Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 323481, 6 pages http://dx.doi.org/10.1155/2013/323481 Research Article Low-Rank Affinity Based Local-Driven Multilabel Propagation Teng Li, 1 Bin Cheng, 2 Xinyu Wu, 3,4 and Jun Wu 5 1 Anhui University, Hefei 230601, China 2 Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China 3 Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China 4 Department of Mechanical and Automation Engineering, Te Chinese University of Hong Kong, Shatin, Hong Kong 5 Institute of Sofware Application Technology, Guangzhou & Chinese Academy of Sciences, Guangzhou 511458, China Correspondence should be addressed to Teng Li; tenglwy@gmail.com Received 21 October 2013; Accepted 29 November 2013 Academic Editor: Shuping He Copyright © 2013 Teng Li et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper presents a novel low-rank afnity based local-driven algorithm to robustly propagate the multilabels from training images to test images. A graph is constructed over the segmented local image regions. Te labels for vertices from the training data are derived based on the context among diferent training images, and the derived vertex labels are propagated to the unlabeled vertices via the graph. Te multitask low-rank afnity, which jointly seeks the sparsity-consistent low-rank afnities from multiple feature matrices, is applied to compute the edge weights between graph vertices. Te inference process of multitask low-rank afnity is formulated as a constrained nuclear norm and ℓ 2,1 -norm minimization problem. Te optimization is conducted efciently with the augmented Lagrange multiplier method. Based on the learned local patch labels we can predict the multilabels for the test images. Experiments on multilabel image annotation demonstrate the encouraging results from the proposed framework. 1. Introduction Graphbased label propagation is an important methodology in machine learning, which has been widely adopted in classifcation tasks such as image annotation [1–3]. It can efectively leverage the unlabeled data in addition to the labeled data for the classifcation and therefore solve the problem of lack of sufcient labeled data in many real applications. Conventional graph-based label propagation mainly focuses on the cases with a single label for each datum and models the semantic relation between images based on the global feature matching. An image is considered as a vertex linking with others in the graph. However, real-world online images are always associated with multiple labels and each corresponds to a local region. Tus the global matching based methods are not well suitable for the multilabel propa- gation and image annotation cases. Recently, local matching based methods have been adopted widely and have shown superior performance to that of the global matching based methods in several classifcation tasks [4]. In graph-based multilabel propagation, [5] proposed to construct the graph based on local feature matching, which is expected to model the multilabel semantics more accurately than conventional global matching based methods. In this work, we are going to follow the local match- ing based way of [5] exploring the graph-based multilabel propagation problem. A critical step in graph-based label propagation is the graph construction. Conventional meth- ods for graph construction include the -nearest-neighbor method and -ball based method, where, for each datum, the samples within its surrounding ball are connected, and then various approaches, for example, binary, Gaussian kernel [6], and ℓ 2 -reconstruction [7], are applied for determining the graph edge weights. In [5] the -ball based method is adopted to construct the local feature graph. However, recent studies [8–10] reveal that sparse representation (SR) and low-rank representation (LRR) for graph construction can lead to several characteristics we desired, such as robustness