Frame-Based Cluster Purification Metrics

In order to detect and filter out the non-speech frames using the detected likelihood property of the non-speech data, two variants of a likelihood-based metric are proposed.

$$\bar{\mathcal{L}}(x[i] \vert \Theta_{A}) = \frac{1}{Q} \sum_{j=-... ...-1} \sum_{m=1}^{\widetilde{M}} log\Big(W_{A}[m] \mathcal{N}_{A,m}(x[i+j])\Big)$$ (4.15)

The two metrics are based in equation 4.15 where $Q$ defines the length of an average window and is used to average the measure around the desired value to avoid noisy values; $\widetilde{M}$ is the number of Gaussian mixtures used to compute the likelihood (where $\widetilde{M} < M$, the number of mixtures in the model); $W_{A}[m]$ is the mixture weight and $\mathcal{N}_{A,m}(x[i+j])(x[\cdot])$ is the result of evaluating $x[\cdot]$ on the Gaussian mixture $\mathcal{N}_{A,m}(x[i+j])$:

Metric 1

A standard smoothed likelihood over 100ms of data ($Q=5$ with 10ms acoustic frames) around each acoustic frame, with $\widetilde{M} = M$ (all mixtures in model $\Theta_{A}$).

Metric 2

The same smoothed likelihood (over 100ms) given a model formed by a subset of all Gaussian mixtures in the speaker model, which include the mixtures assigned to non-speech. The mixtures used are selected by computing the sum of variance over all dimensions and selecting those with smaller accumulated variance, $\widetilde{M}=M_{non-speech}$. This second metric is equivalent to metric 1 when 100% of the Gaussian mixtures are selected.