Nonnegative matrix factorization for analyzing state dependent neuronal network dynamics in calcium recordings

Non-negative subspace feature representation for few-shot learning in medical imaging

Normalized dimensionality reduction using nonnegative matrix factorization

UAVs (unmanned aerial vehicles) have been widely used in many fields, where they need to be detected and controlled. Small-sample UAV recognition requires an effective detecting and recognition method. When identifying a UAV target using the backward propagation (BP) neural network, fully connected neurons of BP neural network and the high-dimensional input features will generate too many weights for training, induce complex network structure, and poor recognition performance. In this paper, a novel recognition method based on non-negative matrix factorization (NMF) with sparseness constraint feature dimension reduction and BP neural network is proposed for the above difficulties. The Edgeboxes are used for candidate regions and Log-Gabor features are extracted in candidate target regions. In order to avoid the complexity of the matrix operation with the high-dimensional Log-Gabor features, preprocessing for feature reduction by downsampling is adopted, which makes the NMF fast and the feature discriminative. The classifier is trained by neural network with the feature of dimension reduction. The experimental results show that the method is better than the traditional methods of dimension reduction, such as PCA (principal component analysis), FLD (Fisher linear discrimination), LPP (locality preserving projection), and KLPP (kernel locality preserving projection), and can identify the UAV target quickly and accurately.

BackgroundIn-vivo single voxel proton magnetic resonance spectroscopy (SV 1H-MRS), coupled with supervised pattern recognition (PR) methods, has been widely used in clinical studies of discrimination of brain tumour types and follow-up of patients bearing abnormal brain masses. SV 1H-MRS provides useful biochemical information about the metabolic state of tumours and can be performed at short (< 45 ms) or long (> 45 ms) echo time (TE), each with particular advantages. Short-TE spectra are more adequate for detecting lipids, while the long-TE provides a much flatter signal baseline in between peaks but also negative signals for metabolites such as lactate. Both, lipids and lactate, are respectively indicative of specific metabolic processes taking place. Ideally, the information provided by both TE should be of use for clinical purposes. In this study, we characterise the performance of a range of Non-negative Matrix Factorisation (NMF) methods in two respects: first, to derive sources correlated with the mean spectra of known tissue types (tumours and normal tissue); second, taking the best performing NMF method for source separation, we compare its accuracy for class assignment when using the mixing matrix directly as a basis for classification, as against using the method for dimensionality reduction (DR). For this, we used SV 1H-MRS data with positive and negative peaks, from a widely tested SV 1H-MRS human brain tumour database.ResultsThe results reported in this paper reveal the advantage of using a recently described variant of NMF, namely Convex-NMF, as an unsupervised method of source extraction from SV1H-MRS. Most of the sources extracted in our experiments closely correspond to the mean spectra of some of the analysed tumour types. This similarity allows accurate diagnostic predictions to be made both in fully unsupervised mode and using Convex-NMF as a DR step previous to standard supervised classification. The obtained results are comparable to, or more accurate than those obtained with supervised techniques.ConclusionsThe unsupervised properties of Convex-NMF place this approach one step ahead of classical label-requiring supervised methods for the discrimination of brain tumour types, as it accounts for their increasingly recognised molecular subtype heterogeneity. The application of Convex-NMF in computer assisted decision support systems is expected to facilitate further improvements in the uptake of MRS-derived information by clinicians.

Calcium imaging has been widely adopted for its ability to record from large neuronal populations. To summarize the time course of neural activity, dimensionality reduction methods, which have been applied extensively to population spiking activity, may be particularly useful. However, it is unclear if the dimensionality reduction methods applied to spiking activity are appropriate for calcium imaging. We thus carried out a systematic study of design choices based on standard dimensionality reduction methods. We also developed a method to perform deconvolution and dimensionality reduction simultaneously (Calcium Imaging Linear Dynamical System, CILDS). CILDS most accurately recovered the single-trial, low-dimensional time courses from simulated calcium imaging data. CILDS also outperformed the other methods on calcium imaging recordings from larval zebrafish and mice. More broadly, this study represents a foundation for summarizing calcium imaging recordings of large neuronal populations using dimensionality reduction in diverse experimental settings.

