I am trying to use a hidden Markov model (HMM) for a problem where I have M states and several independent training sets in Matlab. Each observation in each training set can be allocated to a state, so the states are not hidden as such.
My question is how can i concatenate/join/use each independent training set to train the model and estimate the transition probabilities of the M states? Preferable using Matlab.
Thanks
Not sure if I understood well your question or not. But there is no assumption about the training data in an HMM. The HMM training procedure considers every training sequence as independent with respect to the others.
So, I guess that if you want to represent your different training sets by a unique HMM, you just have to consider your data set as a unique training set. The way the data has to be formatted depends on the function/toolbox you are using for the training.
If using Matlab, you should have a look to the toolbox developed by Kevin Murphy (PTMK Toolbox) that is publicly available and easy to use.
However, if you already know the states of each data sample, and if you are only looking at the transition matrix, you should be able to compute it by hand. It is just a probability computation. (Remember that HMM works with the assumption that the state at time (t+1) only depends on the state at time t, and is totally independent of all the previous states.)