To group similar pathlets, one must define what ``similar'' means. A common approach for clustering data is to derive a measure of similarity or a distance between a pair of elements.
In a first attempt to cluster the pathlets into groups, we used this approach. We built a similarity measure based on the dynamic time warping algorithm commonly used in speech recognition [76]. A clustering algorithm was then used to find the different groups. The algorithm we used for this approach is described in section 5.4.2.
The approach leads to the potential problem of outliers. Grouping the pathlets with our spatiotemporal model of pathlets requires that no outlier is used during the model building. If an outlier is used, then the mean pathlet is shifted and the distribution around the mean pathlet cannot be properly modelled by a Gaussian. This effect leads to an improper pathlet model for the group containing the outlier.
Furthermore, we need pathlet models that are compact; groups with a wide range of different pathlets are unlikely to be modelled properly. The way pathlets are grouped affects the quality of the resulting pathlet models. One has to group the pathlets so that the models of the resulting groups are ``good''. Since we want compact models of groups that do not contain outliers, we define a ``good'' pathlet model as being a model where the variance of the underlying Gaussian is low. We have derived a new grouping algorithm that takes this specific criterion into account. It is presented in section 5.4.3.