scAI: an unsupervised approach for the integrative analysis of parallel single-cell transcriptomic and epigenomic profiles.

Simultaneous measurements of transcriptomic and epigenomic profiles in the same individual cells provide an unprecedented opportunity to understand cell fates. However, effective approaches for the integrative analysis of such data are lacking. Here, we present a single-cell aggregation and integration (scAI) method to deconvolute cellular heterogeneity from parallel transcriptomic and epigenomic profiles. Through iterative learning, scAI aggregates sparse epigenomic signals in similar cells learned in an unsupervised manner, allowing coherent fusion with transcriptomic measurements. Simulation studies and applications to three real datasets demonstrate its capability of dissecting cellular heterogeneity within both transcriptomic and epigenomic layers and understanding transcriptional regulatory mechanisms

Simultaneous non-negative matrix factorization for multiple large scale gene expression datasets in toxicology

Non-negative matrix factorization is a useful tool for reducing the dimension of large datasets. This work considers simultaneous non-negative matrix factorization of multiple sources of data. In particular, we perform the first study that involves more than two datasets. We discuss the algorithmic issues required to convert the approach into a practical computational tool and apply the technique to new gene expression data quantifying the molecular changes in four tissue types due to different dosages of an experimental panPPAR agonist in mouse. This study is of interest in toxicology because, whilst PPARs form potential therapeutic targets for diabetes, it is known that they can induce serious side-effects. Our results show that the practical simultaneous non-negative matrix factorization developed here can add value to the data analysis. In particular, we find that factorizing the data as a single object allows us to distinguish between the four tissue types, but does not correctly reproduce the known dosage level groups. Applying our new approach, which treats the four tissue types as providing distinct, but related, datasets, we find that the dosage level groups are respected. The new algorithm then provides separate gene list orderings that can be studied for each tissue type, and compared with the ordering arising from the single factorization. We find that many of our conclusions can be corroborated with known biological behaviour, and others offer new insights into the toxicological effects. Overall, the algorithm shows promise for early detection of toxicity in the drug discovery process

Multi-omics assessment of dilated cardiomyopathy using non-negative matrix factorization

Dilated cardiomyopathy (DCM), a myocardial disease, is heterogeneous and often results in heart failure and sudden cardiac death. Unavailability of cardiac tissue has hindered the comprehensive exploration of gene regulatory networks and nodal players in DCM. In this study, we carried out integrated analysis of transcriptome and methylome data using nonnegative matrix factorization from a cohort of DCM patients to uncover underlying latent factors and covarying features between whole-transcriptome and epigenome omics datasets from tissue biopsies of living patients. DNA methylation data from Infinium HM450 and mRNA Illumina sequencing of n = 33 DCM and n = 24 control probands were filtered, analyzed and used as input for matrix factorization using R NMF package. Mann-Whitney U test showed 4 out of 5 latent factors are significantly different between DCM and control probands (P<0.05). Characterization of top 10% features driving each latent factor showed a significant enrichment of biological processes known to be involved in DCM pathogenesis, including immune response (P = 3.97E-21), nucleic acid binding (P = 1.42E-18), extracellular matrix (P = 9.23E-14) and myofibrillar structure (P = 8.46E-12). Correlation network analysis revealed interaction of important sarcomeric genes like Nebulin, Tropomyosin alpha-3 and ERC-protein 2 with CpG methylation of ATPase Phospholipid Transporting 11A0, Solute Carrier Family 12 Member 7 and Leucine Rich Repeat Containing 14B, all with significant P values associated with correlation coefficients >0.7. Using matrix factorization, multiomics data derived from human tissue samples can be integrated and novel interactions can be identified. Hypothesis generating nature of such analysis could help to better understand the pathophysiology of complex traits such as DCM

