Incremental Linear Discriminant Analysis Using Sufficient Spanning Sets and Its Applications

This paper presents an incremental learning solution for Linear Discriminant Analysis (LDA) and its applications to object recognition problems. We apply the sufficient spanning set approximation in three steps i.e. update for the total scatter matrix, between-class scatter matrix and the projected data matrix, which leads an online solution which closely agrees with the batch solution in accuracy while significantly reducing the computational complexity. The algorithm yields an efficient solution to incremental LDA even when the number of classes as well as the set size is large. The incremental LDA method has been also shown useful for semi-supervised online learning. Label propagation is done by integrating the incremental LDA into an EM framework. The method has been demonstrated in the task of merging large datasets which were collected during MPEG standardization for face image retrieval, face authentication using the BANCA dataset, and object categorisation using the Caltech101 dataset. © 2010 Springer Science+Business Media, LLC.

Semantic Discriminant mapping for classification and browsing of remote sensing textures and objects

We present a new approach based on Discriminant Analysis to map a high dimensional image feature space onto a subspace which has the following advantages: 1. each dimension corresponds to a semantic likelihood, 2. an efficient and simple multiclass classifier is proposed and 3. it is low dimensional. This mapping is learnt from a given set of labeled images with a class groundtruth. In the new space a classifier is naturally derived which performs as well as a linear SVM. We will show that projecting images in this new space provides a database browsing tool which is meaningful to the user. Results are presented on a remote sensing database with eight classes, made available online. The output semantic space is a low dimensional feature space which opens perspectives for other recognition tasks. © 2005 IEEE.

Development of the 2003 CU-HTK conversational telephone speech transcription system

This paper describes the development of the 2003 CU-HTK large vocabulary speech recognition system for Conversational Telephone Speech (CTS). The system was designed based on a multi-pass, multi-branch structure where the output of all branches is combined using system combination. A number of advanced modelling techniques such as Speaker Adaptive Training, Heteroscedastic Linear Discriminant Analysis, Minimum Phone Error estimation and specially constructed Single Pronunciation dictionaries were employed. The effectiveness of each of these techniques and their potential contribution to the result of system combination was evaluated in the framework of a state-of-the-art LVCSR system with sophisticated adaptation. The final 2003 CU-HTK CTS system constructed from some of these models is described and its performance on the DARPA/NIST 2003 Rich Transcription (RT-03) evaluation test set is discussed.

Sound transmission in strongly-curved slowly-varying cylindrical and annular lined ducts with flow

In this paper we consider the propagation of acoustic waves along a curved hollow or annular duct with lined walls. The curvature of the duct centreline and the wall radii vary slowly along the duct, allowing application of an asymptotic multiple scales analysis. This generalises Rienstra's analysis of a straight duct of varying cross-sectional radius. The result of the analysis is that the modal wavenumbers and mode shapes are determined locally as modes of a torus with the same local curvature, while the amplitude of the modes evolves as the mode propagates along the duct. The duct modes are found numerically at each axial location using a pseudo-spectral method. Unlike the case of a straight duct, there is a fundamental asymmetry between upstream and downstream propagating modes, with some mode shapes tending to be concentrated on either the inside or outside of the bend depending on the direction of propagation. The interaction between the presence of wall lining and curvature is investigated in particular; for instance, in a representative case it is found that the curvature causes the first few acoustic modes to be more heavily damped by the duct boundary than would be expected for a straight duct. Analytical progress can be made in the limit of very high mode order, in which case well-known 'whispering gallery' modes, localised close to the wall, can be identified.

Automatic transcription of conversational telephone speech

This paper discusses the Cambridge University HTK (CU-HTK) system for the automatic transcription of conversational telephone speech. A detailed discussion of the most important techniques in front-end processing, acoustic modeling and model training, language and pronunciation modeling are presented. These include the use of conversation side based cepstral normalization, vocal tract length normalization, heteroscedastic linear discriminant analysis for feature projection, minimum phone error training and speaker adaptive training, lattice-based model adaptation, confusion network based decoding and confidence score estimation, pronunciation selection, language model interpolation, and class based language models. The transcription system developed for participation in the 2002 NIST Rich Transcription evaluations of English conversational telephone speech data is presented in detail. In this evaluation the CU-HTK system gave an overall word error rate of 23.9%, which was the best performance by a statistically significant margin. Further details on the derivation of faster systems with moderate performance degradation are discussed in the context of the 2002 CU-HTK 10 × RT conversational speech transcription system. © 2005 IEEE.

Linear dimensionality reduction: Survey, insights, and generalizations

© 2015 John P. Cunningham and Zoubin Ghahramani. Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, sufficient dimensionality reduction, undercomplete independent component analysis, linear regression, distance metric learning, and more. This optimization framework gives insight to some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This simple optimization framework further allows straightforward generalizations and novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox, objective-agnostic numerical technology.