Classification of Multidimensional Time-Evolving Data using Histograms of Grassmannian Points

K. Dimitropoulos
P. Barmpoutis
A. Kitsikidis
N. Grammalidis
IEEE Transactions on Circuits and Systems for Video Technology (TCSVT),


In this paper we address the problem of classifying multidimensional time-evolving data in dynamic scenes. To take advantage of the correlation between the different channels of data, we introduce a generalized form of a stabilized higher-order linear dynamical system (sh-LDS) and we represent the multidimensional signal as a third order tensor. In addition, we show that the parameters of the proposed model lie on a Grassmann manifold and we attempt to address the classification problem through the study of the geometric properties of the sh-LDS's space. Moreover, to tackle the problem of non-linearity of the observation data, we represent each multidimensional signal as a cloud of points on the Grassmann manifold and we create a codebook by identifying the most representative points. Finally, each multidimensional signal is classified by applying a bag-of-systems approach having first modeled the variation of the class of each codeword on its tangent space instead of the sh-LDS's space. The proposed methodology is evaluated in three different application domains, namely video-based surveillance systems, dynamic texture categorization and human action recognition, showing its great potential.