Faktorizacija matrik nizkega ranga pri učenju z večjedrnimi metodami

The increased rate of data collection, storage, and availability results in a corresponding interest for data analyses and predictive models based on simultaneous inclusion of multiple data sources. This tendency is ubiquitous in practical applications of machine learning, including recommender systems, social network analysis, finance and computational biology. The heterogeneity and size of the typical datasets calls for simultaneous dimensionality reduction and inference from multiple data sources in a single model. Matrix factorization and multiple kernel learning models are two general approaches that satisfy this goal. This work focuses on two specific goals, namely i) finding interpretable, non-overlapping (orthogonal) data representations through matrix factorization and ii) regression with multiple kernels through the low-rank approximation of the corresponding kernel matrices, providing non-linear outputs and interpretation of kernel selection. The motivation for the models and algorithms designed in this work stems from RNA biology and the rich complexity of protein-RNA interactions. Although the regulation of RNA fate happens at many levels - bringing in various possible data views - we show how different questions can be answered directly through constraints in the model design. We have developed an integrative orthogonality nonnegative matrix factorization (iONMF) to integrate multiple data sources and discover non-overlapping, class-specific RNA binding patterns of varying strengths. We show that the integration of multiple data sources improves the predictive accuracy of retrieval of RNA binding sites and report on a number of inferred protein-specific patterns, consistent with experimentally determined properties. A principled way to extend the linear models to non-linear settings are kernel methods. Multiple kernel learning enables modelling with different data views, but are limited by the quadratic computation and storage complexity of the kernel matrix. Considerable savings in time and memory can be expected if kernel approximation and multiple kernel learning are performed simultaneously. We present the Mklaren algorithm, which achieves this goal via Incomplete Cholesky Decomposition, where the selection of basis functions is based on Least-angle regression, resulting in linear complexity both in the number of data points and kernels. Considerable savings in approximation rank are observed when compared to general kernel matrix decompositions and comparable to methods specialized to particular kernel function families. The principal advantages of Mklaren are independence of kernel function form, robust inducing point selection and the ability to use different kernels in different regions of both continuous and discrete input spaces, such as numeric vector spaces, strings or trees, providing a platform for bioinformatics. In summary, we design novel models and algorithms based on matrix factorization and kernel learning, combining regression, insights into the domain of interest by identifying relevant patterns, kernels and inducing points, while scaling to millions of data points and data views.V času pospešenega zbiranja, organiziranja in dostopnosti podatkov se pojavlja potreba po razvoju napovednih modelov na osnovi hkratnega učenja iz več podatkovnih virov. Konkretni primeri uporabe obsegajo področja strojnega učenja, priporočilnih sistemov, socialnih omrežij, financ in računske biologije. Heterogenost in velikost tipičnih podatkovnih zbirk vodi razvoj postopkov za hkratno zmanjšanje velikosti (zgoščevanje) in sklepanje iz več virov podatkov v skupnem modelu. Matrična faktorizacija in jedrne metode (ang. kernel methods) sta dve splošni orodji, ki omogočata dosego navedenega cilja. Pričujoče delo se osredotoča na naslednja specifična cilja: i) iskanje interpretabilnih, neprekrivajočih predstavitev vzorcev v podatkih s pomočjo ortogonalne matrične faktorizacije in ii) nadzorovano hkratno faktorizacijo več jedrnih matrik, ki omogoča modeliranje nelinearnih odzivov in interpretacijo pomembnosti različnih podatkovnih virov. Motivacija za razvoj modelov in algoritmov v pričujočem delu izhaja iz RNA biologije in bogate kompleksnosti interakcij med proteini in RNA molekulami v celici. Čeprav se regulacija RNA dogaja na več različnih nivojih - kar vodi v več podatkovnih virov/pogledov - lahko veliko lastnosti regulacije odkrijemo s pomočjo omejitev v fazi modeliranja. V delu predstavimo postopek hkratne matrične faktorizacije z omejitvijo, da se posamezni vzorci v podatkih ne prekrivajo med seboj - so neodvisni oz. ortogonalni. V praksi to pomeni, da lahko odkrijemo različne, neprekrivajoče načine regulacije RNA s strani različnih proteinov. Z vzključitvijo več podatkovnih virov izboljšamo napovedno točnost pri napovedovanju potencialnih vezavnih mest posameznega RNA-vezavnega proteina. Vzorci, odkriti iz podatkov so primerljivi z eksperimentalno določenimi lastnostmi proteinov in obsegajo kratka zaporedja nukleotidov na RNA, kooperativno vezavo z drugimi proteini, RNA strukturnimi lastnostmi ter funkcijsko anotacijo. Klasične metode matrične faktorizacije tipično temeljijo na linearnih modelih podatkov. Jedrne metode so eden od načinov za razširitev modelov matrične faktorizacije za modeliranje nelinearnih odzivov. Učenje z več jedri (ang. Multiple kernel learning) omogoča učenje iz več podatkovnih virov, a je omejeno s kvadratno računsko zahtevnostjo v odvisnosti od števila primerov v podatkih. To omejitev odpravimo z ustreznimi približki pri izračunu jedrnih matrik (ang. kernel matrix). V ta namen izboljšamo obstoječe metode na način, da hkrati izračunamo aproksimacijo jedrnih matrik ter njihovo linearno kombinacijo, ki modelira podan tarčni odziv. To dosežemo z metodo Mklaren (ang. Multiple kernel learning based on Least-angle regression), ki je sestavljena iz Nepopolnega razcepa Choleskega in Regresije najmanjših kotov (ang. Least-angle regression). Načrt algoritma vodi v linearno časovno in prostorsko odvisnost tako glede na število primerov v podatkih kot tudi glede na število jedrnih funkcij. Osnovne prednosti postopka so poleg računske odvisnosti tudi splošnost oz. neodvisnost od uporabljenih jedrnih funkcij. Tako lahko uporabimo različne, splošne jedrne funkcije za modeliranje različnih delov prostora vhodnih podatkov, ki so lahko zvezni ali diskretni, npr. vektorski prostori, prostori nizov znakov in drugih podatkovnih struktur, kar je prikladno za uporabo v bioinformatiki. V delu tako razvijemo algoritme na osnovi hkratne matrične faktorizacije in jedrnih metod, obravnavnamo modele linearne in nelinearne regresije ter interpretacije podatkovne domene - odkrijemo pomembna jedra in primere podatkov, pri čemer je metode mogoče poganjati na milijonih podatkovnih primerov in virov

