In recent years, covariance descriptors have received considerable attention as a strong representation of a set of points. In this research, we propose a new metric learning algorithm for covariance descriptors based on the Dykstra algorithm, in which the current solution is projected onto a half-space at each iteration, and which runs in O(n3) time. We empirically demonstrate that randomizing the order of half-spaces in the proposed Dykstra-based algorithm significantly accelerates convergence to the optimal solution. Furthermore, we show that the proposed approach yields promising experimental results for pattern recognition tasks.

Classification tasks in computer vision and brain-computer interface research have presented several applications such as biometrics and cognitive training. However, like in any other discipline, determining suitable representation of data has been challenging, and recent approaches have deviated from the familiar form of one vector for each data sample. This paper considers a kernel between vector sets, the mean polynomial kernel, motivated by recent studies where data are approximated by linear subspaces, in particular, methods that were formulated on Grassmann manifolds. This kernel takes a more general approach given that it can also support input data that can be modeled as a vector sequence, and not necessarily requiring it to be a linear subspace. We discuss how the kernel can be associated with the Projection kernel, a Grassmann kernel. Experimental results using face image sequences and physiological signal data show that the mean polynomial kernel surpasses existing subspace-based methods on Grassmann manifolds in terms of predictive performance and efficiency.

Anomaly detection has several practical applications in different areas, including intrusion detection, image processing, and behavior analysis among others. Several approaches have been developed for this task such as detection by classification, nearest neighbor approach, and clustering. This paper proposes alternative clustering algorithms for the task of anomaly detection. By employing a weighted kernel extension of the least squares fitting of linear manifolds, we develop fuzzy clustering algorithms for kernel manifolds. Experimental results show that the proposed algorithms achieve promising performances compared to hard clustering techniques.

Although many 3D structures have been solved for proteins to date, functions of some proteins remain unknown. To predict protein functions, comparison of local structures of proteins with pre-defined model structures, whose functions have been elucidated, is widely performed. For the comparison, the root mean square deviation (RMSD) has been used as a conventional index. In this work, adaptive deviation was incorporated, along with Bregmann Divergence Regularized Machine, in order to detect analogous local structures with such model structures more effectively than the conventional index.