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In various application domains, high-dimensional multi-label data has become more prevalent, presenting two significant challenges: instances with high-dimensional features and a large number of labels. In the context of multi-label feature selection, the objective is to choose a subset of features from a given set that is highly pertinent for predicting multiple labels or categories associated with each instance. However, certain characteristics of multi-label classification, such as label dependencies and imbalanced label distribution, have often been overlooked although they hold valuable insights for designing effective multi-label feature selection algorithms. In this paper, we propose a feature selection model which exploits explicit global and local label correlations to select discriminative features across multiple labels. In addition, by representing the feature matrix and label matrix in a shared latent space, the model aims to capture the underlying correlations between features and labels. The shared representation can reveal common patterns or relationships that exist across multiple labels and features. An objective function involving L 2 , 1 -norm regularization is formulated, and an alternating optimization-based iterative algorithm is designed to obtain the sparse coefficients for multi-label feature selection. The proposed method was evaluated on 14 real-world multi-label datasets using six evaluation metrics, through comprehensive experiments. The results indicate its effectiveness, surpassing that of several representative methods. [ABSTRACT FROM AUTHOR]

Graph clustering is a fundamental technique in machine learning that has widespread applications in various fields. Deep Nonnegative Matrix Factorization (DNMF) was recently emerged to cope with the extraction of several layers of features, and it has been demonstrated to achieve remarkable results on unsupervised tasks. While DNMF has been applied for analyzing graphs, the effectiveness of the current DNMF approaches for graph clustering is generally unsatisfactory: these methods are intrinsically data representation models, and their objective functions do not capture cluster structures, also ignores direction which is crucial in the directed graph clustering problems. To overcome these downsides, this paper proposes a graph-specific DNMF model based on the Asymmetric NMF which can handle undirected and directed graphs. Inspired by hierarchical graph clustering and graph summarization approaches, the Deep Asymmetric Nonnegative Matrix Factorization (DAsNMF) is introduced for the directed graph clustering problem. In a pseudo-hierarchical clustering setting, DAsNMF decomposes the input graph to extract low-level to high-level node representations and graph representations (summarized graphs). In addition, the asymmetric cosine and PageRank-based similarities are imposed on the proposed model to preserve the local and global graph structures. The learning process is formulated as a unified optimization problem to jointly train representation learning model and clustering model. The extensive experimental studies validate the effectiveness of the proposed method on directed graphs. • A graph specific deep matrix factorization model is proposed for graph clustering. • The direction-aware model can learn hierarchical structures and graph summarization. • Two Asymmetric similarities are utilized to preserve the local and global structures. • A unified optimization approach is provided to solve the proposed objective function. • Experiments demonstrate the effectiveness of the method in directed graph clustering. [ABSTRACT FROM AUTHOR]

• A self-supervised semi-supervised NMF method is proposed for data clustering. • We define an effective semi-supervised NMF model with attractive and repulsive interactions. • An ensemble of semi-supervised NMFs is designed to model a self-supervised one. • The self-supervised model generates pseudo supervisory signals to boost semi-supervised learning. • Experimental results demonstrate the effectiveness of the proposed method in semi-supervised clustering tasks. Semi-supervised nonnegative matrix factorization exploits the strengths of matrix factorization in successfully learning part-based representation and is also able to achieve high learning performance when facing a scarcity of labeled data and a large amount of unlabeled data. Its major challenge lies in how to learn more discriminative representations from limited labeled data. Furthermore, self-supervised learning has been proven very effective at learning representations from unlabeled data in various learning tasks. Recent research works focus on utilizing the capacity of self-supervised learning to enhance semi-supervised learning. In this paper, we design an effective Self-Supervised Semi-Supervised Nonnegative Matrix Factorization (S4NMF) in a semi-supervised clustering setting. The S4NMF directly extracts a consensus result from ensembled NMFs with similarity and dissimilarity regularizations. In an iterative process, this self-supervisory information will be fed back to the proposed model to boost semi-supervised learning and form more distinct clusters. The proposed iterative algorithm is used to solve the given problem, which is defined as an optimization problem with a well-formulated objective function. In addition, the theoretical and empirical analyses investigate the convergence of the proposed optimization algorithm. To demonstrate the effectiveness of the proposed model in semi-supervised clustering, we conduct extensive experiments on standard benchmark datasets. The source code for reproducing our results can be found at https://github.com/ChavoshiNejad/S4NMF. [ABSTRACT FROM AUTHOR]

Link prediction is a fundamental problem in complex network analysis, aimed at predicting missing or forthcoming connections. Recent research investigates the potential of Nonnegative Matrix Factorization (NMF) models in reconstructing sparse networks and using deep NMF to uncover the hierarchical structure. Deep models have demonstrated remarkable performance in various domains, but they are susceptible to overfitting, especially on the limited training data. This paper proposes a novel Link Prediction using Adversarial Deep NMF (LPADNMF) to enhance the generalization of network reconstruction in sparse graphs. The main contribution is the introduction of an adversarial training that incorporates a bounded attack on the input, leveraging the L 2 , 1 norm to generate diverse perturbations. This adversarial training aims to improve the model's robustness and prevent overfitting, particularly in scenarios with limited training data. Additionally, the proposed method incorporates first and second-order affinities as input to capture higher-order dependencies and encourage the extraction of informative features from the network structure. To further mitigate overfitting, a smooth L 2 regularization is applied to the model parameters. To optimize the proposed model effectively, we utilize a majorization-minimization algorithm that efficiently updates the perturbation and latent factors in an iterative manner. Our findings demonstrate that the proposed model not only has the ability to uncover and learn complex structures but also possesses generalization capabilities. This method demonstrates superior performance compared to state-of-the-art methods across eight networks. In comparison to the best-performing approach, LPADNMF exhibited improvements of 2.36% in AUC, 4.67% in Precision, 2.21% in Recall, and 3.73% in F-Measure. [ABSTRACT FROM AUTHOR]