for computational simplicity we use a simple average, but other more sophisticated combination methods could be used. In other words, our final probability estimates are given by $$p_{t}^{(c)}=\frac{1}{w}\sum_{i=1}^{w} p_{t,i}^{(c)} \qquad~\text{for}~t=1,2,\hdots,T. \label{average}$$ In some applications, an overall classification of the signal is required rather than probability estimates. In this case, the class $c$ that has the largest probability $p_{t}^{(c)}$ is assigned to the time point $t$ for all $t \in \{1,2,\hdots,T\}$.

A summary of our method for estimating the probability that a given multivariate signal belongs to a particular class $c$ at a particular time is given in Algorithm \[alg:onlineDC\].

[Online dynamic classification]{}

1.  Let $X$ be a $P$-variate signal of length $T$ that we wish to classify using a moving window of length $w$.

2.  Calculate the set of discriminative indices using a set of P-variate training signals of length $w$, whose class assignments are known.

3.  Apply dynamic classification method to the first window of data $X[~,1:w]$ to obtain the probability that the signal belongs to a particular class $c$ for the time points in the window, denoted $p_{t,1}^{(c)}$ for $t=1,2,\hdots,w$.

4.  Iterate for $i$ in $2$ to $T-w+1$

    (a) Apply the online wavelet transform to the new window 