We introduce a new nonnegative matrix factorization (NMF) model called nonnegative Unimodal matrixfactorization (NuMF), which adds on top of NMF the unimodal condition on the columns of the basis matrix. NuMF finds a...
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ISBN:
(纸本)9781728176055
We introduce a new nonnegative matrix factorization (NMF) model called nonnegative Unimodal matrixfactorization (NuMF), which adds on top of NMF the unimodal condition on the columns of the basis matrix. NuMF finds applications for example in analytical chemistry. We propose a simple but naive brute-force heuristics strategy based on accelerated projected gradient. It is then improved by using multi-grid for which we prove that the restriction operator preserves the unimodality. We also present two preliminary results regarding the uniqueness of the solution, that is, the identifiability, of NuMF. Empirical results on synthetic and real datasets confirm the effectiveness of the algorithm and illustrate the theoretical results on NuMF.
nonnegative matrix factorization (NMF) has been widely used in machine learning and signal processing because of its non-subtractive, part-based property which enhances interpretability. It is often assumed that the l...
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ISBN:
(纸本)9781479981311
nonnegative matrix factorization (NMF) has been widely used in machine learning and signal processing because of its non-subtractive, part-based property which enhances interpretability. It is often assumed that the latent dimensionality (or the number of components) is given. Despite the large amount of algorithms designed for NMF, there is little literature about automatic model selection for NMF with theoretical guarantees. In this paper, we propose an algorithm that first calculates an empirical second-order moment from the empirical fourth-order cumulant tensor, and then estimates the latent dimensionality by recovering the support union (the index set of non-zero rows) of a matrix related to the empirical second-order moment. By assuming a generative model of the data with additional mild conditions, our algorithm provably detects the true latent dimensionality. We show on synthetic examples that our proposed algorithm is able to find approximately correct number of components.
In this research, we address distant sound source suppression based on Multichannel nonnegative matrix factorization (MNMF), and propose a new penalized method. A conventional method based on MNMF separates an observe...
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ISBN:
(纸本)9781728130385
In this research, we address distant sound source suppression based on Multichannel nonnegative matrix factorization (MNMF), and propose a new penalized method. A conventional method based on MNMF separates an observed signal into a target signal and other distant sound sources. Un-fortunately, MNMF often degrades the separation performance owing to the basis-sharing problem. Our penalized method forces the target basis to become different from the nontarget one. Experimental results show that the proposed method can improve the separation capability more than the conventional one.
nonnegative matrix factorization (NMF) has been applied to hyperspectral un-mixing (HU) due to its simplicity and effectiveness. There are two shortcomings when applying NMF in HU. First, the solution space of NMF is ...
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ISBN:
(纸本)9781450361248
nonnegative matrix factorization (NMF) has been applied to hyperspectral un-mixing (HU) due to its simplicity and effectiveness. There are two shortcomings when applying NMF in HU. First, the solution space of NMF is large, which is caused by the nonconvex objective function. Second, the part-based property NMF is not strong enough for the HU problem, resulting in a less expressive estimation of endmembers. We present a two-stage active set type NMF algorithm, which uses k-means and obtains an estimation of the endmember matrix. Then, the estimated endmember matrix starts the alternative least squares stage as the initialization matrix. Two reasonable constraints are added in our cost function of NMF, it controls the similarity between the first-factor matrix and the endmember matrix, and the sparsity of the second-factor matrix. Numerical tests show that the accuracy and the stabilization of the solution are achieved when applying our new algorithms in HU.
Transfer learning has been successfully used in recommender systems to deal with the data sparsity problem. Existing techniques assume that the source and target domains share the same feature space. This paper propos...
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ISBN:
(纸本)9783030342234;9783030342227
Transfer learning has been successfully used in recommender systems to deal with the data sparsity problem. Existing techniques assume that the source and target domains share the same feature space. This paper proposes a new direction in transfer learning where the source and target domains can have different feature space. The proposed technique, Feature Selection based nonnegative matrix factorization (FSNMF), selects the useful features that can minimize the cost function of the target domain. The features of the source domain are learned using NMF and their importance is measured using the gradient principle. Experiments with real-world datasets show the effectiveness of FSNMF in comparison to state-of-the-art relevant transfer learning techniques.
nonnegative matrix factorization-based feature selection analysis performed on land based hyperspectral imagery of the Mississippi river identifies ten spectral bands in the visible and near infrared portion of the el...
