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In this paper, we consider the problem of multi-dimensional dynamic texture analysis, and we introduce a new higher order linear dynamical system (h-LDS) descriptor. The proposed h-LDS descriptor is based on the higher order decomposition of the multidimensional image data and enables the analysis of dynamic textures by using information from various image elements. In addition, we propose a methodology for its application to video-based early warning systems that focus on smoke identification. More specifically, the proposed methodology enables the representation of video subsequences as histograms of h-LDS descriptors produced by the smoke candidate image patches in each subsequence. Finally, to further improve the classification accuracy, we propose the combination of multidimensional dynamic texture analysis with the spatiotemporal modeling of smoke by using a particle swarm optimization approach. The ability of the h-LDS to analyze the dynamic texture information is evaluated through a multivariate comparison against the standard LDS descriptor. The experimental results that use two video datasets have shown the great potential of the proposed smoke detection method. [ABSTRACT FROM PUBLISHER]