Bayesian Network Classifiers for Categorizing Cortical GABAergic Interneurons


An accepted classification of GABAergic interneurons of the cerebral cortex is a major goal in neuroscience. A recently proposed taxonomy based on patterns of axonal arborization promises to be a pragmatic method for achieving this goal. It involves characterizing interneurons according to five axonal arborization features, called F1–F5, and classifying them into a set of predefined types, most of which are established in the literature. Unfortunately, there is little consensus among expert neuroscientists regarding the morphological definitions of some of the proposed types. While supervised classifiers were able to categorize the interneurons in accordance with experts’ assignments, their accuracy was limited because they were trained with disputed labels. Thus, here we automatically classify interneuron subsets with different label reliability thresholds (i.e., such that every cell’s label is backed by at least a certain (threshold) number of experts). We quantify the cells with parameters of axonal and dendritic morphologies and, in order to predict the type, also with axonal features F1–F4 provided by the experts. Using Bayesian network classifiers, we accurately characterize and classify the interneurons and identify useful predictor variables. In particular, we discriminate among reliable examples of common basket, horse-tail, large basket, and Martinotti cells with up to 89.52 % accuracy, and single out the number of branches at 180 μm from the soma, the convex hull 2D area, and the axonal features F1–F4 as especially useful predictors for distinguishing among these types. These results open up new possibilities for an objective and pragmatic classification of interneurons.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. 1.

    The prediction of one of the features is almost trivial and was thus not considered here.

  2. 2.

    This was not applied in classification tasks with less than 100 predictors, e.g., when predicting the interneuron type with only F1–F4 as predictor variables.

  3. 3.

    The 100 variables that were selected previous to classifier induction.


  1. Ascoli, G.A., Donohue, D.E., Halavi, M. (2007). a central resource for neuronal morphologies. The Journal of Neuroscience, 27(35), 9247–9251.

    Article  CAS  PubMed  Google Scholar 

  2. Ascoli, G.A., Alonso-Nanclares, L., Anderson, S., Barrionuevo, G., Benavides-Piccione, R., Burkhalter, A., Buzsaki, G., Cauli, B., DeFelipe, J., Fairén, A., et al. (2008). Petilla terminology: nomenclature of features of GABAergic interneurons of the cerebral cortex. Nature Reviews Neuroscience, 9(7), 557–568.

    Article  CAS  PubMed  Google Scholar 

  3. Bielza, C., & Larrañaga, P. (2014). Discrete Bayesian network classifiers: a survey. ACM Computing Surveys, 47(1) (5:1–5:43.

  4. Bielza, C., Li, G., Larranaga, P. (2011). Multi-dimensional classification with Bayesian networks. International Journal of Approximate Reasoning, 52(6), 705–727.

    Article  Google Scholar 

  5. Breiman, L. (1996). Bagging predictors. Machine Learning, 24(2), 123–140.

    Google Scholar 

  6. Cauli, B., Audinat, E., Lambolez, B., Angulo, M.C., Ropert, N., Tsuzuki, K., Hestrin, S., Rossier, J. (1997). Molecular and physiological diversity of cortical nonpyramidal cells. The Journal of Neuroscience, 17(10), 3894–3906.

    CAS  PubMed  Google Scholar 

  7. DeFelipe, J., López-Cruz, P.L., Benavides-Piccione, R., Bielza, C., Larrañaga, P., Anderson, S., Burkhalter, A., Cauli, B., Fairén, A., Feldmeyer, D., et al. (2013). New insights into the classification and nomenclature of cortical GABAergic interneurons. Nature Reviews Neuroscience, 14, 202–216.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  8. Dougherty, J., Kohavi, R., Sahami, M. (1995). Supervised and unsupervised discretization of continuous features. In: Machine learning: proceedings of the twelfth international conference, (pp. 194–202).

  9. Fairén, A., Regidor, J., Kruger, L. (1992). The cerebral cortex of the mouse (a first contribution—the ‘acoustic’ cortex). Somatosensory & Motor Research, 9(1), 3–36.

    Article  Google Scholar 

  10. Friedman, N., Geiger, D., Goldszmidt, M. (1997). Bayesian network classifiers. Machine Learning, 29, 131–163.

    Article  Google Scholar 

  11. Glaser, J.R., & Glaser, E.M. (1990). Neuron imaging with Neurolucida—a PC-based system for image combining microscopy. Computerized Medical Imaging and Graphics, 14(5), 307–317.

    Article  CAS  PubMed  Google Scholar 

  12. Glaser, E.M., & McMullen, N.T. (1984). The fan-in projection method for analyzing dendrite and axon systems. Journal of Neuroscience Methods, 12(1), 37–42.

    Article  CAS  PubMed  Google Scholar 

  13. Gupta, A., Wang, Y., Markram, H. (2000). Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex. Science, 287(5451), 273–278.

    Article  CAS  PubMed  Google Scholar 

  14. Hall, M. (2007). A decision tree-based attribute weighting filter for naive Bayes. Knowledge-Based Systems, 20(2), 120–126.

    Article  Google Scholar 

  15. Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H. (2009). The WEKA data mining software: an update. SIGKDD Explorations Newsletter, 11(1), 10–18.

    Article  Google Scholar 

  16. Hand, D.J., & Yu, K. (2001). Idiot’s Bayes—not so stupid after all? International Statistical Review, 69(3), 385–398.

    Google Scholar 

  17. Hornik, K., Buchta, C., Zeileis, A. (2009). Open-source machine learning: R meets Weka. Computational Statistics, 24(2), 225–232.

