If we use one Guassian model, it cannot handle tha data set generated by multi Guassian models, so we introduce GMM -- use multi Gussain models and mix them to one with certain weights. GMM formula Assume GMM is mixed by KK Guassian models, the density fucntion of GMM is: p(X)=∑k...
formula'spark.gaussianMixture(data, formula, k =2, maxIter =100, tol =0.01)## S4 method for signature 'GaussianMixtureModel'summary(object)## S4 method for signature 'GaussianMixtureModel'predict(object, newData)## S4 method for signature 'GaussianMixtureModel,character'write.ml(object, path, ...
Gaussian mixture model is the conventional approach employed in speaker recognition tasks. Although it is efficient to model specific speaking characteristics of a speaker, especially in quiet environments, its performance in noisy conditions is still far from the human cognitive process. Recently, a ...
These statistical Minkowski distances admit closed-form formula for Gaussian mixture models when parameterized by integer exponents: Namely, we prove that these distances between mixtures are obtained from multinomial expansions, and written by means of weighted sums of inverse exponentials of generalized ...
Gaussian Mixture Model
具体来说呢我们在categorical parameter上加上uniform的prior,然后在Gaussian的mean parameter加一个\mathcal{N}(0, +\infty)的prior,然后解出Gibbs sampling的update formula。下面我们稍稍的abuse一下notation,让\mathcal{N}即代表一个distribution,又代表他的pdf。
? ? ? ( ) ( ) Similarly we can get the estimation formula for p i and Σ i : is the probability density function of a single Gaussian component. The parameter for the single component θ i includes the mean vector ? i and covariance matrix Σ i . ? ? i = ∑ (Pi , j ? z ...
We can write the Gaussian mixture model as a latent-variable model: where: the observable variables are conditionally multivariate normal with mean and variance : the latent variables have the discrete distribution for . In the formulae above we have explicitly written the value of the latent vari...
GMM formula has summation (not multiplication) in distribution, and the log likelihood will then lead to complex expression in regularmaximum likelihood estimation (MLE). These 2 methods will then address this concern by procedural iterative algorithms (which approximate the optimal solutions). ...
An important practical benefit of Gaussian modeling comes from formula (4.91), which shows that mutual information takes the form of a criterion of joint diagonality between the covariance matrices Rȳ(τ). Hence, it is straightforward to minimize it by using the appropriate joint diagonalization...