Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

Modified Kanerva model. Results for real time word recognition

This paper describes results obtained using the modified Kanerva model to perform word recognition in continuous speech after being trained on the multi-speaker Alvey 'Hotel' speech corpus. Theoretical discoveries have recently enabled us to increase the speed of execution of part of the model by two orders of magnitude over that previously reported by Prager & Fallside. The memory required for the operation of the model has been similarly reduced. The recognition accuracy reaches 95% without syntactic constraints when tested on different data from seven trained speakers. Real time simulation of a model with 9,734 active units is now possible in both training and recognition modes using the Alvey PARSIFAL transputer array. The modified Kanerva model is a static network consisting of a fixed nonlinear mapping (location matching) followed by a single layer of conventional adaptive links. A section of preprocessed speech is transformed by the non-linear mapping to a high dimensional representation. From this intermediate representation a simple linear mapping is able to perform complex pattern discrimination to form the output, indicating the nature of the speech features present in the input window.

Spoken document representations for probabilistic retrieval

This paper presents some developments in query expansion and document representation of our spoken document retrieval system and shows how various retrieval techniques affect performance for different sets of transcriptions derived from a common speech source. Modifications of the document representation are used, which combine several techniques for query expansion, knowledge-based on one hand and statistics-based on the other. Taken together, these techniques can improve Average Precision by over 19% relative to a system similar to that which we presented at TREC-7. These new experiments have also confirmed that the degradation of Average Precision due to a word error rate (WER) of 25% is quite small (3.7% relative) and can be reduced to almost zero (0.2% relative). The overall improvement of the retrieval system can also be observed for seven different sets of transcriptions from different recognition engines with a WER ranging from 24.8% to 61.5%. We hope to repeat these experiments when larger document collections become available, in order to evaluate the scalability of these techniques.