The Reasonable Effectiveness of Randomness in Scalable and Integrative Gene Regulatory Network Inference and Beyond

Gene regulation is orchestrated by a vast number of molecules, including transcription factors and co-factors, chromatin regulators, as well as epigenetic mechanisms, and it has been shown that transcriptional misregulation, e.g., caused by mutations in regulatory sequences, is responsible for a plethora of diseases, including cancer, developmental or neurological disorders. As a consequence, decoding the architecture of gene regulatory networks has become one of the most important tasks in modern (computational) biology. However, to advance our understanding of the mechanisms involved in the transcriptional apparatus, we need scalable approaches that can deal with the increasing number of large-scale, high-resolution, biological datasets. In particular, such approaches need to be capable of efficiently integrating and exploiting the biological and technological heterogeneity of such datasets in order to best infer the underlying, highly dynamic regulatory networks, often in the absence of sufficient ground truth data for model training or testing. With respect to scalability, randomized approaches have proven to be a promising alternative to deterministic methods in computational biology. As an example, one of the top performing algorithms in a community challenge on gene regulatory network inference from transcriptomic data is based on a random forest regression model. In this concise survey, we aim to highlight how randomized methods may serve as a highly valuable tool, in particular, with increasing amounts of large-scale, biological experiments and datasets being collected. Given the complexity and interdisciplinary nature of the gene regulatory network inference problem, we hope our survey maybe helpful to both computational and biological scientists. It is our aim to provide a starting point for a dialogue about the concepts, benefits, and caveats of the toolbox of randomized methods, since unravelling the intricate web of highly dynamic, regulatory events will be one fundamental step in understanding the mechanisms of life and eventually developing efficient therapies to treat and cure diseases

GoM DE: interpreting structure in sequence count data with differential expression analysis allowing for grades of membership

Parts-based representations, such as non-negative matrix factorization and topic modeling, have been used to identify structure from single-cell sequencing data sets, in particular structure that is not as well captured by clustering or other dimensionality reduction methods. However, interpreting the individual parts remains a challenge. To address this challenge, we extend methods for differential expression analysis by allowing cells to have partial membership to multiple groups. We call this grade of membership differential expression (GoM DE). We illustrate the benefits of GoM DE for annotating topics identified in several single-cell RNA-seq and ATAC-seq data sets

DNA Microarray Data Analysis: A New Survey on Biclustering

There are subsets of genes that have similar behavior under subsets of conditions, so we say that they coexpress, but behave independently under other subsets of conditions. Discovering such coexpressions can be helpful to uncover genomic knowledge such as gene networks or gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of genes and conditions to identify clusters of genes that are coexpressed under clusters of conditions. This type of clustering is called biclustering.Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to approximate this problem by finding suboptimal solutions. In this paper, we make a new survey on biclustering of gene expression data, also called microarray data