Representative Prototype Sets for Data Characterization and Classification

  • Ludwig Lausser
  • Christoph Müssel
  • Hans A. Kestler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7477)


Common classifier models are designed to achieve high accuracies, while often neglecting the question of interpretability. In particular, most classifiers do not allow for drawing conclusions on the structure and quality of the underlying training data. By keeping the classifier model simple, an intuitive interpretation of the model and the corresponding training data is possible. A lack of accuracy of such simple models can be compensated by accumulating the decisions of several classifiers. We propose an approach that is particularly suitable for high-dimensional data sets of low cardinality, such as data gained from high-throughput biomolecular experiments. Here, simple base classifiers are obtained by choosing one data point of each class as a prototype for nearest neighbour classification. By enumerating all such classifiers for a specific data set, one can obtain a systematic description of the data structure in terms of class coherence. We also investigate the performance of the classifiers in cross-validation experiments by applying stand-alone prototype classifiers as well as ensembles of selected prototype classifiers.


Near Neighbor Learn Vector Quantization Sample Compression Empirical Accuracy Shrunken Centroid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Fix, E., Hodges, J.: Discriminatory Analysis: Nonparametric Discrimination: Consistency Properties. Technical Report Project 21-49-004, Report Number 4, USAF School of Aviation Medicine, Randolf Field, Texas (1951)Google Scholar
  2. 2.
    Kohonen, T.: Learning vector quantization. Neural Networks 1, 303 (1988)CrossRefGoogle Scholar
  3. 3.
    Kohonen, T.: Learning vector quantization. In: Arbib, M. (ed.) The Handbook of Brain Theory and Neural Networks, pp. 537–540. MIT Press, Cambridge (1995)Google Scholar
  4. 4.
    Tibshirani, R., Hastie, T., Narasimhan, B., Chu, G.: Diagnosis of multiple cancer types by shrunken centroids of gene expression. PNAS 99(10), 6567–6572 (2002)CrossRefGoogle Scholar
  5. 5.
    Kuncheva, L., Bezdek, J.: Nearest prototype classification: Clustering, genetic algorithms or random search? IEEE Transactions on Systems, Man, and Cybernetics C28(1), 160–164 (1998)Google Scholar
  6. 6.
    Hart, P.E.: The condensed nearest neighbor rule. IEEE Transactions on Information Theory 14, 515–516 (1968)CrossRefGoogle Scholar
  7. 7.
    Kuncheva, L.: Fitness functions in editing k-nn reference set by genetic algorithms. Pattern Recognition 30(6), 1041–1049 (1997)CrossRefGoogle Scholar
  8. 8.
    Gil-Pita, R., Yao, X.: Using a Genetic Algorithm for Editing k-Nearest Neighbor Classifiers. In: Yin, H., Tino, P., Corchado, E., Byrne, W., Yao, X. (eds.) IDEAL 2007. LNCS, vol. 4881, pp. 1141–1150. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Brighton, H., Mellish, C.: Advances in instance selection for instance-based learning algorithms. Data Mining and Knowledge Discovery 6(2), 153–172 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Dasarathy, B.: Nearest neighbor (NN) norms: NN pattern classification techniques. IEEE Computer Society Press (1991)Google Scholar
  11. 11.
    Littlestone, N., Warmuth, M.: Relating data compression and learnability (1986) (unpublished manuscript)Google Scholar
  12. 12.
    Langford, J.: Tutorial on practical prediction theory for classification. Journal of Machine Learning Research 6, 273–306 (2005)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Yule, G.: On the association of attributes in statistics: With illustrations from the material of the childhood society. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 194, 257–319 (1900)zbMATHCrossRefGoogle Scholar
  14. 14.
    Bittner, M., Meltzer, P., Chen, Y., Jiang, Y., Seftor, E., Hendrix, M., Radmacher, M., Simon, R., Yakhini, Z., Ben-Dor, A., Sampas, N., Dougherty, E., Wang, E., Marincola, F., Gooden, C., Lueders, J., Glatfelter, A., Pollock, P., Carpten, J., Gillanders, E., Leja, D., Dietrich, K., Beaudry, C., Berens, M., Alberts, D., Sondak, V.: Molecular classification of cutaneous malignant melanoma by gene expression profiling. Nature 406(6795), 536–540 (2000)CrossRefGoogle Scholar
  15. 15.
    Golub, T., Slonim, D., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J., Coller, H., Loh, M., Downing, J., Caligiuri, M., Bloomfield, C., Lander, E.: Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring. Science 286(5439), 531–537 (1999)CrossRefGoogle Scholar
  16. 16.
    Dudoit, S., Fridlyand, J., Speed, T.: Comparison of discrimination methods for the classification of tumors using gene expression data. Journal of the American Statistical Association 97(457), 77–87 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Notterman, D., Alon, U., Sierk, A.J., Levine, A.: Transcriptional gene expression profiles of colorectal adenoma, adenocarcinoma, and normal tissue examined by oligonucleotide arrays. Cancer Research 61(7), 3124–3130 (2001)Google Scholar
  18. 18.
    Pomeroy, S., Tamayo, P., Gaasenbeek, M., Sturla, L., Angelo, M., McLaughlin, M., Kim, J., Goumnerova, L., Black, P., Lau, C., Allen, J., Zagzag, D., Olson, J., Curran, T., Wetmore, C., Biegel, J., Poggio, T., Mukherjee, S., Rifkin, R., Califano, A., Stolovitzky, G., Louis, D., Mesirov, J., Lander, E., Golub, T.: Prediction of central nervous system embryonal tumour outcome based on gene expression. Nature 415(6870), 436–442 (2002)CrossRefGoogle Scholar
  19. 19.
    Shipp, M., Ross, K., Tamayo, P., Weng, A., Kutok, J., Aguiar, R., Gaasenbeek, M., Angelo, M., Reich, M., Pinkus, G., Ray, T., Koval, M., Last, K., Norton, A., Lister, T., Mesirov, J., Neuberg, D., Lander, E., Aster, J., Golub, T.: Diffuse large b-cell lymphoma outcome prediction by gene-expression profiling and supervised machine learning. Nature Medicine 8(1), 68–74 (2002)CrossRefGoogle Scholar
  20. 20.
    West, M., Blanchette, C., Dressman, H., Huang, E., Ishida, S., Spang, R., Zuzan, H., Olson, J.J., Marks, J.R., Nevins, J.R.: Predicting the clinical status of human breast cancer by using gene expression profiles. PNAS 98(20), 11462–11467 (2001)CrossRefGoogle Scholar
  21. 21.
    Wolpert, D.: The lack of a priori distinctions between learning algorithms. Neural Computation 8(7), 1341–1390 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ludwig Lausser
    • 1
  • Christoph Müssel
    • 1
  • Hans A. Kestler
    • 1
  1. 1.Research Group Bioinformatics and Systems Biology, Institute of Neural Information ProcessingUlm UniversityUlmGermany

Personalised recommendations