This paper presents a sparse representation based complete kernel marginal Fisher analysis (SCMFA) framework for categorizing fine art images. First, we introduce several Fisher vector based features for feature extraction so as to extract and encode important discriminatory information of the painting image. Second, we propose a complete marginal Fisher analysis method so as to extract two kinds of discriminant information, regular and irregular. In particular, the regular discriminant features are extracted from the range space of the intraclass compactness using the marginal Fisher discriminant criterion whereas the irregular discriminant features are extracted from the null space of the intraclass compactness using the marginal interclass separability criterion. The motivation for extracting two kinds of discriminant information is that the traditional MFA method uses a PCA projection in the initial step that may discard the null space of the intraclass compactness which may contain useful discriminatory information. Finally, we learn a discriminative sparse representation model with the objective to integrate the representation criterion with the discriminant criterion in order to enhance the discriminative ability of the proposed method. The effectiveness of the proposed SCMFA method is assessed on the challenging Painting-91 dataset. Experimental results show that our proposed method is able to (i) achieve the state-of-the-art performance for painting artist and style classification, (ii) outperform other popular image descriptors and deep learning methods, (iii) improve upon the traditional MFA method as well as (iv) discover the artist and style influence to understand their connections in different art movement periods.