Effective tools for exploration and analysis are needed to extract insights from large-scale single-cell measurement data. However, current techniques for handling single-cell studies performed across experimental conditions (e.g., samples, perturbations, or patients) require restrictive assumptions, lack flexibility, or do not adequately deconvolute condition-to-condition variation from cell-to-cell variation. Here, we report that the tensor decomposition method PARAFAC2 (Pf2) enables the dimensionality reduction of single-cell data across conditions. We demonstrate these benefits across two distinct contexts of single-cell RNA-sequencing (scRNA-seq) experiments of peripheral immune cells: pharmacologic drug perturbations and systemic lupus erythematosus (SLE) patient samples. By isolating relevant gene modules across cells and conditions, Pf2 enables straightforward associations of gene variation patterns across specific patients or perturbations while connecting each coordinated change to certain cells without pre-defining cell types. The theoretical grounding of Pf2 suggests a unified framework for many modeling tasks associated with single-cell data. Thus, Pf2 provides an intuitive universal dimensionality reduction approach for multi-sample single-cell studies across diverse biological contexts.

In the past decade, tensors have become increasingly attractive in different aspects of signal and image processing areas. The main reason is the inefficiency of matrices in representing and analyzing multimodal and multidimensional datasets. Matrices cannot preserve the multidimensional correlation of elements in higher-order datasets and this highly reduces the effectiveness of matrix-based approaches in analyzing multidimensional datasets. Besides this, tensor-based approaches have demonstrated promising performances. These together, encouraged researchers to move from matrices to tensors. Among different signal and image processing applications, analyzing biomedical signals and images is of particular importance. This is due to the need for extracting accurate information from biomedical datasets which directly affects patient\'s health. In addition, in many cases, several datasets have been recorded simultaneously from a patient. A common example is recording electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) of a patient with schizophrenia. In such a situation, tensors seem to be among the most effective methods for the simultaneous exploitation of two (or more) datasets. Therefore, several tensor-based methods have been developed for analyzing biomedical datasets. Considering this reality, in this paper, we aim to have a comprehensive review on tensor-based methods in biomedical image analysis. The presented study and classification between different methods and applications can show the importance of tensors in biomedical image enhancement and open new ways for future studies.

Electrophysiologic disturbances due to neurodegenerative disorders such as Alzheimer\'s disease and Lewy Body disease are detectable by scalp EEG and can serve as a functional measure of disease severity. Traditional quantitative methods of EEG analysis often require an a-priori selection of clinically meaningful EEG features and are susceptible to bias, limiting the clinical utility of routine EEGs in the diagnosis and management of neurodegenerative disorders. We present a data-driven tensor decomposition approach to extract the top 6 spectral and spatial features representing commonly known sources of EEG activity during eyes-closed wakefulness. As part of their neurologic evaluation at Mayo Clinic, 11 001 patients underwent 12 176 routine, standard 10-20 scalp EEG studies. From these raw EEGs, we developed an algorithm based on posterior alpha activity and eye movement to automatically select awake-eyes-closed epochs and estimated average spectral power density (SPD) between 1 and 45 Hz for each channel. We then created a three-dimensional (3D) tensor (record × channel × frequency) and applied a canonical polyadic decomposition to extract the top six factors. We further identified an independent cohort of patients meeting consensus criteria for mild cognitive impairment (30) or dementia (39) due to Alzheimer\'s disease and dementia with Lewy Bodies (31) and similarly aged cognitively normal controls (36). We evaluated the ability of the six factors in differentiating these subgroups using a Naïve Bayes classification approach and assessed for linear associations between factor loadings and Kokmen short test of mental status scores, fluorodeoxyglucose (FDG) PET uptake ratios and CSF Alzheimer\'s Disease biomarker measures. Factors represented biologically meaningful brain activities including posterior alpha rhythm, anterior delta/theta rhythms and centroparietal beta, which correlated with patient age and EEG dysrhythmia grade. These factors were also able to distinguish patients from controls with a moderate to high degree of accuracy (Area Under the Curve (AUC) 0.59-0.91) and Alzheimer\'s disease dementia from dementia with Lewy Bodies (AUC 0.61). Furthermore, relevant EEG features correlated with cognitive test performance, PET metabolism and CSF AB42 measures in the Alzheimer\'s subgroup. This study demonstrates that data-driven approaches can extract biologically meaningful features from population-level clinical EEGs without artefact rejection or a-priori selection of channels or frequency bands. With continued development, such data-driven methods may improve the clinical utility of EEG in memory care by assisting in early identification of mild cognitive impairment and differentiating between different neurodegenerative causes of cognitive impairment.

