Related papers: Randomized coupled decompositions
Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the…
Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in large data sets in a relevant way. However, such low-rank…
Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
Recent demands on data privacy have called for federated learning (FL) as a new distributed learning paradigm in massive and heterogeneous networks. Although many FL algorithms have been proposed, few of them have considered the matrix…
Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…
In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…
Non-negative matrix factorization (NMF) is an important tool in signal processing and widely used to separate mixed sources into their components. Algorithms for NMF require that the user choose the number of components in advance, and if…
There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…
The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the…
Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…
Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…
We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals…
Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value…
Coupled tensor decomposition (CTD) can extract joint features from multimodal data in various applications. It can be employed for federated learning networks with data confidentiality. Federated CTD achieves data privacy protection by…
Nonnegative Matrix Factorization (NMF) is an important unsupervised learning method to extract meaningful features from data. To address the NMF problem within a polynomial time framework, researchers have introduced a separability…
Non-negative Matrix Factorization (NMF) is a useful method to extract features from multivariate data, but an important and sometimes neglected concern is that NMF can result in non-unique solutions. Often, there exist a Set of Feasible…
Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…