# Multi dimensionnal Gaussian Mixture Model

I'm a little confused about the GMM. I need to make clusterization. Actually, I have four dimensions : speed in Km/H, mileAge in Km, acceleration in m/s^2 and braking in m/s(^2). Each of those dimensions appears to be a gaussian. But, for each of this distribution, there is only one gaussian (this is not a mixture of gaussians).

As I understand at the beginnig, because all of my dimensions seems like a gaussian, it was perfect to apply the EM algorythm on it (used by the GMM). But, looking deeper, I start to think that I need to have several gaussian for each dimension.

So my question is : When we talk about "mixture of gaussian", it means to have several gaussians in the same dimension or a mixture of dimensions that contains one gaussian ?

• In general GMM is a multiple Gaussians in multiple dimensions. Even if your single dimension (I guess you mean feature/attribute) shows a unimodal distribution, it can happen that there is a multimodal distribution when you consider all the features. – DataD'oh Aug 29 '17 at 11:14

A mixture of Gaussians can be defined as $f(x) = \sum_{i}^{N} p_{i} \exp\big(-\frac{1}{2}(x-\mu_{i})^T\Sigma_{i}^{-1}(x-\mu_{i})\big)$. So it is $N$ Gaussians. The dimension of $x$ and $\mu_{i}$ can be one or bigger than one.