###### Abstract  
Dictionary learning has been an important role in the success of data representation. As a complete view of data representation, hybrid dictionary learning (HDL) is still in its infant stage. In previous HDL approaches, the scheme of how to learn an effective hybrid dictionary for image classification has not been well addressed. In this paper, we proposed a locality preserving and label-aware constraint-based hybrid dictionary learning (LPLC-HDL) method, and apply it in image classification effectively. More specifically, the locality information of the data is preserved by using a graph Laplacian matrix based on the shared dictionary for learning the commonality representation, and a label-aware constraint with group regularization is imposed on the coding coefficients corresponding to the class-specific dictionary for learning the particularity representation. Moreover, all the introduced constraints in the proposed LPLC-HDL method are based on the \(l_{2}\)-norm regularization, which can be solved efficiently via employing an alternative optimization strategy. The extensive experiments on the benchmark image datasets demonstrate that our method is an improvement over previous competing methods on both the hand-crafted and deep features. locality preserving; label-aware constraint; hybrid dictionary learning; image classification +
Footnote †: journal: Medical  
The class-shared DL methods generally force the coding coefficients to be discriminative via learning a single dictionary shared by all the classes. Based on the K-SVD algorithm, [PERSON] and [PERSON] [5] proposed the Discriminative K-SVD (D-KSVD) method to construct a classification error term for learning a linear classifier. [PERSON] et al. [6] further proposed the Label Consistent K-SVD (LC-KSVD) which encourages the coding coefficients from the same class to be as similar as possible. Considering the characteristics of atoms, [PERSON] et al. [12] designed an indicator function to regularize the class-shared dictionary to improve the discriminative ability of coding coefficients. In general, the computation of the test stage is very efficient in the class-shared DL methods, but it is hard to improve the coefficients' discriminativity for better classification performance as the class-shared dictionary is not enough for fitting the complex data. In the class-specific dictionary learning, each sub-dictionary is assigned to a single class and the sub-dictionaries with the different classes are encouraged to be as independent as possible. As a representative class-specific DL method, Fisher Discrimination Dictionary Learning (FDDL) [13] employs Fisher discrimination criterion on the coding coefficients, then utilizes the representation residual of each class to establish the discriminative term. Using with the incoherence constraint, [PERSON] et al. [14] proposed a structured dictionary learning scheme to promote the discriminative ability of the class-specific sub-dictionaries. [PERSON] et al. [15] developed a Joint discriminative Bayesian Dictionary and Classifier learning (JBDC) model to associate the dictionary atoms by the class labels with Bernoulli distributions. The class-specific DL methods usually associate a dictionary atom to a single class directly; hence, the reconstruction error with respect to each class can be used for classification. However, the test stage of this category often requires the coefficient computation of test data over many sub-dictionaries. In the hybrid dictionary learning, a dictionary is designed to have a set of class-shared atoms in addition to the class-specific sub-dictionaries. [PERSON] and [PERSON] [16] proposed a hybrid dictionary dubbed DL-COPAR to explicitly separate the common and particular features of the data, which also encourages the class-specific sub-dictionaries to be incoherent. [PERSON] et al. [17] developed a Low-Rank Shared Dictionary Learning (LRSDL) method to preserve the common features of samples. [PERSON] et al.