Related papers: Curvature Corrected Nonnegative Manifold Data Fact…
Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this paper, we…
In many applications in engineering and sciences analysts have simultaneous access to multiple data sources. In such cases, the overall cost of acquiring information can be reduced via data fusion or multi-fidelity (MF) modeling where one…
Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical…
Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…
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…
Gaussian processes are widely used for the analysis of spatial data due to their nonparametric flexibility and ability to quantify uncertainty, and recently developed scalable approximations have facilitated application to massive datasets.…
In this article we propose a method to refine the clustering results obtained with the nonnegative matrix factorization (NMF) technique, imposing consistency constraints on the final labeling of the data. The research community focused its…
Community discovery is an important task for graph mining. Owing to the nonstructure, the high dimensionality, and the sparsity of graph data, it is not easy to obtain an appropriate community partition. In this paper, a deep graph…
Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper…
Point cloud data are widely used in manufacturing applications for process inspection, modeling, monitoring and optimization. The state-of-art tensor regression techniques have effectively been used for analysis of structured point cloud…
Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative…
Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent…
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),…
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…
Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which raises the question if one can learn an efficient neural…
This work developed novel complex matrix factorization methods for face recognition; the methods were complex matrix factorization (CMF), sparse complex matrix factorization (SpaCMF), and graph complex matrix factorization (GraCMF). After…