    Article  Google Scholar 

  18. Kawaguchi, Y. (1993). Physiological, morphological, and histochemical characterization of three classes of interneurons in rat neostriatum. The Journal of Neuroscience, 13(11), 4908–4923.

    CAS  PubMed  Google Scholar 

  19. Kuhn, M., Wing, J., Weston, S., Williams, A., Keefer, C., Engelhardt, A., Cooper, T. (2013). caret: classification and regression training. R package version 5.17-7.

  20. Langley, P., & Sage, S. (1994). Induction of selective Bayesian classifiers. In: Proceedings of the 10th conference on uncertainty in artificial intelligence. Morgan Kaufmann, (pp. 399–406).

  21. Maccaferri, G., & Lacaille, J.C. (2003). Interneuron diversity series: hippocampal interneuron classifications–making things as simple as possible, not simpler. Trends in Neurosciences, 26(10), 564–571.

    Article  CAS  PubMed  Google Scholar 

  22. McMullen, N.T., Glaser, E.M., Tagamets, M. (1984). Morphometry of spine-free nonpyramidal neurons in rabbit auditory cortex. Journal of Comparative Neurology, 222(3), 383–395.

    Article  CAS  PubMed  Google Scholar 

  23. Mihaljevic, B., Bielza, C., Larrañaga, P. (2013). bayesslass: an R package for learning Bayesian network classifiers. In Proceedings of useR!—the R user conference (p. 53).

  24. Mihaljević, B., Benavides-Piccione, R., Guerra, L., DeFelipe, J., Larrañaga, P., Bielza, C. (2014). Classifying GABAergic interneurons with semi-supervised projected model-based clustering. Artificial Intelligence in Medicine, (in press).

  25. Minsky, M. (1961). Steps toward artificial intelligence. Transactions on Institute of Radio Engineers, 49, 8–30.

    Google Scholar 

  26. Morales, D., Vives-Gilabert, Y., Gómez-Ansón, B., Bengoetxea, E., Larrañaga, P., Bielza, C., Pagonabarraga, J., Kulisevsky, J., Corcuera-Solano, I., Delfino, M. (2013). Predicting dementia development in Parkinson’s disease using Bayesian network classifiers. Psychiatry Research: NeuroImaging, 213, 92–98.

    Article  PubMed  Google Scholar 

  27. Panico, J., & Sterling, P. (1995). Retinal neurons and vessels are not fractal but space-filling. Journal of Comparative Neurology, 361(3), 479–490.

    Article  CAS  PubMed  Google Scholar 

  28. Pearl, J. (1988). Probabilistic reasoning in intelligent systems. San Francisco: Morgan Kaufmann.

    Google Scholar 

  29. Peters, A., & Jones, E.G. (1984). Cerebral cortex: volume 1: cellular components of the cerebral cortex. New York: Plenum Press.

    Google Scholar 

  30. R Core Team. (2012). R: a language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.

    Google Scholar 

  31. Raykar, V.C., Yu, S., Zhao, L.H., Valadez, G.H., Florin, C., Bogoni, L., Moy, L. (2010). Learning from crowds. The Journal of Machine Learning Research, 11, 1297–1322.

    Google Scholar 

  32. Sadler, M., & Berry, M. (1983). Morphometric study of the development of Purkinje cell dendritic trees in the mouse using vertex analysis. Journal of Microscopy, 131(3), 341–354.

    Article  CAS  PubMed  Google Scholar 

  33. Smialowski, P., Frishman, D., Kramer, S. (2010). Pitfalls of supervised feature selection. Bioinformatics, 26(3), 440–443.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  34. Somogyi, P., Tamás, G., Lujan, R., Buhl, E.H. (1998). Salient features of synaptic organisation in the cerebral cortex. Brain Research Reviews, 26(2), 113–135.

    Article  CAS  PubMed  Google Scholar 

  35. Yang, Y., & Webb, G.I. (2003). Weighted proportional k-interval discretization for naive-Bayes classifiers. In Advances in knowledge discovery and data mining (pp. 501–512). Springer.

  36. Yang, Y., Webb, G.I., Wu, X. (2010). Discretization methods. In Data mining and knowledge discovery handbook (pp. 101–116). Springer.

  37. Zaidi, N.A., Cerquides, J., Carman, M.J., Webb, G.I. (2013). Alleviating naive Bayes attribute independence assumption by attribute weighting. Journal of Machine Learning Research, 14, 1947–1988.

    Google Scholar 

Download references


This work was supported by grants from the following entities: the Spanish Ministry of Economy and Competitiveness (grants TIN2013-41592-P to B.M., C.B., and P.L.; BFU2012-34963 to J.DF.), CIBERNED CB06/05/0066 to J.DF., the Cajal Blue Brain Project (C080020-09; the Spanish partner of the Blue Brain Project initiative from EPFL) to B.M., C.B., J.DF., and P.L., and the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 604102 (Human Brain Project) to C.B., J.DF., and P.L. R.B.-P. was supported by the Spanish Ministry of Economy and Competitiveness (CSIC).

Author information



Corresponding author

Correspondence to Bojan Mihaljević.

Additional information

Information Sharing Statement

All used data—the 237 interneuron cell reconstructions and the corresponding experts’ characterizations according to features F1 to F6—are available at The bnclassify R package will be made available on the CRAN repository ( before end of 2014 whereas the remaining software used is publicly available: caret and RWeka on CRAN and Weka at

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mihaljević, B., Benavides-Piccione, R., Bielza, C. et al. Bayesian Network Classifiers for Categorizing Cortical GABAergic Interneurons. Neuroinform 13, 193–208 (2015).

Download citation


  • Neuronal classification
  • Morphological features
  • Label reliability
  • Multiple annotators
  • Weighted naive Bayes