MOTIVATION: Most functions within the cell emerge thanks to protein-protein interactions (PPIs), yet experimental determination of PPIs is both expensive and time-consuming. PPI networks present significant levels of noise and incompleteness. Predicting interactions using only PPI-network topology (topological prediction) is difficult but essential when prior biological knowledge is absent or unreliable. METHODS: Network embedding emphasizes the relations between network proteins embedded in a low-dimensional space, in which protein pairs that are closer to each other represent good candidate interactions. To achieve network denoising, which boosts prediction performance, we first applied minimum curvilinear embedding (MCE), and then adopted shortest path (SP) in the reduced space to assign likelihood scores to candidate interactions. Furthermore, we introduce (i) a new valid variation of MCE, named non-centred MCE (ncMCE); (ii) two automatic strategies for selecting the appropriate embedding dimension; and (iii) two new randomized procedures for evaluating predictions. RESULTS: We compared our method against several unsupervised and supervisedly tuned embedding approaches and node neighbourhood techniques. Despite its computational simplicity, ncMCE-SP was the overall leader, outperforming the current methods in topological link prediction. CONCLUSION: Minimum curvilinearity is a valuable non-linear framework that we successfully applied to the embedding of protein networks for the unsupervised prediction of novel PPIs. The rationale for our approach is that biological and evolutionary information is imprinted in the non-linear patterns hidden behind the protein network topology, and can be exploited for predicting new protein links. The predicted PPIs represent good candidates for testing in high-throughput experiments or for exploitation in systems biology tools such as those used for network-based inference and prediction of disease-related functional modules. AVAILABILITY: https://sites.google.com/site/carlovittoriocannistraci/home. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Nonlinear small datasets, which are characterized by low numbers of samples and very high numbers of measures, occur frequently in computational biology, and pose problems in their investigation. Unsupervised hybrid-two-phase (H2P) procedures-specifically dimension reduction (DR), coupled with clustering-provide valuable assistance, not only for unsupervised data classification, but also for visualization of the patterns hidden in high-dimensional feature space. METHODS: 'Minimum Curvilinearity' (MC) is a principle that-for small datasets-suggests the approximation of curvilinear sample distances in the feature space by pair-wise distances over their minimum spanning tree (MST), and thus avoids the introduction of any tuning parameter. MC is used to design two novel forms of nonlinear machine learning (NML): Minimum Curvilinear embedding (MCE) for DR, and Minimum Curvilinear affinity propagation (MCAP) for clustering. RESULTS: Compared with several other unsupervised and supervised algorithms, MCE and MCAP, whether individually or combined in H2P, overcome the limits of classical approaches. High performance was attained in the visualization and classification of: (i) pain patients (proteomic measurements) in peripheral neuropathy; (ii) human organ tissues (genomic transcription factor measurements) on the basis of their embryological origin. CONCLUSION: MC provides a valuable framework to estimate nonlinear distances in small datasets. Its extension to large datasets is prefigured for novel NMLs. Classification of neuropathic pain by proteomic profiles offers new insights for future molecular and systems biology characterization of pain. Improvements in tissue embryological classification refine results obtained in an earlier study, and suggest a possible reinterpretation of skin attribution as mesodermal. AVAILABILITY: https://sites.google.com/site/carlovittoriocannistraci/home.