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Federated Learning (FL) is currently one of the most popular technologies in the field of Artificial Intelligence (AI) due to its collaborative learning and ability to preserve client privacy. However, it faces challenges such as…

Integrating various data modalities brings valuable insights into underlying phenomena. Multimodal factor analysis (FA) uncovers shared axes of variation underlying different simple data modalities, where each sample is represented by a…

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large…

In recent years, methods that combine contrastive learning with graph neural networks have emerged to address the challenges of recommendation systems, demonstrating powerful performance and playing a significant role in this domain.…

A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an…

Federated Learning (FL) is currently the most widely adopted framework for collaborative training of (deep) machine learning models under privacy constraints. Albeit it's popularity, it has been observed that Federated Learning yields…

The self-expressive property of data points, i.e., each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering methods. Most self-expressive methods usually…

Semi-Non-negative Matrix Factorization is a technique that learns a low-dimensional representation of a dataset that lends itself to a clustering interpretation. It is possible that the mapping between this new representation and our…

Matrix Factorization has been very successful in practical recommendation applications and e-commerce. Due to data shortage and stringent regulations, it can be hard to collect sufficient data to build performant recommender systems for a…

Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…

Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric. Traditional approaches to model-based clustering often fail for high dimensional data, e.g., due to…

Reconstruction based subspace clustering methods compute a self reconstruction matrix over the samples and use it for spectral clustering to obtain the final clustering result. Their success largely relies on the assumption that the…

We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed with certain properties, the result is a model…

Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…

Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…

We discuss a randomized strong rank-revealing QR factorization that effectively reveals the spectrum of a matrix $\textbf{M}$. This factorization can be used to address problems such as selecting a subset of the columns of $\textbf{M}$,…

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…

We consider clustering in group decision making where the opinions are given by pairwise comparison matrices. In particular, the k-medoids model is suggested to classify the matrices since it has a linear programming problem formulation…

The study of cells and their responses to genetic or chemical perturbations promises to accelerate the discovery of therapeutic targets. However, designing adequate and insightful models for such data is difficult because the response of a…

We introduce a probabilistic formalism subsuming Markov random fields of bounded tree width and probabilistic context free grammars. Our models are based on a representation of Boolean formulas that we call case-factor diagrams (CFDs). CFDs…