Non-linear Techniques for Dimension Reduction
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National Institute for Standards and Technology
The main goal of the SVM Nuisance Attribute Projection (NAP) method is to reduce the impact of channel variations (called also session variability). It uses an appropriate projection matrix P in the SVM supervector space (a supervector is obtained by concatenating the Gaussian means) to remove the subspace that contains the session variability. s 0 ¼ P s;
ð1Þ
where, s is a GMM supervector. The projection matrix can be written as follow: P ¼ ðI VV t Þ;
ð2Þ
where, V ¼ ½v1 ; :::; vk is a rectangular matrix of low rank whose columns are orthonormal. The vectors vk are obtained from the k eigenvectors having the k largest eigenvalues of the following covariance matrix: ns S 1X 1X si Þð si Þt ð ms m msi m S s ¼1 ns i¼1 i
ð3Þ
si represents the GMM supervector of the ith where m session of the sth speaker. S is the number of speaker in V -Matrix training data. ns is the number of different si is the mean sessions belonging to the sth speaker. m GMM supervector obtained overall the sessions belonging to the sth speaker: si m
ns 1X s : ¼ m ns i¼1 i
▶ Session Effects on Speaker Modeling
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2009 Springer Science+Business Media, LLC
ð4Þ
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1002
N
Near Infrared (NIR)
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NEXUS
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