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ISBN:
(数字)9781510617742
ISBN:
(纸本)9781510617742
nonnegative matrix factorization-based feature selection analysis performed on land based hyperspectral imagery of the Mississippi river identifies ten spectral bands in the visible and near infrared portion of the electromagnetic spectrum that are significant contributors to the resulting structural image clustering of sediment-laden water. Different distance metrics provide clear evidence of the potency of these spectral bands for class separation of turbid, sediment-laden water from clear water, provided that the data contains low noise. In addition, feature ranking of spectral band subsets of the identified characteristic spectral bands allows insight into the relative importance of smaller spectral band subsets for water-sediment characterization. Results support present day multispectral satellite design methods for land-water imagery where payload power resources are relegated to certain spectral bands at the expense of others.
This paper proposes a distributed algorithm for multiple agents to perform the nonnegative matrix factorization (NMF) based on the Euclidean distance. The matrix to be factorized is partitioned into multiple blocks, a...
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ISBN:
(纸本)9781728124858
This paper proposes a distributed algorithm for multiple agents to perform the nonnegative matrix factorization (NMF) based on the Euclidean distance. The matrix to be factorized is partitioned into multiple blocks, and each block is assigned to one of the agents forming a two-dimensional grid network. Each agent handles a small number of entries of the factor matrices corresponding to the assigned block, and updates their values by using information coming from the neighbors. It is shown that the proposed algorithm simulates the hierarchical alternating least squares method, which is well known as a fast algorithm for NMF based on the Euclidean distance, by making use of a finite-time distributed consensus algorithm.
We introduce a method for detecting latent hierarchical structure in data based on nonnegative matrix factorization. Datasets with hierarchical structure arise in a wide variety of fields, such as document classificat...
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ISBN:
(纸本)9781728155494
We introduce a method for detecting latent hierarchical structure in data based on nonnegative matrix factorization. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification, image processing, and bioinformatics. The proposed method, Neural NMF, recursively applies topic modeling in layers to discover over-arching topics encompassing the lower-level features. We derive a backpropagation scheme that allows us to frame our method as a neural network. Numerical results on a synthetic dataset demonstrate that Neural NMF outperforms similar algorithms on a hierarchical classification task.
In this paper we propose a quasi-Newton algorithm for the celebrated nonnegative matrix factorization (NMF) problem. The proposed algorithm falls into the general framework of Gauss-Newton and Levenberg-Marquardt meth...
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ISBN:
(纸本)9781728127231
In this paper we propose a quasi-Newton algorithm for the celebrated nonnegative matrix factorization (NMF) problem. The proposed algorithm falls into the general framework of Gauss-Newton and Levenberg-Marquardt methods. However, these methods were not able to handle constraints, which is present in NME One of the key contributions in this paper is to apply alternating direction method of multipliers (ADMM) to obtain the iterative update from this Gauss-Newton-like algorithm. Furthermore, we carefully study the structure of the Jacobian Gramian matrix given by the Gauss-Newton updates, and designed a way of exactly inverting the matrix with complexity (O(mnk), which is a significant reduction compared to the naive implementation of complexity (O((m + n)(3)k(3)). The resulting algorithm, which we call NLS-ADMM, enjoys fast convergence rate brought by the quasi-Newton algorithmic framework, while maintaining low per-iteration complexity similar to that of alternating algorithms. Numerical experiments on synthetic data confirms the efficiency of our proposed algorithm.
Hyperspectral unmixing is a critical processing step for many remote sensing applications. nonnegative matrix factorization (NMF) has drawn extensive attention in hyperspectral image analysis recently. Considering tha...
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ISBN:
(纸本)9781538691540
Hyperspectral unmixing is a critical processing step for many remote sensing applications. nonnegative matrix factorization (NMF) has drawn extensive attention in hyperspectral image analysis recently. Considering that the abundance matrix is generally sparse and smooth, we propose a sparsity-constrained NMF with adaptive total variation (SNMF-ATV) algorithm for hyperspectral unmixing. Specifically, the ATV could promote the smoothness of the estimated abundances while avoid the staircase effect caused by TV model. The comparison with other unmixing methods on both synthetic and real data sets demonstrates the effectiveness and superiority of the proposed SNMF-ATV algorithm with regard to the other considered methods.
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