MOTIVATION: Molecular signatures are critical for inferring the proportions of cell types from bulk transcriptomics data. However, the identification of these signatures is based on a methodology that relies on prior biological knowledge of the cell types being studied. When working with less known biological material, a data-driven approach is required to uncover the underlying classes and generate ad hoc signatures from healthy or pathogenic tissue. RESULTS: We present a new approach, A2Sign: Agnostic Algorithms for Signatures, based on a non-negative tensor factorization (NTF) strategy that allows us to identify cell-type-specific molecular signatures, greatly reduce collinearities and also account for inter-individual variability. We propose a global framework that can be applied to uncover molecular signatures for cell-type deconvolution in arbitrary tissues using bulk transcriptome data. We also present two new molecular signatures for deconvolution of up to 16 immune cell types using microarray or RNA-seq data. AVAILABILITY AND IMPLEMENTATION: All steps of our analysis were implemented in annotated Python notebooks (https://github.com/paulfogel/A2SIGN). To perform NTF, we used the NMTF package, which can be downloaded using Python pip install. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model that represents data as an ordered network of subtensors of order-2 or order-3 has, so far, not been widely considered in these fields, although this so-called tensor network (TN) decomposition has been long studied in quantum physics and scientific computing. In this article, we present novel algorithms and applications of TN decompositions, with a particular focus on the tensor train (TT) decomposition and its variants. The novel algorithms developed for the TT decomposition update, in an alternating way, one or several core tensors at each iteration and exhibit enhanced mathematical tractability and scalability for large-scale data tensors. For rigor, the cases of the given ranks, given approximation error, and the given error bound are all considered. The proposed algorithms provide well-balanced TT-decompositions and are tested in the classic paradigms of blind source separation from a single mixture, denoising, and feature extraction, achieving superior performance over the widely used truncated algorithms for TT decomposition.

We propose a novel decomposition approach to impute missing values in tensor data. The method uses smaller scale multiway patches to model the whole data or a small volume encompassing the observed missing entries. Simulations on color images show that our method can recover color images using only 5–10% of pixels, and outperforms other available tensor completion methods.

BACKGROUND: High-throughput flow cytometry experiments produce hundreds of large multivariate samples of cellular characteristics. These samples require specialized processing to obtain clinically meaningful measurements. A major component of this processing is a form of cell subsetting known as gating. Manual gating is time-consuming and subjective. Good automatic and semi-automatic gating algorithms are very beneficial to high-throughput flow cytometry. RESULTS: We develop a statistical procedure, named curvHDR, for automatic and semi-automatic gating. The method combines the notions of significant high negative curvature regions and highest density regions and has the ability to adapt well to human-perceived gates. The underlying principles apply to dimension of arbitrary size, although we focus on dimensions up to three. Accompanying software, compatible with contemporary flow cytometry infor-matics, is developed. CONCLUSION: The method is seen to adapt well to nuances in the data and, to a reasonable extent, match human perception of useful gates. It offers big savings in human labour when processing high-throughput flow cytometry data whilst retaining a good degree of efficacy.