[...]... range of pattern recognition tasks In the case of speech recognition, the patterns we wish to recognise are spoken words which are audio signals against time Indeed, the value of Markov models to model speech was recognised by Shannon 26 as early as 1948 In the case of hand gesture recognition, the patterns are hand movements in both space and time — we call this a spatio-temporal pattern recognition. .. for all classes and the number of features is restricted to if — 1 The LDA can be extended to include the difference in covariance matrix by using the Chernoff criterion instead of the Fisher criterion 23 4 Error estimation At various stages in the design of a pattern classification system an estimation of the performance of a procedure, or the separability of a set of classes is needed Examples are... behavior of classification systems Some examples of such error curves are: Learning curve : the error as a function of the number of training samples Simple classifiers decrease faster, but have often a higher asymptotic value than more complex ones Complexity curve : the error as a function of the complexity of the classifier, e.g the feature size or the number of hidden units Such a curve often shows... classifiers offer a richer set of tools with more possibilities to learn from examples, thereby bridging the gap between structural and statistical pattern recognition Several problems, however, have still to be solved, like the selection of a representation set, optimal modifications of a given dissimilarity measure and the construction of dedicated classifiers More complicated pattern recognition. .. effective in one-dimensional pattern recognition problems such as speech recognition Research is now focussed on extending HMMs to 2-D and possibly 3-D applications which arise in gesture, face, and handwriting recognition Although the HMM has become a major workhorse of the pattern recognition community, there are few analytical results which can explain its remarkably good pattern recognition performance... E R 1.1 STATISTICAL PATTERN RECOGNITION R.P.W Duin, D.M.J Tax Information and Communication Theory Group Faculty of Electrical Engineering, Mathematics and Computer Science Delft University of Technology P.O.Box 5031, 2600 GA, Delft, The Netherlands E-mail: {R.P W.Duin,D M.J Tax} @ ewi.tudelft.nl A review is given of the area of statistical pattern recognition: the representation of objects and the... performance of a number of alternatives to the traditional Baum-Welch algorithm for learning HMM parameters We then compare the best of these strategies to Baum-Welch on a real hand gesture recognition system in an attempt to develop insights into these fundamental aspects of learning 1 Introduction There is an enormous volume of literature on the application of hidden Markov Models (HMMs) to a broad range of. .. References 1 J.A Anderson Logistic discrimination In P.R Kirshnaiah and L.N Kanal, editors, Classification, Pattern Recognition and Reduction of Dimensionality, volume 2 of Handbook of Statistics, pages 169-191 North Holland, Amsterdam, 1982 2 A.G Arkadev and E.M Braverman Computers and Pattern Recognition Thompson, Washington, D.C., 1966 3 C Bhattacharyya, L.R Grate, A Rizki, D Radisky, F.J Molina,... problem of one-class classification is harder than the problem of conventional two-class classification In conventional classification problems the decision boundary is supported from both sides by examples of both classes Because in the case of one-class classification only one set of data is available, only one side of the boundary is supported It is therefore hard to decide, on the basis of just... conditions Fig 1 confidences The pattern recognition system 5 may increase the class separability, but, may also decrease the statistical accuracy of the training procedure It is thereby important to have a small number of good features In section 3 a review is given of ways to reduce the number of features by selection or by combination (so called feature extraction) The evaluation of classifiers, discussed . Bayes classifiers and approximations A classifier should assign a new object x to the most likely class. In a probabilistic setting this means that the label of the class with the highest posterior. formulation yields an identical shape of w as the expression in (14), although the classifiers use very different starting assumptions! Most classifiers which have been discussed so far, have a . the special case is considered where just one of the classes is reli- ably sampled. The last section, 2.6, discusses the possibilities to combine several (non-optimal) classifiers. 2.1. Bayes