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With the proliferation of Graph Neural Network (GNN) methods stemming from contrastive learning, unsupervised node representation learning for graph data is rapidly gaining traction across various fields, from biology to molecular dynamics,…

Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals…

Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the…

Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…

The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…

We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity…

Graph anomaly detection technology has broad applications in financial fraud and risk control. However, existing graph anomaly detection methods often face significant challenges when dealing with complex and variable abnormal patterns, as…

Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and…

Tensor-based methods have recently emerged as a more natural and effective formulation to address many problems in hyperspectral imaging. In hyperspectral unmixing (HU), low-rank constraints on the abundance maps have been shown to act as a…

Graph neural networks (GNNs) have been extensively studied for prediction tasks on graphs. As pointed out by recent studies, most GNNs assume local homophily, i.e., strong similarities in local neighborhoods. This assumption however limits…

Recent research on graph neural networks (GNNs) has explored mechanisms for capturing local uncertainty and exploiting graph hierarchies to mitigate data sparsity and leverage structural properties. However, the synergistic integration of…

Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…

For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data.…

Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional…

In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs,…

Nonnegative Matrix Factorization (NMF) is a data analysis technique which allows compression and interpretation of nonnegative data. NMF became widely studied after the publication of the seminal paper by Lee and Seung (Learning the Parts…

We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative…

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…