title: Verifying the fully "Laplacianised" posterior Naïve Bayesian approach and more.
abstract: BACKGROUND
  In a recent paper, Mussa, Mitchell and Glen (MMG) have mathematically demonstrated that the "Laplacian Corrected Modified Naïve Bayes" (LCMNB) algorithm can be viewed as a variant of the so-called Standard Naïve Bayes (SNB) scheme, whereby the role played by absence of compound features in classifying/assigning the compound to its appropriate class is ignored. MMG have also proffered guidelines regarding the conditions under which this omission may hold. Utilising three data sets, the present paper examines the validity of these guidelines in practice. The paper also extends MMG's work and introduces a new version of the SNB classifier: "Tapered Naïve Bayes" (TNB). TNB does not discard the role of absence of a feature out of hand, nor does it fully consider its role. Hence, TNB encapsulates both SNB and LCMNB.
  
  
  RESULTS
  LCMNB, SNB and TNB performed differently on classifying 4,658, 5,031 and 1,149 ligands (all chosen from the ChEMBL Database) distributed over 31 enzymes, 23 membrane receptors, and one ion-channel, four transporters and one transcription factor as their target proteins. When the number of features utilised was equal to or smaller than the "optimal" number of features for a given data set, SNB classifiers systematically gave better classification results than those yielded by LCMNB classifiers. The opposite was true when the number of features employed was markedly larger than the "optimal" number of features for this data set. Nonetheless, these LCMNB performances were worse than the classification performance achieved by SNB when the "optimal" number of features for the data set was utilised. TNB classifiers systematically outperformed both SNB and LCMNB classifiers.
  
  
  CONCLUSIONS
  The classification results obtained in this study concur with the mathematical based guidelines given in MMG's paper-that is, ignoring the role of absence of a feature out of hand does not necessarily improve classification performance of the SNB approach; if anything, it could make the performance of the SNB method worse. The results obtained also lend support to the rationale, on which the TNB algorithm rests: handled judiciously, taking into account absence of features can enhance (not impair) the discriminatory classification power of the SNB approach.
authors.affiliation: Department of Chemistry, Centre for Molecular Informatics, Lensfield Road, Cambridge, England CB2 1EW UK ; EaStCHEM School of Chemistry and Biomedical Sciences Research Complex, University of St Andrews, North Haugh, St Andrews, Scotland KY16 9ST UK.
authors.forename: Hamse Y
authors.initials: HY
authors.lastname: Mussa
authors.affiliation: European Bioinformatics Institute (EMBL-EBI), European Molecular Biology Laboratory, Wellcome Trust Genome Campus, Hinxton, Cambridge, England CB10 1SD UK.
authors.forename: David
authors.initials: D
authors.lastname: Marcus
authors.affiliation: EaStCHEM School of Chemistry and Biomedical Sciences Research Complex, University of St Andrews, North Haugh, St Andrews, Scotland KY16 9ST UK.
authors.forename: John B O
authors.initials: JB
authors.lastname: Mitchell
authors.affiliation: Department of Chemistry, Centre for Molecular Informatics, Lensfield Road, Cambridge, England CB2 1EW UK.
authors.forename: Robert C
authors.initials: RC
authors.lastname: Glen
keywords: Classification; Features; Naïve Bayes; Tapering