Dynamic transition embedding for image feature extraction and recognition

In this paper, we propose a novel method called dynamic transition embedding (DTE) for linear dimensionality reduction. Differing from the recently proposed manifold learning-based methods, DTE introduces the dynamic transition information into the objective function by characterizing the Markov transition processes of the data set in time t(t > 0). In the DTE framework, running the Markov chain forward in time, or equivalently, taking the larger powers of Markov transition matrices integrates the local geometry and, therefore, reveals relevant geometric structures of the data set at different timescales. Since the Markov transition matrices defined by the connectivity on a graph contain the intrinsic geometry information of the data points, the elements of the Markov transition matrices can be viewed as the probabilities or the similarities between two points. Thus, minimizing the errors of the probability reconstruction or similarity reconstruction instead of the least-square reconstruction in the well-known manifold learning algorithms will obtain the optimal linear projections with respect to preserving the intrinsic Markov processes of the data set. Comprehensive comparisons and extensive experiments show that DTE achieves higher recognition rates than some well-known linear dimensionality reduction techniques.