Mass spectrometry imaging (MSI) is a powerful scientific tool for understanding the spatial distribution of biochemical compounds in tissue structures. In this paper, we introduce three novel approaches in MSI data processing to perform the tasks of data augmentation, feature ranking, and image registration. We use these approaches in conjunction with non-negative matrix factorization (NMF) to resolve two of the biggest challenges in MSI data analysis, namely: 1) the large file sizes and associated computational resource requirements and 2) the complexity of interpreting the very high dimensional raw spectral data. There are many dimensionality reduction techniques that address the first challenge but do not necessarily result in readily interpretable features, leaving the second challenge unaddressed. We demonstrate that NMF is an effective dimensionality reduction algorithm that reduces the size of MSI datasets by three orders of magnitude with limited loss of information, yielding spatial and spectral components with meaningful correlation to tissue structure that may be used directly for subsequent data analysis without the need for additional clustering steps. This analysis is demonstrated on an MSI dataset from female Sprague-Dawley rats for an animal model of comorbid visceral pain hypersensitivity (CPH). We find that high-dimensional MSI data (∼ 100,000 ions per pixel) can be reduced to 20 spectral NMF components with < 20% loss in reconstruction accuracy. The resulting spatial NMF components are reproducible and correlate well with H&E-stained tissue images. These components may also be used to generate images with enhanced specificity for different tissue types. Small patches of NMF data (i.e., 20 spatial NMF components over 20 × 20 pixels) provide an accuracy of ∼ 87% in classifying CPH vs naïve control subjects. This paper presents the novel data processing methodologies that were used to produce these results, encompassing novel data processing pipelines for data augmentation to support training for classification, ranking of features according to their contribution to classification, and image registration to enhance tissue-specific imaging.

K-nearest-neighbors induced topological PCA for single cell RNA-sequence data analysis

Non-negative Matrix Factorization (NMF) and Singular Value Decomposition (SVD) are widely recognized as pivotal dimensionality reduction techniques in the literature, particularly for deep learning applications involving large and high-dimensional datasets like SEM images. This study systematically evaluates the impact of SVD and NMF on the performance, efficiency, and energy consumption of four deep learning architectures: GoogleNet, AlexNet, ResNet, and SqueezeNet. By applying these techniques to reduce dataset dimensions, we observed that SVD excelled in computational efficiency, achieving up to 35% faster processing times compared to raw datasets. NMF, on the other hand, provided superior feature interpretability, which proved beneficial for tasks requiring meaningful pattern extraction. Energy consumption analysis revealed that SVD led to a 28% reduction in computational energy cost on average, making it a practical choice for resource-constrained environments. Among the evaluated models, ResNet consistently delivered the highest classification accuracy after dimensionality reduction, showing an improvement of 4-6% over models trained on non-reduced data. These findings underscore the critical role of dimensionality reduction in enhancing the scalability, energy efficiency, and classification accuracy of deep learning models, offering valuable insights for optimizing high-dimensional data applications in both academic and industrial contexts.

In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful basis vector for the set of data, and indicate which data use which basis vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the basis matrix, and the basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the basis matrix may not be smooth. We think that the basis vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, basis vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for basis vectors. However, the proposed method introduces the sparsity for coefficient vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient vectors and the smoothness for the basis vectors, can extract the smooth basis vectors and the original economical data are approximated as the weighted sum of the few bases vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.

A majorization–minimization based solution to penalized nonnegative matrix factorization with orthogonal regularization

Nonnegative Matrix Factorization (NMF), as a popular feature extraction technique, has recently attracted increasing attentions in high-dimensional data analysis, due to the strong ability of dimension reduction and semantic representation. In order to utilize the partial label information in practice, several semi-supervised NMF methods have been proposed. However, existing semi-supervised NMF variants only consider the global label constraint of data, but ignore the local label information embedded in geometric structure, which is very crucial for data representation. To address the above issue, we propose an improved NMF method, namely local and global regularized semi-supervised NMF (LGNMF), by considering the local and global label constraints simultaneously. Specifically, the local label constraint is depicted in a graph, which is pre-computed by metric learning. In addition, to explore the global label information, we construct an indicator matrix to restrict the coefficient matrix in LGNMF. For the formulated LGNMF, a multiplicative update rule (MUR) is developed. Extensive experiments on several real datasets demonstrate the superiority of the proposed method over the state-of-the-art methods in terms of clustering accuracy and normalized mutual information.

