ai)i = 1m of nonzero vectors in En + 1 is generated, where m denotes the number of elements in the set X = X1 ∪ X2. If the sets X1 and X2 are linearly separable, then each of the members ai determines a hyperplane Hi ⊂ En separating the subsets Xji = XϵXj:XϵXqq = 1i, j = 1, 2, of the set X = xii = 1m, where (Xi)i = 1m denotes a sequence obtained by arbitrary ordering of X. Thus, to get the information as to whether the considered sets are linearly separable, it is sufficient to check if each of the hyperplanes Hi separates the sets X1i and X2i. If this is the case, then Hm separates X1 and X2. In the opposite case, the procedure of generation of the sequence (ai)i = 1m is stopped when any hyperplane Hi does not separate the sets X1i and X2i. Index i of the recently generated vector ai informs us as to how far the realization of the method is advanced.
A method is presented for finding all vertices and all hyperplanes containing the faces of a convex polyhedron spanned by a given finite set X in Euclidean space E-n. The present paper indicates how this method can be...
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A method is presented for finding all vertices and all hyperplanes containing the faces of a convex polyhedron spanned by a given finite set X in Euclidean space E-n. The present paper indicates how this method can be applied to the investigation of linear separability of two given finite sets X-1 and X-2 in E-n. In the case of linear separability of these sets the proposed method makes it possible to find the separating hyperplane.
A self-supervised learning algorithm using fuzzy set and the concept of guard zones around the class representative vectors is presented and demonstrated for vowel recognition. An optimum guard zone having the best ma...
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A self-supervised learning algorithm using fuzzy set and the concept of guard zones around the class representative vectors is presented and demonstrated for vowel recognition. An optimum guard zone having the best match with the fully supervised performance is determined. Results are also compared with that of nonsupervised case for various orders of input patterns.
We propose a committee machine whose each committee member is a network of two threshold elements. This improves upon the ability of the usual committee machine. The subsidiary discriminant function in this case is a ...
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We propose a committee machine whose each committee member is a network of two threshold elements. This improves upon the ability of the usual committee machine. The subsidiary discriminant function in this case is a kind of piecewise linear discriminant function instead of a linear function. We show a sophisticated representation of the discriminant function realized by the proposed committee machine, and give a rational learning algorithm based on the function. We also show that the proposed committee machine, which is a kind of three-layer network of threshold elements, cannot be equivalently transformed to a two-layer network. This fact asserts that the proposed committee machine provides a family of discriminant functions which is intrinsically wider than that of the usual committee machine.
In order to improve the pattern classification power of the committee machine, a two-level committee machine, which is a committee machine with several lower committees, is proposed and the learning algorithm for it i...
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In order to improve the pattern classification power of the committee machine, a two-level committee machine, which is a committee machine with several lower committees, is proposed and the learning algorithm for it is described. The discriminant function realized by the two-level committee machine can be considered as the general piecewise linear discriminant function which includes Chang's definition. (15) The proposed algorithm is a kind of error-correction procedure, and the learning procedure of the usual committee machine and the perceptron are clearly explained as special cases of the proposed algorithm.
The efficient utilization of a two-level directly executable memory system is investigated. After defining the time and space product resulting from static allocation of the most often referenced pages, from paging, a...
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In general, four-layer series-coupled machines can be divided into two types according to learning methods. One is the machine in which the change of variable connecting coefficients depends upon the state of associat...
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In general, four-layer series-coupled machines can be divided into two types according to learning methods. One is the machine in which the change of variable connecting coefficients depends upon the state of association units in both layers AI and AII. The other type is the machine in which the change depends upon the state of association units in only layer AI. In this paper, four-layer series-coupled machines of the latter type are discussed. They can be classified into six types according to the properties of the units and the learning algorithm. Some mathematical models of the machines are developed in which both excitory and inhibitory stimuli are used. The performance of these models compare favourably with machines in which only excitory stimuli are used. learning procedure in each machine is analyzed and the convergence conditions are derived. Furthermore, some applications of the fourlayer machines to multi-category classification are discussed.
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