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Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…
We consider the problem of accurately and efficiently querying a remote server to retrieve information about images captured by a mobile device. In addition to reduced transmission overhead and computational complexity, the retrieval…
Nonnegative Matrix Factorization (NMF) is a powerful tool for decomposing mixtures of audio signals in the Time-Frequency (TF) domain. In the source separation framework, the phase recovery for each extracted component is necessary for…
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…
Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been recently introduced and shown to work remarkably well for…
Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent…
Nonnegative matrix factorization (NMF) seeks a low-rank approximation $X \approx UV^T$ with nonnegative factors and is commonly solved using interior methods that enforce feasibility throughout optimization. We show that such…
CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender…
In the non-negative matrix factorization (NMF) problem, the input is an $m\times n$ matrix $M$ with non-negative entries and the goal is to factorize it as $M\approx AW$. The $m\times k$ matrix $A$ and the $k\times n$ matrix $W$ are both…
We propose a method for computing binary orthogonal non-negative matrix factorization (BONMF) for clustering and classification. The method is tested on several representative real-world data sets. The numerical results confirm that the…
Plastic sorting is a very essential step in waste management, especially due to the presence of multilayer plastics. These monomaterial and multimaterial plastics are widely employed to enhance the functional properties of packaging,…
Multi-view clustering has attracted broad attention due to its capacity to utilize consistent and complementary information among views. Although tremendous progress has been made recently, most existing methods undergo high complexity,…
Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive…
We apply the vectorized Non-negative Matrix Factorization (NMF) method to post-processing of direct imaging data for exoplanetary systems such as circumstellar disks. NMF is an iterative approach, which first creates a non-orthogonal and…
Non-negative matrix factorization (NMF) based topic modeling is widely used in natural language processing (NLP) to uncover hidden topics of short text documents. Usually, training a high-quality topic model requires large amount of textual…
We present a numerical algorithm for nonnegative matrix factorization (NMF) problems under noisy separability. An NMF problem under separability can be stated as one of finding all vertices of the convex hull of data points. The research…
The paper discusses a pooling mechanism to induce subsampling in graph structured data and introduces it as a component of a graph convolutional neural network. The pooling mechanism builds on the Non-Negative Matrix Factorization (NMF) of…
Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. Generally, existing NMF methods represent each sample with several centroids, and find the optimal…
We propose a geometric assumption on nonnegative data matrices such that under this assumption, we are able to provide upper bounds (both deterministic and probabilistic) on the relative error of nonnegative matrix factorization (NMF). The…
Semi-Nonnegative Matrix Factorization (semi-NMF) extends classical Nonnegative Matrix Factorization (NMF) by allowing the basis matrix to contain both positive and negative entries, making it suitable for decomposing data with mixed signs.…