Breast cancer remains a critical global health concern, requiring advanced and reliable diagnostic methods for early detection and effective intervention. This work introduces an integrated ensemble framework that combines multiple dimensionality reduction (DR) techniques, including Principal Component Analysis (PCA), Non-negative Matrix Factorization (NMF), and Singular Value Decomposition (SVD), with robust machine learning (ML) classifiers for improved breast cancer detection. The publicly available Wisconsin Breast Cancer Dataset (WBCD) was utilized, with rigorous data preprocessing performed to address missing values, anomalies, and class imbalance through stratified sampling and median imputation. To mitigate overfitting and underfitting, dimensionality reduction was coupled with cross-validation and ensemble strategies. The predictive performance of Logistic Regression (LR), Support Vector Machine (SVM), Random Forest (RF), Decision Tree (DT), and Multi-Layer Perceptron (MLP) was systematically evaluated. Experimental results show that SVM consistently achieves a maximum accuracy of 97.9 % across all applied DR techniques, while MLP and LR also reach 97.9 % accuracy with PCA and NMF, though MLP exhibits performance variability depending on the selected DR method. The findings provide practical guidance for healthcare practitioners and researchers, supporting the adoption of explainable and scalable AI-driven diagnostic tools. Limitations include the reliance on a single dataset and the need for further validation on larger and more diverse clinical cohorts. Future work will focus on enhancing model interpretability, external validation, and real-world deployment in resource-constrained settings.

The hippocampus and associated cholinergic inputs have important roles in spatial memory in rodents. Muscarinic acetylcholine receptors (mAChRs) are involved in the communication of cholinergic signals and regulate spatial memory. They have been found to impact the memory encoding process, but the effect on memory retrieval is controversial. Previous studies report that scopolamine (a non-selective antagonist of mAChR) induces cognitive deficits on animals, resulting in impaired memory encoding, but the effect on memory retrieval is less certain. We tested the effects of blocking mAChRs on hippocampal network activity and neural ensembles that had previously encoded spatial information. The activity of hundreds of neurons in mouse hippocampal CA1 was recorded using calcium imaging with a miniaturised fluorescent microscope and properties of place cells and neuronal ensemble behaviour in a linear track environment were observed. We found that the decoding accuracy and the stability of spatial representation revealed by hippocampal neural ensemble were significantly reduced after the administration of scopolamine. Several other parameters, including neural firing rate, total number of active neurons, place cell number and spatial information content were affected. Similar results were also observed in a simulated hippocampal network model. This study enhances the understanding of the function of mAChRs on spatial memory impairment.

Face age prediction based on face image is an important research direction in the field of face recognition, and it is also a difficult point. Non-negative matrix factorization (NMF) dimensionality reduction method can fix the number of features after dimensionality reduction. In this paper, an optimization algorithm based on NMF is proposed for improving the accuracy of age prediction based on face images. It was confirmed that the maximum performance was shown for precision 0.19 in category 1 (21-24 ages), recall 0.20 in category 5 (40-44 ages), and f1-score 0.18 in categories 1-3 (21-34 ages) and 5. In addition, the mean absolute error (MAE) of the proposed algorithm is 1.92, which is about 31.85% lower than that of other algorithms.

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex, by using the theory of Completely Positive Factorization. We subsequently explore four novel approaches to finding globally-optimal NMF solutions using various ideas from convex optimization. We then develop a new method, isometric NMF (isoNMF), which preserves non-negativity while also providing an isometric embedding, simultaneously achieving two properties which are helpful for interpretation. Though it results in a more difficult optimization problem, we show experimentally that the resulting method is scalable and even achieves more compact spectra than standard NMF.