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.

Proteomic analysis may be useful to investigate disorders of the central nervous system, in order to explore the protein content of cells and of biological fluids in respect of the onset and evolution of diseases. Today, one of the most used proteomic approach includes the separation and visualization of proteins by means of two-dimensional gel electrophoresis (2DE). However the development of fully automatic strategies in extracting information from gel images is still a challenging task. In this paper we applied a computational strategy to the aim of obtaining a compact representation of the original data. This method was applied to an experimental protocol including two different clinical groups of amyotrophic lateral sclerosis (ALS) and peripheral neuropathy patients : 32 2DE maps generated from cerebrospinal fluid (24 pathologic and 8 control subjects) were processed. Quantitative features were extracted to describe each image and dealt with the dimension reduction technique of local tangent space alignment (LTSA). The discovered low-dimensional structure allows to see the gel of the dataset as separable, according to their clinical conditions, showing the informativeness of the adopted descriptors and providing the bases for classification of this kind of samples.