AAAI Conferences

Various sparse regularizers have been applied to machine learning problems, among which structured sparsity has been proposed for a better adaption to structured data. In this paper, motivated by effectively classifying linked data (e.g. Web pages, tweets, articles with references, and biological network data) where a group structure exists over the whole dataset and links exist between specific samples, we propose a joint sparse representation model that combines group sparsity and graph sparsity, to select a small number of connected components from the graph of linked samples, meanwhile promoting the sparsity of edges that link samples from different groups in each connected component. Consequently, linked samples are selected from a few sparsely-connected groups. Both theoretical analysis and experimental results on four benchmark datasets show that the joint sparsity model outperforms traditional group sparsity model and graph sparsity model, as well as the latest group-graph sparsity model.

Structured Sparsity with Group-Graph Regularization

AAAI Conferences

In many learning tasks with structural properties, structural sparsity methods help induce sparse models, usually leading to better interpretability and higher generalization performance. One popular approach is to use group sparsity regularization that enforces sparsity on the clustered groups of features, while another popular approach is to adopt graph sparsity regularization that considers sparsity on the link structure of graph embedded features. Both the group and graph structural properties co-exist in many applications. However, group sparsity and graph sparsity have not been considered simultaneously yet. In this paper, we propose a g 2 -regularization that takes group and graph sparsity into joint consideration, and present an effective approach for its optimization. Experiments on both synthetic and real data show that, enforcing group-graph sparsity lead to better performance than using group sparsity or graph sparsity only.

Learning Sparse Representations from Datasets with Uncertain Group Structures: Model, Algorithm and Applications

AAAI Conferences

Group sparsity has drawn much attention in machine learning. However, existing work can handle only datasets with certain group structures, where each sample has a certain membership with one or more groups. This paper investigates the learning of sparse representations from datasets with uncertain group structures, where each sample has an uncertain member-ship with all groups in terms of a probability distribution. We call this problem uncertain group sparse representation (UGSR in short), which is a generalization of the standard group sparse representation (GSR). We formulate the UGSR model and propose an efficient algorithm to solve this problem. We apply UGSR to text emotion classification and aging face recognition. Experiments show that UGSR outperforms standard sparse representation (SR) and standard GSR as well as fuzzy kNN classification.

Dictionary Learning with Mutually Reinforcing Group-Graph Structures

AAAI Conferences

In this paper, we propose a novel dictionary learning method in the semi-supervised setting by dynamically coupling graph and group structures. To this end, samples are represented by sparse codes inheriting their graph structure while the labeled samples within the same class are represented with group sparsity, sharing the same atoms of the dictionary. Instead of statically combining graph and group structures, we take advantage of them in a mutually reinforcing way — in the dictionary learning phase, we introduce the unlabeled samples into groups by an entropy-based method and then update the corresponding local graph, resulting in a more structured and discriminative dictionary. We analyze the relationship between the two structures and prove the convergence of our proposed method. Focusing on image classification task, we evaluate our approach on several datasets and obtain superior performance compared with the state-of-the-art methods, especially in the case of only a few labeled samples and limited dictionary size.

Dual Averaging Method for Online Graph-structured Sparsity Artificial Intelligence

Online learning algorithms update models via one sample per iteration, thus efficient to process large-scale datasets and useful to detect malicious events for social benefits, such as disease outbreak and traffic congestion on the fly. However, existing algorithms for graph-structured models focused on the offline setting and the least square loss, incapable for online setting, while methods designed for online setting cannot be directly applied to the problem of complex (usually non-convex) graph-structured sparsity model. To address these limitations, in this paper we propose a new algorithm for graph-structured sparsity constraint problems under online setting, which we call \textsc{GraphDA}. The key part in \textsc{GraphDA} is to project both averaging gradient (in dual space) and primal variables (in primal space) onto lower dimensional subspaces, thus capturing the graph-structured sparsity effectively. Furthermore, the objective functions assumed here are generally convex so as to handle different losses for online learning settings. To the best of our knowledge, \textsc{GraphDA} is the first online learning algorithm for graph-structure constrained optimization problems. To validate our method, we conduct extensive experiments on both benchmark graph and real-world graph datasets. Our experiment results show that, compared to other baseline methods, \textsc{GraphDA} not only improves classification performance, but also successfully captures graph-structured features more effectively, hence stronger interpretability.