As an effective strategy for reducing the noisy and redundant information for hyperspectral imagery (HSI), hyperspectral band selection intends to select a subset of original hyperspectral bands, which boosts the subsequent different tasks. In this paper, we introduce a multi-dimensional high-order structure preserved clustering method for hyperspectral band selection, referred to as MHSPC briefly. By regarding original hyperspectral images as a tensor cube, we apply the tensor CP (CANDECOMP/PARAFAC) decomposition on it to exploit the multi-dimensional structural information as well as generate a low-dimensional latent feature representation. In order to capture the local geometrical structure along the spectral dimension, a graph regularizer is imposed on the new feature representation in the lower dimensional space. In addition, since the low rankness of HSIs is an important global property, we utilize a nuclear norm constraint on the latent feature representation matrix to capture the global data structure information. Different to most of previous clustering based hyperspectral band selection methods which vectorize each band as a vector without considering the 2-D spatial information, the proposed MHSPC can effectively capture the spatial structure as well as the spectral correlation of original hyperspectral cube in both local and global perspectives. An efficient alternatively updating algorithm with theoretical convergence guarantee is designed to solve the resultant optimization problem, and extensive experimental results on four benchmark datasets validate the effectiveness of the proposed MHSPC over other state-of-the-arts.

OBJECTIVE: Parkinson disease (PD) is a common progressive neurodegenerative disorder in our ageing society. Early-stage PD biomarkers are desired for timely clinical intervention and understanding of pathophysiology. Since one of the characteristics of PD is the progressive loss of dopaminergic neurons in the substantia nigra pars compacta, we propose a feature extraction method for analysing the differences in the substantia nigra between PD and non-PD patients.
METHODS: We propose a feature-extraction method for volumetric images based on a rank-1 tensor decomposition. Furthermore, we apply a feature selection method that excludes common features between PD and non-PD. We collect neuromelanin images of 263 patients: 124 PD and 139 non-PD patients and divide them into training and testing datasets for experiments. We then experimentally evaluate the classification accuracy of the substantia nigra between PD and non-PD patients using the proposed feature extraction method and linear discriminant analysis.
RESULTS: The proposed method achieves a sensitivity of 0.72 and a specificity of 0.64 for our testing dataset of 66 non-PD and 42 PD patients. Furthermore, we visualise the important patterns in the substantia nigra by a linear combination of rank-1 tensors with selected features. The visualised patterns include the ventrolateral tier, where the severe loss of neurons can be observed in PD.
CONCLUSIONS: We develop a new feature-extraction method for the analysis of the substantia nigra towards PD diagnosis. In the experiments, even though the classification accuracy with the proposed feature extraction method and linear discriminant analysis is lower than that of expert physicians, the results suggest the potential of tensorial feature extraction.

Executive functions are essential for adaptive behavior. One executive function is the so-called \'interference control\' or conflict monitoring another one is inhibitory control (i.e., action restraint and action cancelation). Recent evidence suggests an interplay of these processes, which is conceptually relevant given that newer conceptual frameworks imply that nominally different action/response control processes are explainable by a small set of cognitive and neurophysiological processes. The existence of such overarching neural principles has as yet not directly been examined. In the current study, we therefore use EEG tensor decomposition methods, to look into possible common neurophysiological signatures underlying conflict-modulated action restraint and action cancelation as mechanism underlying response inhibition. We show how conflicts differentially modulate action restraint and action cancelation processes and delineate common and distinct neural processes underlying this interplay. Concerning the spatial information modulations are similar in terms of an importance of processes reflected by parieto-occipital electrodes, suggesting that attentional selection processes play a role. Especially theta and alpha activity seem to play important roles. The data also show that tensor decomposition is sensitive to the manner of task implementation, thereby suggesting that switch probability/transitional probabilities should be taken into consideration when choosing tensor decomposition as analysis method. The study provides a blueprint of how to use tensor decomposition methods to delineate common and distinct neural mechanisms underlying action control functions using EEG data.

Many complex chemical problems encoded in terms of physics-based models become computationally intractable for traditional numerical approaches due to their unfavorable scaling with increasing molecular size. Tensor decomposition techniques can overcome such challenges by decomposing unattainably large numerical representations of chemical problems into smaller, tractable ones. In the first two decades of this century, algorithms based on such tensor factorizations have become state-of-the-art methods in various branches of computational chemistry, ranging from molecular quantum dynamics to electronic structure theory and machine learning. Here, we consider the role that tensor decomposition schemes have played in expanding the scope of computational chemistry. We relate some of the most prominent methods to their common underlying tensor network formalisms, providing a unified perspective on leading tensor-based approaches in chemistry and materials science.

