By thinking of each state in a hidden Markov model as corresponding to some spatial region of a fictitious topology space it is possible to naturally define neighbouring states as those which are connected in that space. The transition matrix can then be constrained to allow transitions only between neighbours; this means that all valid state sequences correspond to connected paths in the topol...

How can we apply machine learning to data that is represented as a sequence of observations over time? For instance, we might be interested in discovering the sequence of words that someone spoke based on an audio recording of their speech. Or we might be interested in annotating a sequence of words with their part-of-speech tags. These notes provides a thorough mathematical introduction to the...

Today’s state-of-the-art speech recognition systems typically use continuous density hidden Markov models with mixture of Gaussian distributions. Such speech recognition systems have problems; they require too much memory to run, and are too slow for large vocabulary applications. Two approaches are proposed for the design of compact acoustic models, namely, subspace distribution clustering hid...

Article history: Received 14 April 2009 Available online 17 November 2009