• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.849-852
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• 2005

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored from is a good estimate of the complexity of a logic function, and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube Boolean subexpression pairs from given expression. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Brayton's co-kernel cube matrix.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.1
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• pp.17-27
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• 2000

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored form is a good estimate of the complexity of a logic function. and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to build an extended co-kernel cube matrix using co-kernel/kernel pairs and kernel/kernel pairs together. The extended co-kernel cube matrix makes it possible to yield a Boolean factored form. We also propose a heuristic method for covering of the extended co-kernel cube matrix. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Brayton's co-kernel cube matrix.

• Journal of the Korea Computer Industry Society
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• v.7 no.4
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• pp.293-298
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• 2006

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored form is a good estimate of the complexity of a logic function, and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube Boolean subexpression pairs from given expression. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Bryton's co-kernel cube matrix.

• Journal of information and communication convergence engineering
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• v.1 no.4
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• pp.209-212
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• 2003

In this paper, we proposed new speech feature parameter through parts-based feature extraction of speech spectrum using Non-Negative Matrix Factorization (NMF). NMF can effectively reduce dimension for multi-dimensional data through matrix factorization under the non-negativity constraints, and dimensionally reduced data should be presented parts-based features of input data. For speech feature extraction, we applied Mel-scaled filter bank outputs to inputs of NMF, than used outputs of NMF for inputs of speech recognizer. From recognition experiment result, we could confirm that proposed feature parameter is superior in recognition performance than mel frequency cepstral coefficient (MFCC) that is used generally.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.49-52
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• 2003

In this paper, we propose new speech feature parameter using NMf(Non-Negative Matrix Factorization). NMF can represent multi-dimensional data based on effective dimensional reduction through matrix factorization under the non-negativity constraint, and reduced data present parts-based features of input data. In this paper, we verify about usefulness of NMF algorithm for speech feature extraction applying feature parameter that is got using NMF in Mel-scaled filter bank output. According to recognition experiment result, we could confirm that proposal feature parameter is superior in recognition performance than MFCC(mel frequency cepstral coefficient) that is used generally.

• ETRI Journal
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• v.39 no.1
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• pp.21-29
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• 2017

This paper addresses the problem of unsupervised speech separation based on robust non-negative matrix factorization (RNMF) with ${\beta}$-divergence, when neither speech nor noise training data is available beforehand. We propose a robust version of non-negative matrix factorization, inspired by the recently developed sparse and low-rank decomposition, in which the data matrix is decomposed into the sum of a low-rank matrix and a sparse matrix. Efficient multiplicative update rules to minimize the ${\beta}$-divergence-based cost function are derived. A convolutional extension of the proposed algorithm is also proposed, which considers the time dependency of the non-negative noise bases. Experimental speech separation results show that the proposed convolutional RNMF successfully separates the repeating time-varying spectral structures from the magnitude spectrum of the mixture, and does so without any prior training.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.299-312
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• 2004

ILUS factorization has many desirable properties such as its amenability to the skyline format, the ease with which stability may be monitored, and the possibility of constructing a preconditioner with symmetric structure. In this paper we introduce a new preconditioning technique for general sparse linear systems based on the ILUS factorization strategy. The resulting preconditioner has the same properties as the ILUS preconditioner. Some theoretical properties of the new preconditioner are discussed and numerical experiments on test matrices from the Harwell-Boeing collection are tested. Our results indicate that the new preconditioner is cheaper to construct than the ILUS preconditioner.

• The Journal of Korean Association of Computer Education
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• v.15 no.1
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• pp.65-72
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• 2012

Generally, a logic function has many factored forms. The problem of finding more compact factored form is one of the basic operations in logic synthesis. In this paper, we present a new method for factoring Boolean functions to assist in educational logic designs. Our method for factorization is to implement two-cube Boolean division with supports of an expression. The number of literals in a factored form is a good estimate of the complexity of a logic function. Our empirical evaluation shows the improvements in literal counts over previous other factorization methods.

• Journal of Computing Science and Engineering
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• v.4 no.2
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• pp.97-109
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• 2010

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, which is to decompose a data matrix into a product of two factor matrices with all entries restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering), but in some cases NMF produces the results inappropriate to the clustering problems. In this paper, we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. The result of orthogonal NMF can be clearly interpreted for the clustering problems, and also the performance of clustering is usually better than that of the NMF. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.

• East Asian mathematical journal
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• v.36 no.2
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• pp.291-315
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• 2020

In this study, the geometric model of 11 factorization formulas presented in the 2015 revised national curriculum was constructed and the necessary mathematical conditions were derived in the process. As a result of the study, all of the 11 factorization formulas are geometrically modeled and 12 conditions are derived in the process. However, the basic method of directly cutting and attaching a given shape was limited to not being able to make a rectangle or rectangular parallelepiped. Therefore, the problem was solved by changing the perspective and focusing on whether rectangle or rectangular parallelepiped with the same area or volume could be constructed.