Classification of Graph Sequences Utilizing the Eigenvalues of the Distance Matrices and Hidden Markov Models

In this paper, the classification of human activities based on sequences of camera images utilizing hidden Markov models is investigated. In the first step of the proposed data processing procedure, the locations of the person's body parts (hand, head, etc.) and objects (table, cup, etc.) which are relevant for the classification of the person's activity have to be estimated for each camera image. In the next processing step, the distances between all pairs of detected objects are computed and the eigenvalues of this Euclidean distance matrix are calculated. This set of eigenvalues built the input for a single camera image and serve as the inputs to Gaussian mixture models, which are utilized to estimate the emission probabilities of hidden Markov models. It could be demonstrated, that the eigenvalues are powerful features, which are invariant with respect to the labeling of the nodes (if they are utilized sorted by size) and can also deal with graphs, which differ in the number of their nodes.