Theory behind Cluster Decoder

Regression Method and EM Algorithm

Hierarchical Method

Sequential Method

The sequential method is characterized by a first strong hypothesis which supposes that the k states of the signal will follow one after the other without ever reappearing, even if each ones of them can have a different duration. For example, we could have a signal where the states follow each other in this way 1-2-3-4-… but not such as 1-2-1-3-4-2-3-…

The fit method of the sequential algorithm proceeds as follows:

We initialize an error e0 by first assuming an uniform distribution in time of the k states. Thus for each state we will take into account only the relevant part of the X and y which allows us to calculate a decoding matrix for each state. Once this is done, we then calculate the cumulative error on each state by computing the distance between y and X*Wk (Wk the decoding matrix). After that we launch a loop that will do the same thing as before but choosing random distributions of states in time. If the error is smaller we save this distribution then we continue the loop. At the end we obtain a distribution as well as decoding matrices that have minimized the error on Max_iter random draws.