Gaussian Mixture Models Sample Clauses

Gaussian Mixture Models. ‌ Since human speech is, to some extent, a random phenomenon, probability models are usually used to describe it. When we extract data from a speech record during ASR, we get data samples – feature vectors. These samples are generated by a speaker’s personal speech model and bear signs of a certain probability distribution. The most common and most natural probability model for these purposes is Gaussian distribution (or Normal distribution). The probability density function for GMM is given by the following formula: , Σ ) = 𝑒− 1 (𝑥−𝜇𝑘)𝑇 Σ−1(𝑥−𝜇𝑘)𝑞 𝑘 𝑘 2 𝑘 𝐷 1 (2𝜋) 2 |Σ𝑘| 2 where D is the dimensionality of the feature vector. ” However, because speech is a very inhomogeneous phenomenon, it is usually better to describe the speaker with a greater number of Gaussian models. Such a set of multiple distributions can be merged into one unit, creating the so-called Gaussian Mixture Model ( GMM“). According to [8], GMM is defined as a family of mixture models in which the probability density function of each of has Gaussian distribution. The image 3.3 illustrates a two-dimensional GMM that could be used as a speaker model. After extracting the feature vectors, speech samples of a speaker, whose model is illustrated, would show signs that they were generated by this model. During the ASR, where the speaker’s model described by GMM is considered, we look for the value of likelihood-ratio. It tells us, with what certainty the speech sample was generated by such model. The Likelihood ratio is calculated from the following relationship: ≥ ⇒ 𝑆(𝑋) = 𝑃 (𝑋|𝐻𝑡𝑎𝑟𝑔𝑒𝑡) Φ 𝑡𝑎𝑟𝑔𝑒𝑡 𝑃 (𝑋|𝐻𝑖𝑚𝑝𝑜𝑠𝑡𝑜𝑟 ) | | where 𝑃 (𝑋 𝐻𝑡𝑎𝑟𝑔𝑒𝑡) and 𝑃 (𝑋 ��𝑖𝑚𝑝𝑜𝑠𝑡𝑜𝑟) are the likelihoods of X with the assumption that X is uttered (or is not) by the speaker. If the computed score 𝑆(𝑋) is greater than the threshold Φ, the conclusion is then that the segment X was uttered by the tested speaker (viz [12]).