Learning dictionary on manifolds for image classification

At present, dictionary based models have been widely used in image classification. The image features are approximated as a linear combination of bases selected from the dictionary in a sparse space, resulting in compact patterns. The features applied to image classification usually reside on low dimensional manifolds embedded in a high dimensional ambient space; traditional sparse coding algorithm, however, does not consider this topological structure. It can be characterized naturally by linear coefficients that reconstruct each data point from its neighbors. One of the central issues here is how to determine the neighbors and learn the coefficients. In this paper, the geometrical structures are encoded in two situations. In simple cases when data points distribute on a single manifold, it is explicitly modeled by locally linear embedding algorithm combined with k-nearest neighbors. Nevertheless, in real-world scenarios, complex data points often lie on multiple manifolds. Sparse representation algorithm combined with k-nearest neighbors is instead utilized to construct the topological structures, because it is capable of approximating the data point by selecting its homogenous neighbors adaptively to guarantee the smoothness of each manifold. After obtaining the local fitting relationship, these two topological structures are then embedded into sparse coding algorithm as regularization terms to formulate the corresponding objective functions of dictionary learning on single manifold (DLSM) and dictionary learning on multiple manifolds (DLMM), respectively. Upon this, a coordinate descent scheme is proposed to solve the unified optimization problems. Experimental results on several benchmark data sets, such as Caltech-256, Caltech-101, Scene 15, and UIUC-Sports, show that our proposed algorithms equal or outperform other state-of-the-art image classification algorithms.

► Proposed dictionary learning method on single manifold.
► Proposed dictionary learning method on multiple manifolds.
► A novel algorithm is proposed to solve the optimization problem.
► It achieves superior performance in image classification task.