Related papers: Randomized coupled decompositions
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…
Multi-view clustering (MVC) has been extensively studied to collect multiple source information in recent years. One typical type of MVC methods is based on matrix factorization to effectively perform dimension reduction and clustering.…
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
Nonnegative matrix factorization (NMF) is a widely used tool for learning parts-based, low-dimensional representations of nonnegative data, with applications in vision, text, and bioinformatics. In clustering applications, orthogonal NMF…
Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
Community is a fundamental and critical characteristic of an undirected social network, making community detection be a vital yet thorny issue in network representation learning. A symmetric and non-negative matrix factorization (SNMF)…
By combining related objects, unsupervised machine learning techniques aim to reveal the underlying patterns in a data set. Non-negative Matrix Factorization (NMF) is a data mining technique that splits data matrices by imposing…
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
Multi-view subspace clustering always performs well in high-dimensional data analysis, but is sensitive to the quality of data representation. To this end, a two stage fusion strategy is proposed to embed representation learning into the…
We propose a federated algorithm for reconstructing images using multimodal tomographic data sourced from dispersed locations, addressing the challenges of traditional unimodal approaches that are prone to noise and reduced image quality.…
The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…
Low-rank matrix approximation is extremely useful in the analysis of data that arises in scientific computing, engineering applications, and data science. However, as data sizes grow, traditional low-rank matrix approximation methods, such…
In biomedical research and other fields, it is now common to generate high content data that are both multi-source and multi-way. Multi-source data are collected from different high-throughput technologies while multi-way data are collected…
To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…
Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms…