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Biological pathway maps are highly relevant tools for many tasks in molecular biology. They reduce the complexity of the overall biological network by partitioning it into smaller manageable parts. While this reduction of complexity is their biggest strength, it is, at the same time, their biggest weakness. By removing what is deemed not important for the primary function of the pathway, biologists lose the ability to follow and understand cross-talks between pathways. Considering these cross-talks is, however, critical in many analysis scenarios, such as judging effects of drugs. In this paper we introduce Entourage, a novel visualization technique that provides contextual information lost due to the artificial partitioning of the biological network, but at the same time limits the presented information to what is relevant to the analyst's task. We use one pathway map as the focus of an analysis and allow a larger set of contextual pathways. For these context pathways we only show the contextual subsets, i.e., the parts of the graph that are relevant to a selection. Entourage suggests related pathways based on similarities and highlights parts of a pathway that are interesting in terms of mapped experimental data. We visualize interdependencies between pathways using stubs of visual links, which we found effective yet not obtrusive. By combining this approach with visualization of experimental data, we can provide domain experts with a highly valuable tool. We demonstrate the utility of Entourage with case studies conducted with a biochemist who researches the effects of drugs on pathways. We show that the technique is well suited to investigate interdependencies between pathways and to analyze, understand, and predict the effect that drugs have on different cell types. [ABSTRACT FROM AUTHOR]

The adoption of microarray techniques in biological and medical research provides a new way for cancer diagnosis and treatment. In order to perform successful diagnosis and treatment of cancer, discovering and classifying cancer types correctly is essential. Class discovery is one of the most important tasks in cancer classification using biomolecular data. Most of the existing works adopt single clustering algorithms to perform class discovery from biomolecular data. However, single clustering algorithms have limitations, which include a lack of robustness, stability, and accuracy. In this paper, we propose a new cluster ensemble approach called knowledge based cluster ensemble (KCE) which incorporates the prior knowledge of the data sets into the cluster ensemble framework. Specifically, KCE represents the prior knowledge of a data set in the form of pairwise constraints. Then, the spectral clustering algorithm (SC) is adopted to generate a set of clustering solutions. Next, KCE transforms pairwise constraints into confidence factors for these clustering solutions. After that, a consensus matrix is constructed by considering all the clustering solutions and their corresponding confidence factors. The final clustering result is obtained by partitioning the consensus matrix. Comparison with single clustering algorithms and conventional cluster ensemble approaches, knowledge based cluster ensemble approaches are more robust, stable and accurate. The experiments on cancer data sets show that: 1) KCE works well on these data sets; 2) KCE not only outperforms most of the state-of-the-art single clustering algorithms, but also outperforms most of the state-of-the-art cluster ensemble approaches. [ABSTRACT FROM PUBLISHER]

Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse, and complex molecular and biomolecular datasets because of the limited understanding of its potential power in dimensionality reduction and its ability to encode essential chemical and biological information in differentiable manifolds. Results: We put forward a differential geometry‐based geometric learning (DG‐GL) hypothesis that the intrinsic physics of three‐dimensional (3D) molecular structures lies on a family of low‐dimensional manifolds embedded in a high‐dimensional data space. We encode crucial chemical, physical, and biological information into 2D element interactive manifolds, extracted from a high‐dimensional structural data space via a multiscale discrete‐to‐continuum mapping using differentiable density estimators. Differential geometry apparatuses are utilized to construct element interactive curvatures in analytical forms for certain analytically differentiable density estimators. These low‐dimensional differential geometry representations are paired with a robust machine learning algorithm to showcase their descriptive and predictive powers for large, diverse, and complex molecular and biomolecular datasets. Extensive numerical experiments are carried out to demonstrate that the proposed DG‐GL strategy outperforms other advanced methods in the predictions of drug discovery‐related protein‐ligand binding affinity, drug toxicity, and molecular solvation free energy. Availability and implementation: http://weilab.math.msu.edu/DG‐GL/ Contact: wei@math.msu.edu Differential geometry offers a set of high‐level abstractions of complex biomolecular structures in terms of low‐dimensional differentiable manifolds that enable the study of biomolecular structure‐function relationships locally via mathematical tools, such as vector fields, tensor fields, Riemannian metrics, and differential forms. We introduce differential geometry to encode intermolecular and intramolecular non‐covalent interactions into element interactive manifolds (EIMs) in a scalable manner so that various biomolecular structures can be compared on an equal footing via machine learning. The predictions of protein‐ligand binding affinity, drug toxicity, and molecular solvation free energy demonstrate the predictive power of the present method. [ABSTRACT FROM AUTHOR]