BACKGROUND: Electronic health records are a valuable source of patient information that must be properly deidentified before being shared with researchers. This process requires expertise and time. In addition, synthetic data have considerably reduced the restrictions on the use and sharing of real data, allowing researchers to access it more rapidly with far fewer privacy constraints. Therefore, there has been a growing interest in establishing a method to generate synthetic data that protects patients\' privacy while properly reflecting the data.
OBJECTIVE: This study aims to develop and validate a model that generates valuable synthetic longitudinal health data while protecting the privacy of the patients whose data are collected.
METHODS: We investigated the best model for generating synthetic health data, with a focus on longitudinal observations. We developed a generative model that relies on the generalized canonical polyadic (GCP) tensor decomposition. This model also involves sampling from a latent factor matrix of GCP decomposition, which contains patient factors, using sequential decision trees, copula, and Hamiltonian Monte Carlo methods. We applied the proposed model to samples from the MIMIC-III (version 1.4) data set. Numerous analyses and experiments were conducted with different data structures and scenarios. We assessed the similarity between our synthetic data and the real data by conducting utility assessments. These assessments evaluate the structure and general patterns present in the data, such as dependency structure, descriptive statistics, and marginal distributions. Regarding privacy disclosure, our model preserves privacy by preventing the direct sharing of patient information and eliminating the one-to-one link between the observed and model tensor records. This was achieved by simulating and modeling a latent factor matrix of GCP decomposition associated with patients.
RESULTS: The findings show that our model is a promising method for generating synthetic longitudinal health data that is similar enough to real data. It can preserve the utility and privacy of the original data while also handling various data structures and scenarios. In certain experiments, all simulation methods used in the model produced the same high level of performance. Our model is also capable of addressing the challenge of sampling patients from electronic health records. This means that we can simulate a variety of patients in the synthetic data set, which may differ in number from the patients in the original data.
CONCLUSIONS: We have presented a generative model for producing synthetic longitudinal health data. The model is formulated by applying the GCP tensor decomposition. We have provided 3 approaches for the synthesis and simulation of a latent factor matrix following the process of factorization. In brief, we have reduced the challenge of synthesizing massive longitudinal health data to synthesizing a nonlongitudinal and significantly smaller data set.

In recent years, data-driven inference of cell-cell communication has helped reveal coordinated biological processes across cell types. Here, we integrate two tools, LIANA and Tensor-cell2cell, which, when combined, can deploy multiple existing methods and resources to enable the robust and flexible identification of cell-cell communication programs across multiple samples. In this work, we show how the integration of our tools facilitates the choice of method to infer cell-cell communication and subsequently perform an unsupervised deconvolution to obtain and summarize biological insights. We explain how to perform the analysis step by step in both Python and R and provide online tutorials with detailed instructions available at https://ccc-protocols.readthedocs.io/. This workflow typically takes ∼1.5 h to complete from installation to downstream visualizations on a graphics processing unit-enabled computer for a dataset of ∼63,000 cells, 10 cell types, and 12 samples.

The accurate identification of disease-associated genes is crucial for understanding the molecular mechanisms underlying various diseases. Most current methods focus on constructing biological networks and utilizing machine learning, particularly deep learning, to identify disease genes. However, these methods overlook complex relations among entities in biological knowledge graphs. Such information has been successfully applied in other areas of life science research, demonstrating their effectiveness. Knowledge graph embedding methods can learn the semantic information of different relations within the knowledge graphs. Nonetheless, the performance of existing representation learning techniques, when applied to domain-specific biological data, remains suboptimal. To solve these problems, we construct a biological knowledge graph centered on diseases and genes, and develop an end-to-end knowledge graph completion framework for disease gene prediction using interactional tensor decomposition named KDGene. KDGene incorporates an interaction module that bridges entity and relation embeddings within tensor decomposition, aiming to improve the representation of semantically similar concepts in specific domains and enhance the ability to accurately predict disease genes. Experimental results show that KDGene significantly outperforms state-of-the-art algorithms, whether existing disease gene prediction methods or knowledge graph embedding methods for general domains. Moreover, the comprehensive biological analysis of the predicted results further validates KDGene\'s capability to accurately identify new candidate genes. This work proposes a scalable knowledge graph completion framework to identify disease candidate genes, from which the results are promising to provide valuable references for further wet experiments. Data and source codes are available at https://github.com/2020MEAI/KDGene.