Multi-omics data have revolutionized biomedical research by providing a comprehensive understanding of biological systems and the molecular mechanisms of disease development. However, analyzing multi-omics data is challenging due to high dimensionality and limited sample sizes, necessitating proper data-reduction pipelines to ensure reliable analyses. Additionally, its multimodal nature requires effective data-integration pipelines. While several dimensionality reduction and data fusion algorithms have been proposed, crucial aspects are often overlooked. Specifically, the choice of projection space dimension is typically heuristic and uniformly applied across all omics, neglecting the unique high dimension small sample size challenges faced by individual omics. This paper introduces a novel multi-modal dimensionality reduction pipeline tailored to individual views. By leveraging intrinsic dimensionality estimators, we assess the curse-of-dimensionality impact on each view and propose a two-step reduction strategy for significantly affected views, combining feature selection with feature extraction. Compared to traditional uniform reduction pipelines in a crucial and supervised multi-omics analysis setting, our approach shows significant improvement. Additionally, we explore three effective unsupervised multi-omics data fusion methods rooted in the main data fusion strategies to gain insights into their performance under crucial, yet overlooked, settings.

MOTIVATION: Precision medicine leverages patient-specific multimodal data to improve prevention, diagnosis, prognosis, and treatment of diseases. Advancing precision medicine requires the non-trivial integration of complex, heterogeneous, and potentially high-dimensional data sources, such as multi-omics and clinical data. In the literature, several approaches have been proposed to manage missing data, but are usually limited to the recovery of subsets of features for a subset of patients. A largely overlooked problem is the integration of multiple sources of data when one or more of them are completely missing for a subset of patients, a relatively common condition in clinical practice. RESULTS: We propose miss-Similarity Network Fusion (miss-SNF), a novel general-purpose data integration approach designed to manage completely missing data in the context of patient similarity networks. miss-SNF integrates incomplete unimodal patient similarity networks by leveraging a non-linear message-passing strategy borrowed from the SNF algorithm. miss-SNF is able to recover missing patient similarities and is "task agnostic", in the sense that can integrate partial data for both unsupervised and supervised prediction tasks. Experimental analyses on nine cancer datasets from The Cancer Genome Atlas (TCGA) demonstrate that miss-SNF achieves state-of-the-art results in recovering similarities and in identifying patients subgroups enriched in clinically relevant variables and having differential survival. Moreover, amputation experiments show that miss-SNF supervised prediction of cancer clinical outcomes and Alzheimer's disease diagnosis with completely missing data achieves results comparable to those obtained when all the data are available. AVAILABILITY AND IMPLEMENTATION: miss-SNF code, implemented in R, is available at https://github.com/AnacletoLAB/missSNF.

Patient similarity networks (PSNs), where patients are represented as nodes and their similarities as weighted edges, are being increasingly used in clinical research. These networks provide an insightful summary of the relationships among patients and can be exploited by inductive or transductive learning algorithms for the prediction of patient outcome, phenotype and disease risk. PSNs can also be easily visualized, thus offering a natural way to inspect complex heterogeneous patient data and providing some level of explainability of the predictions obtained by machine learning algorithms. The advent of high-throughput technologies, enabling us to acquire high-dimensional views of the same patients (e.g. omics data, laboratory data, imaging data), calls for the development of data fusion techniques for PSNs in order to leverage this rich heterogeneous information. In this article, we review existing methods for integrating multiple biomedical data views to construct PSNs, together with the different patient similarity measures that have been proposed. We also review methods that have appeared in the machine learning literature but have not yet been applied to PSNs, thus providing a resource to navigate the vast machine learning literature existing on this topic. In particular, we focus on methods that could be used to integrate very heterogeneous datasets, including multi-omics data as well as data derived from clinical information and medical imaging.

