HMM topology

[Jiahn K]

What is topology exactly? Would it be right if I understand it as different types of how states are connected with arcs with different directions? (e.g. left-to-right model, parallel path left-to-right model and ergodic model)

And is the topology that we’re using for speech is left-to right model and parallel path left-to-right model? I actually don’t quite understand why sometimes Prof.King says transition arcs that is right to left is valid during the lecture.

Thanks!

[Simon]

Yes, you are correct: “topology” just means the shape of the Hidden Markov Model (HMM) = how many states it has and what transitions between them are possible.

For modelling speech, a left-to-right topology is the correct choice. Speech does not time-reverse, the phones in a word must appear in the correct order, etc.

For speech, we do not generally use “parallel path” HMMs, which have transitions that allow some states to be skipped. We use strictly left-to-right models in which the only valid paths pass through all the emitting states in order.

The only exception to this might be an HMM for noise or silence in which we might add some other transitions, or connect all emitting states with all other emitting states with transitions in both directions to make an ergodic HMM.

So, in the general case, an HMM could have transitions between any pair of states, including self-transitions. That’s why, when we derive algorithms for doing computations with HMMs, we must consider all possible transitions and not restrict ourselves to a left-to-right topology.

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