Performance Of Non-negative Matrix Factorization Research Articles

Systematic reduction of hyperspectral images for high-throughput plastic characterization

Hyperspectral Imaging (HSI) combines microscopy and spectroscopy to assess the spatial distribution of spectroscopically active compounds in objects, and has diverse applications in food quality control, pharmaceutical processes, and waste sorting. However, due to the large size of HSI datasets, it can be challenging to analyze and store them within a reasonable digital infrastructure, especially in waste sorting where speed and data storage resources are limited. Additionally, as with most spectroscopic data, there is significant redundancy, making pixel and variable selection crucial for retaining chemical information. Recent high-tech developments in chemometrics enable automated and evidence-based data reduction, which can substantially enhance the speed and performance of Non-Negative Matrix Factorization (NMF), a widely used algorithm for chemical resolution of HSI data. By recovering the pure contribution maps and spectral profiles of distributed compounds, NMF can provide evidence-based sorting decisions for efficient waste management. To improve the quality and efficiency of data analysis on hyperspectral imaging (HSI) data, we apply a convex-hull method to select essential pixels and wavelengths and remove uninformative and redundant information. This process minimizes computational strain and effectively eliminates highly mixed pixels. By reducing data redundancy, data investigation and analysis become more straightforward, as demonstrated in both simulated and real HSI data for plastic sorting.

Nonnegative Matrix Factorization: A Review

Recent developments in Non-negative Matrix Factorization (NMF) have focused on addressing several challenges and advancing its applicability. New algorithmic variations, such as robust NMF, deep NMF, and graph-regularized NMF, have emerged to improve NMF's performance in various domains. These developments aim to enhance the interpretability, scalability, and robustness of NMF-based solutions. NMF is now widely used in audio source separation, text mining, recommendation systems, and image processing. However, NMF still faces challenges, including sensitivity to initialization, the determination of the appropriate rank, and computational complexity. Overlapping sources in audio and data sparsity in some applications remain challenging issues. Additionally, ensuring the consistency and stability of NMF results in noisy environments is a subject of ongoing research. The quest for more efficient and scalable NMF algorithms continues, especially for handling large datasets. While NMF has made significant strides in recent years, addressing these challenges is crucial for unlocking its full potential in diverse data analysis and source separation tasks.

Structured Joint Sparse Orthogonal Nonnegative Matrix Factorization for Fault Detection

As modern industrial processes become complicated, and some faults are difficult to be detected due to noises and nonlinearity of data, data-driven fault detection has been extensively used to detect abnormal events in functional units. In order to obtain the better fault detection performance of nonnegative matrix factorization, this paper first proposes a fault detection method using the structured joint sparse orthogonal nonnegative matrix factorization. The core idea is to incorporate the graph regularization, sparsity and orthogonality constraints into the classical nonnegative matrix factorization, which enjoys stronger discriminative ability, removes redundancy of different basis vectors and improves the fault interpretability. More importantly, an optimization algorithm based on the proximal alternating nonnegative least squares is developed, which can guarantee and speed up the convergence. Finally, the effectiveness of the proposed method is demonstrated by the experiments on the benchmark Tennessee Eastman Process and two practical bearing datasets. Particularly, compared with the classical nonnegative matrix factorization, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> statistic has a gain of 33.13% for the fault IDV(16) on the Tennessee Eastman Process. The results show that the proposed model and algorithms are promising for the fault detection.

Subspace Clustering Constrained Sparse NMF for Hyperspectral Unmixing

As one of the most important information of hyperspectral images (HSI), spatial information is usually simulated with the similarity among pixels to enhance the unmixing performance of nonnegative matrix factorization (NMF). Nevertheless, the similarity is generally calculated based on the Euclidean distance between pairwise pixels, which is sensitive to noise and fails in capturing subspace information of hyperspectral data. In addition, it is independent of the NMF framework. In this article, we propose a novel unmixing method called subspace clustering constrained sparse NMF (SC-NMF) for hyperspectral unmixing to more accurately extract endmembers and correspond abundances. First, the nonnegative subspace clustering is embedded into the NMF framework to learn a similar graph, which takes full advantage of the characteristics of the reconstructed data itself to extract the spatial correlation of pixels for unmixing. It is noteworthy that the similar graph and NMF will be simultaneously updated. Second, to mitigate the influence of noise in HSI, only the $k$ largest values are retained in each self-expression vector. Finally, we use the idea of subspace clustering to extract endmembers by linearly combining of all pixels in spectral subspace, aiming at giving a reasonable physical significance to the endmembers. We evaluate the proposed SC-NMF on both synthetic and real hyperspectral data, and experimental results demonstrate that the proposed method is effective and superior by comparing with the state-of-the-art methods.

Comparison of Initialization Techniques for the Accurate Extraction of Muscle Synergies from Myoelectric Signals via Nonnegative Matrix Factorization.

The main goal of this work was to assess the performance of different initializations of matrix factorization algorithms for an accurate identification of muscle synergies. Currently, nonnegative matrix factorization (NNMF) is the most commonly used method to identify muscle synergies. However, it has been shown that NNMF performance might be affected by different kinds of initialization. The present study aims at optimizing the traditional NNMF initialization for data with partial or complete temporal dependencies. For this purpose, three different initializations are used: random, SVD-based, and sparse. NNMF was used to identify muscle synergies from simulated data as well as from experimental surface EMG signals. Simulated data were generated from synthetic independent and dependent synergy vectors (i.e., shared muscle components), whose activation coefficients were corrupted by simulating controlled degrees of correlation. Similarly, EMG data were artificially modified, making the extracted activation coefficients temporally dependent. By measuring the quality of identification of the original synergies underlying the data, it was possible to compare the performance of different initialization techniques. Simulation results demonstrate that sparse initialization performs significantly better than all other kinds of initialization in reconstructing muscle synergies, regardless of the correlation level in the data.

Detecting heterogeneity in single-cell RNA-Seq data by non-negative matrix factorization.

Single-cell RNA-Sequencing (scRNA-Seq) is a fast-evolving technology that enables the understanding of biological processes at an unprecedentedly high resolution. However, well-suited bioinformatics tools to analyze the data generated from this new technology are still lacking. Here we investigate the performance of non-negative matrix factorization (NMF) method to analyze a wide variety of scRNA-Seq datasets, ranging from mouse hematopoietic stem cells to human glioblastoma data. In comparison to other unsupervised clustering methods including K-means and hierarchical clustering, NMF has higher accuracy in separating similar groups in various datasets. We ranked genes by their importance scores (D-scores) in separating these groups, and discovered that NMF uniquely identifies genes expressed at intermediate levels as top-ranked genes. Finally, we show that in conjugation with the modularity detection method FEM, NMF reveals meaningful protein-protein interaction modules. In summary, we propose that NMF is a desirable method to analyze heterogeneous single-cell RNA-Seq data. The NMF based subpopulation detection package is available at: https://github.com/lanagarmire/NMFEM.