BACKGROUND: Cis-regulatory regions (CRRs) are non-coding regions of the DNA that fine control the spatio-temporal pattern of transcription; they are involved in a wide range of pivotal processes such as the development of specific cell-lines/tissues and the dynamic cell response to physiological stimuli. Recent studies showed that genetic variants occurring in CRRs are strongly correlated with pathogenicity or deleteriousness. Considering the central role of CRRs in the regulation of physiological and pathological conditions, the correct identification of CRRs and of their tissue-specific activity status through Machine Learning methods plays a major role in dissecting the impact of genetic variants on human diseases. Unfortunately, the problem is still open, though some promising results have been already reported by (deep) machine-learning based methods that predict active promoters and enhancers in specific tissues or cell lines by encoding epigenetic or spectral features directly extracted from DNA sequences. RESULTS: We present the experiments we performed to compare two Deep Neural Networks, a Feed-Forward Neural Network model working on epigenomic features, and a Convolutional Neural Network model working only on genomic sequence, targeted to the identification of enhancer- and promoter-activity in specific cell lines. While performing experiments to understand how the experimental setup influences the prediction performance of the methods, we particularly focused on (1) automatic model selection performed by Bayesian optimization and (2) exploring different data rebalancing setups for reducing negative unbalancing effects. CONCLUSIONS: Results show that (1) automatic model selection by Bayesian optimization improves the quality of the learner; (2) data rebalancing considerably impacts the prediction performance of the models; test set rebalancing may provide over-optimistic results, and should therefore be cautiously applied; (3) despite working on sequence data, convolutional models obtain performance close to those of feed forward models working on epigenomic information, which suggests that also sequence data carries informative content for CRR-activity prediction. We therefore suggest combining both models/data types in future works.

MOTIVATION: Automated protein function prediction is a complex multi-class, multi-label, structured classification problem in which protein functions are organized in a controlled vocabulary, according to the Gene Ontology (GO). 'Hierarchy-unaware' classifiers, also known as 'flat' methods, predict GO terms without exploiting the inherent structure of the ontology, potentially violating the True-Path-Rule (TPR) that governs the GO, while 'hierarchy-aware' approaches, even if they obey the TPR, do not always show clear improvements with respect to flat methods, or do not scale well when applied to the full GO. RESULTS: To overcome these limitations, we propose Hierarchical Ensemble Methods for Directed Acyclic Graphs (HEMDAG), a family of highly modular hierarchical ensembles of classifiers, able to build upon any flat method and to provide 'TPR-safe' predictions, by leveraging a combination of isotonic regression and TPR learning strategies. Extensive experiments on synthetic and real data across several organisms firstly show that HEMDAG can be used as a general tool to improve the predictions of flat classifiers, and secondly that HEMDAG is competitive versus state-of-the-art hierarchy-aware learning methods proposed in the last CAFA international challenges. AVAILABILITY AND IMPLEMENTATION: Fully tested R code freely available at https://anaconda.org/bioconda/r-hemdag. Tutorial and documentation at https://hemdag.readthedocs.io. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: The protein ki67 (pki67) is a marker of tumor aggressiveness, and its expression has been proven to be useful in the prognostic and predictive evaluation of several types of tumors. To numerically quantify the pki67 presence in cancerous tissue areas, pathologists generally analyze histochemical images to count the number of tumor nuclei marked for pki67. This allows estimating the ki67-index, that is the percentage of tumor nuclei positive for pki67 over all the tumor nuclei. Given the high image resolution and dimensions, its estimation by expert clinicians is particularly laborious and time consuming. Though automatic cell counting techniques have been presented so far, the problem is still open. RESULTS: In this paper we present a novel automatic approach for the estimations of the ki67-index. The method starts by exploiting the STRESS algorithm to produce a color enhanced image where all pixels belonging to nuclei are easily identified by thresholding, and then separated into positive (i.e. pixels belonging to nuclei marked for pki67) and negative by a binary classification tree. Next, positive and negative nuclei pixels are processed separately by two multiscale procedures identifying isolated nuclei and separating adjoining nuclei. The multiscale procedures exploit two Bayesian classification trees to recognize positive and negative nuclei-shaped regions. CONCLUSIONS: The evaluation of the computed results, both through experts' visual assessments and through the comparison of the computed indexes with those of experts, proved that the prototype is promising, so that experts believe in its potential as a tool to be exploited in the clinical practice as a valid aid for clinicians estimating the ki67-index. The MATLAB source code is open source for research purposes.

