• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• The Journal of the Acoustical Society of Korea
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• v.24 no.4
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• pp.210-216
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• 2005

We Propose a new feature normalization scheme based on eigenspace for achieving robust speech recognition. In general, mean and variance normalization (MVN) is Performed in cepstral domain. However, another MVN approach using eigenspace was recently introduced. in that the eigenspace normalization Procedure Performs normalization in a single eigenspace. This Procedure consists of linear PCA matrix feature transformation followed by mean and variance normalization of the transformed cepstral feature. In this method. 39 dimensional feature distribution is represented using only a single eigenspace. However it is observed to be insufficient to represent all data distribution using only a sin91e eigenvector. For more specific representation. we apply unique na independent eigenspaces to cepstra, delta and delta-delta cepstra respectively in this Paper. We also normalize training data in eigenspace and get the model from the normalized training data. Finally. a feature space rotation procedure is introduced to reduce the mismatch of training and test data distribution in noisy condition. As a result, we obtained a substantial recognition improvement over the basic eigenspace normalization.