LIST OF SYMBOLS

$$\mbox{\boldmath$x$}$$ input vector

$$\mbox{\boldmath$m$}_i$$ ith reference vector

$$\mbox{\boldmath$m$}_i \mbox{\boldmath$x$}$$ c

$$\mbox{\boldmath$m$}_i \mbox{\boldmath$x$}$$ c'

N number of reference vectors

t discrete time index

h_ci neighborhood function in SOM

$$\alpha$$ learning rate

r neighborhood radius in SOM

D dimension of the input vectors

M dimension of the SOM display

$$\mbox{\boldmath$1$}_r$$ vector of zeros except the rth component is 1

$$\mbox{\boldmath$I$}_i$$ location of the ith SOM unit on the SOM grid

$$p(\mbox{\boldmath$x$}) \mbox{\boldmath$x$}$$

$$\epsilon$$ stabilizing constant factor for LVQ3

C_i ith class in LVQ

M number classes in LVQ

$$g_i(\mbox{\boldmath$x$})$$ discriminant function of the ith class

$$d_k(\mbox{\boldmath$x$}) \mbox{\boldmath$x$} \in C_k$$

$$\mbox{\boldmath$O$}$$ sequence observation vectors of a system

q sequence of states a system undergoes

N number of states in an HMM system

a_ij transition probability from state i to state j

$$b_i(\mbox{\boldmath$O$}_t)$$ output probability density model of state i

$$\pi_i$$ starting probability of state i

$$\lambda$$ description of an HMM

$$\mbox{\boldmath$\mu$}_{jm}$$ mean vector of mth Gaussian in jth codebook

$$\mbox{\boldmath$c$}_{im}$$ weight of mth Gaussian for state i

K number of best matching units used in density approximations

d average quantization error