ROUGH · Applications of the theory of rough paths to speech recognition
6РП — Действия „Мария Кюри“
- Период
- 2006-01-01 → 2007-12-31
- Финансиране от ЕС
- 78 710 €
- Участници
- 1
- Схема
- IRG
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Накратко на български
Динамичните системи, като реакцията на автомобил при спиране, се анализират чрез нов математически метод за работа с бързо променящи се данни. Това помага да се предвиди как една система ще реагира на външни влияния, дори когато те са нестабилни.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Final Activity Report Summary - ROUGH (Applications of the theory of rough paths to speech recognition)
Suppose that you are driving a car and you suddenly see an obstacle in front of you. To avoid it, you turn the wheel and press the break. How is the car going to react? The change in the velocity of the car (the 'response' or the 'output') will depend on its current velocity and will be proportional to the changes in the forces that drive the car, caused by the wheel and the break. This is an example of a dynamical system driven by different forces (input). Most 'input - output' or 'driving force - response' systems, either in nature or man-made, can be modelled in this way - we call them dynamical system. But how does the change in the output depend on its current state? Answering this question is vital for making predictions on how a dynamical system will react to a change and can be rather involved, depending on the dimensions or the input and output and the properties of the input. We have developed a method for estimating the dependence of the change on the current state for a large class of systems, assuming that we know the driving forces. Our method is very general and can tackle situations that have not been considered before: in particular, our method can be applied even when the input is 'rough', i.e. changes very fast (this can be made mathematically precise).
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
We propose a novel approach to speech recognition, using new tools from stochastic analysis (the theory of rough paths) and machine learning theory (diffusion maps).The goals of this research are:(i) to develop new algorithms for speech recognition,(ii) t o advance our understanding of the mathematical tools to be used for this purpose and(iii) through this research, to create the conditions for the smooth re-integration of the researcher in the European mathematical community.We model the speech recognition process as a multi-scale dynamical system. The lowest scale consists of the acoustic signal and its delays driving a distribution on the set of phonemes, which in turn drives a distribution on the set of words and so on.We are mainly interested in the lowest scale. According to the theory of rough paths, all the information should be contained in the first p iterated integrals, where p is the roughness" of the signal. The first problem is how to estimate p from a discrete sample of the signal. One way is to look at the rate of decay of the iterated integrals. Another way is to treat the signal as a discrete signal and look for the q for which p-variation becomes "negligible". By considering the first p iterated integrals, we have embedded the signal in a much bigger space. Note though that we are only interested in a particular response, namely the distribution on the phonemes. We need to find those components that contain this information.To do this, we use a database of speech signals for which this response is known. Using a metric on the responses, we define a "kernel on similarity" on the samples, which we use to construct the diffusion map. These can be extended to all speech signals and be used to define a distance compatible with the known responses. The above methodology can be generalized to any case where we need to find those characteristics of a rough signal that cause a particular type of response."
Оригинален текст от CORDIS (на английски).
Участници
- UNIVERSITY OF WARWICK · COVENTRYКоординаторОбединеното кралство
Връзки
Данни: CORDIS, © Европейски съюз