Consider a simple classification task with a single continuous channel, such as the three streams shown in figure 3.1. Stream I and II are very similar, except that in stream II the ``hump'' happens a little later. In many domains (though not all) we want to classify I and II as ``similar'' in some sense, and III as belonging to a different class. If we simply compare values at the same time, we get a misleading measure of similarity, since on a time-by-time comparison, stream III is closer (using, for example, a least-squares comparison) to stream I than stream II is.
Figure 3.1: Temporal mismatches
This is because we are ``mismatching'' time in streams I and II. In this particular case, it was caused by delay, but it could have equally been caused by the hump being longer or shorter.
It is certainly possible to try to minimise the mismatch between I and II by stretching. This is very similar in many regards to dynamic time warping as discussed in section 2.3.