Formulation of problem

Let the signal sequence be $\mbox{\boldmath$X$}= ( \mbox{\boldmath$x$}_t ) (t=1,2,...,T)$ , which is generated by $n$ signal sources, as is shown in Fig.1. It is assumed that the sequence consists of $K$ blocks $\mbox{\boldmath$X$}_k$ $(k=1,2,...,K)$ , and each block is generated from one of $N(\leq K)$ categories $\mbox{\boldmath$C$}_j$ $(j=1,2,...,N)$ . Block $\mbox{\boldmath$X$}_k$ is written as $( \mbox{\boldmath$x$}_{t_{k-1}+1} ... \mbox{\boldmath$x$}_{t_k} )$ (where $t_0 = 0 , t_K = T$), and the time sequence is set as $M_k$ ($=t_k-t_{k-1}$). The unknown-multiple signal source clustering problem is that, where the signal sources are given, to find the block boundaries $t_k (k=1,2,...,K-1)$ based on signal characteristics. The $K$ blocks are to be classified into $N(\leq K)$ categories. Also, the number of categories $N$ is to be estimated.

図 1: Definition of $N$-signal Problem