Dimensionality of the Hidden Space

Dimensionality of the Hidden Space
HBR 180898

For the results shown on this page, we experimented with different dimensionalities for the hidden space.

Each time, we trained the HDM (Hidden Dynamic Model) on the training data shown in Fig 1. We then synthesised a copy of the training data using the same segmentation, and these copies are shown in Figs 2 to 4 for 1 to 3 hidden dynamic parameters respectively.

Conditions:

1-3 hidden parameters.
12 MFCCs for the acoustic representation.
6 vowel/silence target vectors.
Fixed target pliances.
MLP with 40 units in 1 hidden layer.

Fig 1. Spectrogram of original training data.

Fig 2. Reproduction of training data using only one dimension for the hidden space.

Fig 3. Reproduction of training data using two dimensions for the hidden space.

Fig 4. Reproduction of training data using three dimensions for the hidden space.

Firstly, it is obvious that the HDM has serious difficulty reproducing natural transitions using only one hidden dynamic parameter.

Surprisingly, however, two dimensions seems perfectly adequate to represent this vowel data, and little extra detail is afforded by increasing the number of hidden dimensions to three parameters.

The acoustic data is now represented by only two numbers per frame. As the data has been distilled down to only two parameters, perhaps we should not be surprised that these numbers have some phonetic relevance. This hidden dynamic representation is examined on the next page.