can be then represented as $$\mathbf{X}_{t}=\displaystyle\sum_{j} \displaystyle\sum_{k} \displaystyle\sum_{c=1}^{N_{c}} \mathbb{I}_{c}[C_{X}(k)]\mathbf{V}_{j}^{c}\psi_{j,k}(t)\mathbf{z}_{j,k}, $$ where $\mathbf{V}_{j}^{c}$ is the class specific transfer function which is constrained to be constant over time and $\mathbb{I}_{c}[C_{X}(k)]$ represents an indicator function which equals 1 if $C_{X}(k)=c$ and 0 otherwise.

To classify the multivariate signal $\mathbf{X}_{t}$, the approach makes use of a set of $N_{i}$ training signals, denoted $\big\{Y_{t}^{(i)}\big\}$ for $i \in \{1,2,\hdots,N_{i}\}$. It is assumed that the class membership of these training signals over time, $C_{Y^{(i)}}(t)$, is known. For each training signal, the LWS matrix $\hat{\mathbf{S}}_{jk;Y^{(i)}}$ and coherence matrix $\boldsymbol{\rho}_{jk;Y^{(i)}}$ can be estimated, as discussed in Section \[subsec:MvLSWmodel\].

The aim of this classification method is to calculate the probability of the signal belonging to a particular class at a given time point. To do this, the likelihood of the signal belonging to each class given the information contained in the training signals is calculated. It is necessary to apply a Fisher-z transform to the coherence estimates to ensure that the estimates can be approximated by a Gaussian distribution. For a class $c$, the transformed coherence $\zeta_{j}^{(c)}$ is given by $$\label{eq:fisher}
\zeta_{j}^{(c)}=\text{tanh}^{-1}\rho_{j}^{(c)}.$$ The mean and variance of the transformed coherence for class $c$ can be estimated using the transformed coherence 