###### Abstract
[18] developed a Category-specific and Shared Dictionary Learning (CSDL) approach for fine-grained image classification. [PERSON] et al. [19] designed a structured dictionary consisting of label-particular atoms corresponding to some class and shared atoms commonly used by all the classes, and introduced a Cross-Label Suppression for Dictionary Learning (CLSDL) to generate approximate sparse coding vectors for classification. To some extent, the hybrid dictionary is very effective at preserving the complex structure of the visual data. However, it is nontrivial to design the class-specific and shared dictionaries with the proper number of atoms, which often has a severe effect on classification performance. In addition to utilizing the class label information, more and more supervised DL approaches have been proposed to incorporate the locality information of the data into the learned dictionary. By calculating the distances between the bases (atoms) and the training samples, [PERSON] et al. [20] developed a Locality-constrained Linear Coding (LLC) model to select the k-nearest neighbor bases for coding, and set the coding coefficients of other atoms to zero. [PERSON] et al. [21] proposed locality-sensitive dictionary learning to enhance the power of discrimination for sparse coding. [PERSON] et al. [22] integrated the locality constraints into the multi-layer discriminative dictionary to avoid the appearance of over-fitting. By coupling the locality reconstruction and the label reconstruction, the LCLE-DL method [7] ensures that the locality-based and label-based coding coefficients are as approximate to each other as possible. It is noted that the locality constraint in LCLE-DL may cause the dictionary atoms from the different classes to be similar, which weakens the discriminative ability of the learned dictionary. It is observed that the real-world object categories are not only a marked difference, but are also strongly correlated in terms of the visual property, e.g., faces from the different persons often share similar illumination and pose variants; objects in the Caltech 101 dataset [23] have the correlated background. These correlations are not very helpful to distinguish the different categories, but without them the data with common features cannot be well represented. Thus, the dictionary learning approach should learn the distinctive features with the class-specific dictionary, and simultaneously exploit the common features of the correlated classes by learning a commonality dictionary. To this end, we proposed the locality preserving and label-aware constraint-based hybrid dictionary learning (LPLC-HDL) method for image classification, which is composed of a label-aware constraint, a group regularization and a locality constraint. The main contributions are summarized as follows. 1. The proposed LPLC-HDL method learns the hybrid dictionary by fully exploiting the locality information and the label information of the data. In this way, the learned hybrid dictionary can not only preserve the complex structural information of the data, but also have strong discriminativity for image classification. 2. In LPLC-HDL, a locality constraint is constructed to encourage the samples from different classes with similar features to have similar commonality representation; then, a label-aware constraint is integrated to make the class-specific dictionary sparsely represent the samples from the same class, so that the robust particularity-commonality representation can be obtained by the proposed LPLC-HDL. 3. In a departure from the competing methods which impose the \(l_{0}\)-norm or \(l_{1}\)-norm on the coefficients, LPLC-HDL consists of \(l_{2}\)-norm constraints that can be calculated efficiently. The objective function is solved elegantly by employing an alternative optimization technique. The rest of this paper is outlined as follows. Section 2 reviews the related work on our LPLC-HDL method. Then Section 3 presents the details of LPLC-HDL and an effective optimization is introduced in Section 4.