Speaker biometrics is a field of Speech processing which focuses on identifying a unique speaker from several audio recorings. This can be useful for access control or suspect identification for example. Most of my understanding of this field was built from an excellent thesis, “Speaker Verification using I-vector Features” by Ahilan Kanagasundaram from Queensland University of Technology.

# Overview of Speaker Biometrics

Speaker biometrics is split into:

• Speaker identification: determine an unknown speaker’s identify among a group of speakers
• Speaker verification: verify the claimed identity of a person through speech signal

Speaker verification is used in access security and in suspect identification mainly, and is therefore the most commonly studied problem. This field has been an active field of research since the 1950s.

The main known issues in this field of research are:

• the amount of data needed
• the mismatch between the training data (enrolment) and the testing data (verification)

# Overview of Speaker Verification Techniques

Speech conveys a lot of information:

• the signal itself
• the language spoken
• the emotion
• the gender
• the age
• the identify of the speaker

Speaker verification aims at determining whether the identity of the speaker matches the claimed identify, and requires typically 1 comparison. On the other hand, speaker identification among a group of size N requires N comparisons.

There are 2 types of speaker verification techniques:

• Text-dependant: the speaker must pronounce a known word or phrase. In such case, short training data are enough.
• Text-independent: users are not restricted to say anything specific. In such cas, the training data must be sufficiently long, but the solution is more flexible.

A common example of text-dependant speaker verification would be the “Hey Siri” of most iPhones now. The phrase to pronounce is known in advance, and we must verify the identity of the person. Once the identity has been verified, a Speech-to-Text pipeline translates what the user pronounced into a query.

## Steps

The main steps of speaker verification are:

• Development: learn speaker-idenpendent parameters using large amount of data. This is a pre-training part.
• Enrolment: learn distinct characteristics of a speaker’s voice. This step typically creates one model per unique speaker considered. This is the training part.
• Verification: distinct characteristics of a claimant’s voice are compared with previously enrolled claimed speaker models. This is the prediction part.

The difference between the training and testing data might come from:

• the microphones
• the environment
• the transmission channel (landdline, VoIP…)
• the speaker himself

There are techniques to handle this issue which fall under the umbrella of channel compensation. The methods introduced below are called GMM-UBM, which stands for Gaussian Mixture Model - Universal Background Model.

### Speech acquisition

Speech acquisition is done through Voice Activity Detection (VAD). A common approach is the Gaussian-based VAD. The aim of a VAD is to aquire speech only when it occurs.

The main steps behin building a VAD are:

• Break audio signal into frames
• Extract features from each frame
• Train a classifier on a known set of speech and silence frames
• Classify unseen frames as speech or silence

But this will be the topic of another article. VAD performs well on audio with relatively low signal-to-noice ratio (SNR), a ratio which compares the level of a desired signal to the level of background noise.

### Feature extraction

Once we can efficiently acquire a speech signal, we should extract features from the signal to convert the raw signal into a sequence of acoustic feature vectures which we will use to identify the speaker.

A common choice for the features to extract from the signal is the Mel Frequency Cepstral Coefficients (MFCC). These features are derivedd from Fast Fourier Transform. There are several steps and options for extracting MFCC features, both in time and frequency domains, but again, I’ll dive deeper into this topic in another article.

### A note on Gaussian Mixture Models

For the next sections, we will need to introduce Gaussian Mixture Models (GMMs). A GMM is a weighted sum of M components Gaussian densities.

A density of a Gaussian can be defined as:

Where:

• $x$ is a D-dimensional feature vector
• $w_k, k = 1, 2, …, M$ is the mixture weights
• $\mu_k, k = 1, 2, …, M$ is mean of each Gaussian
• $\Sigma_k, k = 1, 2, …, M$ is the covariance of each Gaussian
• $g(x \mid \mu_k, \Sigma_k)$ are the Gaussian densities such that:

The parameters of the GMM are therefore : $\lambda = (w_k, \mu_k, \Sigma_k), k = 1, 2, 3, ..., M$.

How do we solve GMM? Using Expectation-Maximization (EM) algorithm. EM algorithm is an interative algorithm which, at each steap, tries to update the parameters in order to maximize the likelihood, and eventually finds the maximum likelihood.

Formally, EM algorithm iterative update of the parameters should lead to :

$\prod_{n=1}^N P(x_n \mid \lambda) ≥ \prod_{n=1}^N P(x_n \mid \lambda^{old})$. The maximization problem of the EM algorithm is in fact:

Where :

$P(k \mid x) = \frac{w_k g(x \mid \mu_k, \Sigma_k)}{P(x \mid \lambda^{old})}$.

The starting parameters are usually identified by k-means approach. That being said, let’s get back to the steps of our speaker verification model.

### Universal Background Model : Development

The next step, once we extracted the features, is to train a universal background model (UBM). We train such algorithm because there is typically not enough data available to train the speaker models.

A UBM is a high-order Gaussian Mixture Model trained on a large quantity of speech, from a wide population. This step is used to learn speaker-independent distribution of features.

### Speaker Enrolment

The last step before the verification is to perform the speaker enrolement. The aim is still to train a Gaussian Mixture Model on the extracted features. GMMs are typically solved iteratively by an Expectation Maximization (EM) algorithm, an algorithm which tries to maximize the likelihood of the training data by adjusting the parameters of the GMM.

The issue is always to initialize the parameters of the GMM the right way. Since we pre-trained a GMM in the development step, we simply start the EM algorithm with the parameters learned by the UBM.

Through this step, we only adapt the mean, and not the covariance, since updating the covariance does not improve the performance.

For the mean to update, we perform a maximum a posteriori adaptation :

Where :

• $\alpha_k = \frac{n_k}{n_k + \tau_k}$ is the mean adaptation coefficient
• $n_k$ is the count for the adaptation data
• $\tau_k$ is the relevance factor, between 8 and 32

### Speaker Verification

The Speaker Verification is finally computed using the likelihood ratio, since GMM is a generative model.

We test the following underlying hypothesis:

• $H_0$ : Sample X belongs to claimed speaker s
• $H_1$ : Sample X does not belong to claimedd speaker s

The likelihood ratio is then defined as :

We compare this ratio to a threshold, and if it is greater than the defined threshold, we accept that the sample X belongs to the claimed speaker s.

# Limits of GMM-UBM

Nowadays, GMM-UBM are not state-of-the-art approaches anymore. Indeed, it requires too much training data in general. Better performing approaches have been developed such as :

• SVM-based methods
• I-vector methods
• Deep-learning based methods

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