BACKGROUND: One of the main issues in the automated protein function prediction (AFP) problem is the integration of multiple networked data sources. The UNIPred algorithm was thereby proposed to efficiently integrate -in a function-specific fashion- the protein networks by taking into account the imbalance that characterizes protein annotations, and to subsequently predict novel hypotheses about unannotated proteins. UNIPred is publicly available as R code, which might result of limited usage for non-expert users. Moreover, its application requires efforts in the acquisition and preparation of the networks to be integrated. Finally, the UNIPred source code does not handle the visualization of the resulting consensus network, whereas suitable views of the network topology are necessary to explore and interpret existing protein relationships. RESULTS: We address the aforementioned issues by proposing UNIPred-Web, a user-friendly Web tool for the application of the UNIPred algorithm to a variety of biomolecular networks, already supplied by the system, and for the visualization and exploration of protein networks. We support different organisms and different types of networks -e.g., co-expression, shared domains and physical interaction networks. Users are supported in the different phases of the process, ranging from the selection of the networks and the protein function to be predicted, to the navigation of the integrated network. The system also supports the upload of user-defined protein networks. The vertex-centric and the highly interactive approach of UNIPred-Web allow a narrow exploration of specific proteins, and an interactive analysis of large sub-networks with only a few mouse clicks. CONCLUSIONS: UNIPred-Web offers a practical and intuitive (visual) guidance to biologists interested in gaining insights into protein biomolecular functions. UNIPred-Web provides facilities for the integration of networks, and supplies a framework for the imbalance-aware protein network integration of nine organisms, the prediction of thousands of GO protein functions, and a easy-to-use graphical interface for the visual analysis, navigation and interpretation of the integrated networks and of the functional predictions.

BACKGROUND: Several problems in network biology and medicine can be cast into a framework where entities are represented through partially labeled networks, and the aim is inferring the labels (usually binary) of the unlabeled part. Connections represent functional or genetic similarity between entities, while the labellings often are highly unbalanced, that is one class is largely under-represented: for instance in the automated protein function prediction (AFP) for most Gene Ontology terms only few proteins are annotated, or in the disease-gene prioritization problem only few genes are actually known to be involved in the etiology of a given disease. Imbalance-aware approaches to accurately predict node labels in biological networks are thereby required. Furthermore, such methods must be scalable, since input data can be large-sized as, for instance, in the context of multi-species protein networks. RESULTS: We propose a novel semi-supervised parallel enhancement of COSNET, an imbalance-aware algorithm build on Hopfield neural model recently suggested to solve the AFP problem. By adopting an efficient representation of the graph and assuming a sparse network topology, we empirically show that it can be efficiently applied to networks with millions of nodes. The key strategy to speed up the computations is to partition nodes into independent sets so as to process each set in parallel by exploiting the power of GPU accelerators. This parallel technique ensures the convergence to asymptotically stable attractors, while preserving the asynchronous dynamics of the original model. Detailed experiments on real data and artificial big instances of the problem highlight scalability and efficiency of the proposed method. CONCLUSIONS: By parallelizing COSNET we achieved on average a speed-up of 180x in solving the AFP problem in the S. cerevisiae, Mus musculus and Homo sapiens organisms, while lowering memory requirements. In addition, to show the potential applicability of the method to huge biomolecular networks, we predicted node labels in artificially generated sparse networks involving hundreds of thousands to millions of nodes.