Continuous multi-way shape measure for dissimilarity representation

For many applications, a straightforward representation of objects is by multi-dimensional arrays e.g. signals. However, there are only a few classification tools which make a proper use of this complex structure to obtain a better discrimination between classes. Moreover, they do not take into account context information that can also be very beneficial in the classification process. Such is the case of multi-dimensional continuous data, where there is a connectivity between the points in all directions, a particular (differentiating) shape in the surface of each class of objects. The dissimilarity representation has been recently proposed as a tool for the classification of multi-way data, such that the multi-dimensional structure of objects can be considered in their dissimilarities. In this paper, we introduce a dissimilarity measure for continuous multi-way data and a new kernel for gradient computation. It allows taking the connectivity between the measurement points into account, using the information on how the shape of the surface varies in all directions. Experiments show the suitability of this measure for classifying continuous multi-way data