How to get a good initial guess of the means for continuous Hidden Markov Models?

I'm currently implementing the continuous HMMs to recognize eating gestures during meal. My question is that I have read Rabiner's paper on continuous HMMs. (See link's here Some Properties of continuous HMM Representations). He mentioned that,

Continuous HMMs characterized by mixture densities are most sensitive to the means of each mixture density.

I agree with that but cannot find any specific method to "choose" a good initial guess of the mean.

For my knowledge, I know that for continuous HMMs, mostly we use GMM to model the emission (observation) density of each state $j$:

$$b_j(x) = \sum_{m=1}^M c_{jm}*N(x,\mu_{jm}, U_{jm}),\qquad j=1, ..., N$$

where $M$ is the number of Gaussians to model the emission probability, $\mu$ and $U$ is the mean and covariance of each Gaussian. We can use clustering methods to form the initial guess of Gaussian distributions per state, such as k-means or random (choose center randomly from data).

I prefer k-means but have no idea of how many clusters are appropriate for k-means.

I would like to visually check the distribution of the observation sequence but it's high dimension (5 dimension). Does anyone have any advice of either visually checking the distribution or other methods of determining the number of clusters? Or how to get good initial guess of the mean for HMMs?

• Come on! Can anyone help me? I think this problem is quite common for continuous HMMs! – Yiru Shen Sep 29 '16 at 16:58