Sparse learning based feature selection has been widely investigated in recent years. In this study, we focus on the l2,0-norm based feature selection, which is effective for exact top-k feature selection but challenging to optimize. To solve the general l2,0-norm constrained problems, we novelly develop a parameter-free optimization framework based on the coordinate descend (CD) method, termed CD-LSR. Specifically, we devise a skillful conversion from the original problem to solving one continuous matrix and one discrete selection matrix. Then the nontrivial l2,0-norm constraint can be solved efficiently by solving the selection matrix with CD method. We impose the l2,0-norm on a vanilla least square regression (LSR) model for feature selection and optimize it with CD-LSR. Extensive experiments exhibit the efficiency of CD-LSR, as well as the discrimination ability of l2,0-norm to identify informative features. More importantly, the versatility of CD-LSR facilitates the applications of the l2,0-norm in more sophisticated models. Based on the competitive performance of l2,0-norm on the baseline LSR model, the satisfactory performance of its applications is reasonably expected. The source MATLAB code are available at: https://github.com/solerxl/Code_For_AAAI_2023.

Feature selection is widely used in multimedia applications to determine informative features from high-dimensional data. Due to the explosive growth of the data size and the expensive cost of obtaining labeled data, it is increasingly demanded to utilize both labeled and unlabeled data for feature selection. In this paper, we introduce the l2,0-norm in semi-supervised feature selection, which is able to select exact k informative features. Due to the non-convexity of l2,0-norm, we further devise an efficient coordinate-descent-based algorithm to solve the l2,0-norm constraint, which facilitates the application of l2,0-norm to more complex applications, including but not limited to the proposed model in this study. We experimentally verify the effectiveness of the proposed l2,0-norm-based semi-supervised method and the efficiency of the proposed optimization algorithm.

Feature selection (FS) plays an important role in machine learning, which extracts important features and accelerates the learning process. In this paper, we propose a deep FS method that simultaneously conducts feature selection and differentiable $ k $-NN graph learning based on the Dirichlet Energy. The Dirichlet Energy identifies important features by measuring their smoothness on the graph structure, and facilitates the learning of a new graph that reflects the inherent structure in new feature subspace. We employ Optimal Transport theory to address the non-differentiability issue of learning $ k $-NN graphs in neural networks, which theoretically makes our method applicable to other graph neural networks for dynamic graph learning. Furthermore, the proposed framework is interpretable, since all modules are designed algorithmically. We validate the effectiveness of our model with extensive experiments on both synthetic and real-world datasets.

As a natural extension of the traditional graph model, hypergraph has been extensively exploited and applied in many tasks such as image clustering, classification, etc. The performance of these tasks highly depends on building an informative hypergraph to accurately and robustly formulate the underlying data correlation. Existing hypergraph construction methods can only be suitable for simple Gaussian or outlier noise assumptions, which cannot be applied to more complex noise scenario in practical applications. To address this challenge, we propose a robust hypergraph learning model by adopting the Mixture of Gaussians (MoG) noise modeling strategy. In particular, our model adopts low-rank representation and sparse representation simultaneously to construct an informative hypergraph. The Correlation among nodes and the weights of edges can be obtained by seeking a low-rank and sparse representation matrix. The so-obtained hypergraph can capture both the global mixture of subspaces structure (by low-rank) and the locally linear structure (by sparse) of the data. Furthermore, an efficient Expectation-Maximization-like optimization algorithm is designed to solve the proposed model. Finally, the superiority of our model is demonstrated by extensive experiments on image clustering.

Alzheimer's disease (AD) is one of the most common neurodegenerative diseases. Understanding AD progression can empower the patients in taking proactive care. Mini Mental State Examination (MMSE) and AD Assessment Scale Cognitive subscale (ADAS-Cog) are two prevailing clinical measures designed to evaluate the AD progression. In this paper, we propose a weakly supervised Temporal Multitask Matrix Completion (TMMC) framework, which combines a novel transductive multitask feature selection scheme, to simultaneously predict AD progression measured by MMSE and ADAS-Cog, and identify related biomarkers trackable of AD progression. Specifically, by treating the prediction of cognitive scores at each time point as a regression task, we first formulate AD progression problem as a standard Multitask Matrix Completion (MMC) model. Secondly, considering the limited number of samples available in this study, we introduce a transductive feature selection scheme to jointly select the task-shared features for multiple time points and the task-specific features for different time points, and thus alleviate the over-fitting defect caused by Small-Sample-Size issue. Thirdly, aiming at the small change of cognitive scores between successive time points for a patient, we employ a temporal regularization scheme to capture the temporal smoothness of cognitive scores. Furthermore, we design an efficient optimization algorithm based on Alternative Minimization and Difference of Convex Programming techniques to solve the proposed TMMC framework. Finally, the extensive experiments performed on real-world Alzheimer's disease dataset demonstrate the effectiveness of our TMMC framework.