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Hidden Markov models (HMMs) have been widely used to model speech signals for speech recognition. However, they cannot precisely model the time dependency of feature parameters. In order to overcome this limitation, several researchers have proposed extensions, such as segmental unit input HMM (Nakagawa & Yamamoto, 1996). Segmental unit input HMM has been widely used for its effectiveness and tractability. In segmental unit input HMM, the immediate use of several successive frames as an input vector inevitably increases the number of dimensions. The concatenated vectors may have strong correlations among dimensions, and may include nonessential information. In addition, high-dimensional data require a heavy computational load. Therefore, to reduce dimensionality, a feature transformation method is often applied. Linear discriminant analysis (LDA) is widely used to reduce dimensionality and a powerful tool to preserve discriminative information. LDA assumes each class has the same class covariance. However, this assumption does not necessarily hold for a real data set. In order to remove this limitation, several methods have been proposed. Heteroscedastic linear discriminant analysis (HLDA) could deal with unequal covariances because the maximum likelihood estimation was used to estimate parameters for different Gaussians with unequal covariances. Heteroscedastic discriminant analysis (HDA) was proposed as another objective function, which employed individual weighted contributions of the classes. The effectiveness of these methods for some data sets has been experimentally demonstrated. However, it is difficult to find one particular criterion suitable for any kind of data set. In this chapter we show that these three methods have a strong mutual relationship, and provide a new interpretation for them. Then, we present a new framework that we call power linear discriminant analysis (PLDA) (Sakai et al., 2007), which can describe various criteria including the discriminant analyses with one control parameter. Because PLDA can describe various criteria for dimensionality reduction, it can flexibly adapt to various environments such as a noisy environment. Thus, PLDA can provide robustness to a speech recognizer in realistic environments. Moreover, the presented technique can combine a discriminative training, such as maximum mutual information (MMI) and minimum phone error (MPE). Experimental results show the effectiveness of the presented technique. O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

Feature Transformation Based on Generalization of Linear Discriminant Analysis