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The best warp factor for speaker is estimated by maximizing the likelihood of the warped features with respect to the HMM model and transcriptions : (9).
Initially, the HMM set is trained from unwarped utterances, and this model is used to estimate the best warp factor for each speaker.
Here, we define the following terms as in [7]: (i) denotes the set of feature vectors for all of the available utterances from speaker, warped by warp factor, (ii) denotes the set of transcriptions of all utterances, (iii) denotes the best warp factor for speaker, (iv) denotes a given HMM trained from a large population of speakers.
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Afterwards, every speaker's utterances are parameterized with the estimated best warp factor and then the HMM model set is re-estimated from this warped feature set.
In [13], a Brent search was used in order to efficiently obtain the best warp factor.
However, it was computationally cumbersome and required a substantial amount of speech from each speaker in order to estimate the best warp factor.
First, all utterances from a single speaker are recognized with noncanonical HMM set, and best warp factors are estimated using the result of this recognition.
The procedure employed to estimate the best BLT warp factor for each speaker, on the other hand, has substantial differences.
As mentioned above, Acero used a vector quantization distortion measure in order to estimate the best BLT warp factor for each speaker.
This observation leads to the idea of using a specific self-normalization warp factor for each speaker.
Assume that we have utterances from speaker and would like to estimate the warp factor for this speaker.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com