title: Nonlinear dimension reduction and clustering by Minimum Curvilinearity unfold neuropathic pain and tissue embryological classes.
abstract: BACKGROUND
  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.
  
  
  CONCLUSIONS
  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.
  
  
  BACKGROUND
  https://sites.google.com/site/carlovittoriocannistraci/home.
authors.affiliation: Computational Bioscience Research Center, Division of Chemical and Life Sciences and Engineering, King Abdullah University for Science and Technology (KAUST), Jeddah, Kingdom of Saudi Arabia. kalokagathos.agon@gmail.com
authors.forename: Carlo Vittorio
authors.initials: CV
authors.lastname: Cannistraci
authors.forename: Timothy
authors.initials: T
authors.lastname: Ravasi
authors.forename: Franco Maria
authors.initials: FM
authors.lastname: Montevecchi
authors.forename: Trey
authors.initials: T
authors.lastname: Ideker
authors.forename: Massimo
authors.initials: M
authors.lastname: Alessio
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D002460:Cell Line; D016000:Cluster Analysis; D003627:Data Interpretation, Statistical; D004622:Embryo, Mammalian / Q000166:cytology; D006801:Humans; D010146:Pain / Q000145:classification*; D010523:Peripheral Nervous System Diseases / Q000134:cerebrospinal fluid / Q000503:physiopathology*; D014157:Transcription Factors / Q000235:genetics
chemical_list: D014157:Transcription Factors
references.citation: Science. 2007 Feb 16;315(5814):972-6
references.pmid: 17218491
references.citation: Proteomics. 2005 Nov;5(17):4558-67
references.pmid: 16196102
references.citation: Bioinformatics. 2007 Oct 15;23(20):2708-15
references.pmid: 17895277
references.citation: Eur J Pain. 2001;5(4):379-89
references.pmid: 11743704
references.citation: Proteomics. 2009 Nov;9(21):4908-19
references.pmid: 19862762
references.citation: Exp Biol Med (Maywood). 2008 Apr;233(4):483-91
references.pmid: 18367638
references.citation: Nat Clin Pract Neurol. 2006 Feb;2(2):95-106
references.pmid: 16932531
references.citation: Science. 2000 Dec 22;290(5500):2323-6
references.pmid: 11125150
references.citation: Bioinformatics. 2006 Jan 15;22(2):202-8
references.pmid: 16287938
references.citation: Science. 2000 Dec 22;290(5500):2319-23
references.pmid: 11125149
references.citation: Nat Immunol. 2002 Apr;3(4):311-3
references.pmid: 11919565
references.citation: Proteomics Clin Appl. 2008 Dec;2(12):1628-37
references.pmid: 21136813
references.citation: Bioinformatics. 2010 Feb 1;26(3):440-3
references.pmid: 19880370
references.citation: Nat Clin Pract Neurol. 2006 Feb;2(2):107-15
references.pmid: 16932532
references.citation: Science. 2002 Jan 4;295(5552):7
references.pmid: 11778013
references.citation: Cell. 2010 Mar 5;140(5):744-52
references.pmid: 20211142