On the use of i-vector posterior distributions in Probabilistic Linear Discriminant Analysis

The i-vector extraction process is affected by several factors such as the noise level, the acoustic content of the observed features, the channel mismatch between the training conditions and the test data, and the duration of the analyzed speech segment. These factors influence both the i-vector estimate and its uncertainty, represented by the i-vector posterior covariance. This paper presents a new PLDA model that, unlike the standard one, exploits the intrinsic i-vector uncertainty. Since the recognition accuracy is known to decrease for short speech segments, and their length is one of the main factors affecting the i-vector covariance, we designed a set of experiments aiming at comparing the standard and the new PLDA models on short speech cuts of variable duration, randomly extracted from the conversations included in the NIST SRE 2010 extended dataset, both from interviews and telephone conversations. Our results on NIST SRE 2010 evaluation data show that in different conditions the new model outperforms the standard PLDA by more than 10% relative when tested on short segments with duration mismatches, and is able to keep the accuracy of the standard model for long enough speaker segments. This technique has also been successfully tested in the NIST SRE 2012 evaluation

Dimensionality reduction of clustered data sets

We present a novel probabilistic latent variable model to perform linear dimensionality reduction on data sets which contain clusters. We prove that the maximum likelihood solution of the model is an unsupervised generalisation of linear discriminant analysis. This provides a completely new approach to one of the most established and widely used classification algorithms. The performance of the model is then demonstrated on a number of real and artificial data sets

Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction

We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler models at greater speeds. Here an orthogonal basis is treated as a single point on a manifold and is associated with a linear subspace on which observations vary maximally. Throughout this paper, we employ the Grassmann and Stiefel manifolds for various dimensionality reduction problems, explore the connection between the two manifolds, and use Hybrid Monte Carlo for posterior sampling on the Grassmannian for the first time. We delineate in which situations either manifold should be considered. Further, matrix manifold models are used to yield scientific insight in the context of cognitive neuroscience, and we conclude that our methods are suitable for basic inference as well as accurate prediction.Comment: All datasets and computer programs are publicly available at http://www.ics.uci.edu/~babaks/Site/Codes.htm