Skip to main content
SpringerLink
Log in

Granular Computing Techniques for Bioinformatics Pattern Recognition Problems in Non-metric Spaces

  • Chapter
  • First Online:
Computational Intelligence for Pattern Recognition

Part of the book series: Studies in Computational Intelligence ((SCI,volume 777))

Abstract

Computational intelligence and pattern recognition techniques are gaining more and more attention as the main computing tools in bioinformatics applications. This is due to the fact that biology by definition, deals with complex systems and that computational intelligence can be considered as an effective approach when facing the general problem of complex systems modelling. Moreover, most data available on shared databases are represented by sequences and graphs, thus demanding the definition of meaningful dissimilarity measures between patterns, which are often non-metric in nature. Especially in such cases, evolutive and fully automatic machine learning systems are mandatory for dealing with parametric dissimilarity measures and/or for performing suitable feature selection. Besides other approaches, such as kernel methods and embedding in dissimilarity spaces, granular computing is a very promising framework not only for designing effective data-driven modelling systems able to determine automatically the correct representation (abstraction) level, but also for giving to field-experts (biologists) the possibility to investigate information granules (frequent substructures) that have been discovered by the machine learning system as the most relevant for the problem at hand. We expect that many important discoveries in biology and medicine in the next future will be determined by an increasingly stronger integration between the ongoing research efforts of natural sciences and modern inductive modelling tools based on computational intelligence, pattern recognition and granular computing techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For example, let us consider a classification/clustering algorithm driven by the Euclidean distance. A common problem with the Euclidean distance is that features spanning a wider range of values have more influence in the resulting distance measure, therefore normalising all attributes in the same range (usually [0, 1] or \([-1,+1]\)) ensures fair contribution from all attributes, regardless of their original range.

  2. 2.

    In Statistics, outliers are “anomalous data” that for a given dissimilarity measure lie far away from most observations.

  3. 3.

    Non sunt multiplicanda entia sine necessitate (Entities are not to be multiplied without necessity), commonly known as “The Ockham’s Razor” Criterion (William of Ockham, circa 1287–1347). This criterion states that among a set of predicting models sharing the same performances, the simplest one (i.e. the one with the simplest decision surfaces) should be preferred. It is for sure one of the fundamental axioms for thoughtful and practical data-driven modelling.

  4. 4.

    Also known as hyperparameters in the Machine Learning terminology.

  5. 5.

    That is why evolutionary optimisation metaheuristics fall within the derivative-free methods.

  6. 6.

    A common choice for a genetic algorithm fitness function takes into account both the model performance and its structural complexity. Specifically, whilst the former should be maximised, the latter should be minimised in order to avoid overfitting (cf. the Ockham’s Razor Criterion).

  7. 7.

    That is why in most of the Chapter, unless explicitly specified, the generic term (dis)similarity will be used.

  8. 8.

    Indeed, the anatomical structure changes in the order of months/years depending on the age of subjects.

  9. 9.

    A finite set of points equipped with a notion of distance in a finite multidimensional space.

  10. 10.

    According to which the distance between two strings of equal length is given by the number of mismatches.

  11. 11.

    Also known as the Gram Matrix, after Danish mathematician Jørgen Pedersen Gram.

  12. 12.

    If the similarity measure at hand is not symmetric, patterns’ distance vectors as taken by rows or columns will be different. In order to overcome this problem, one can ‘force’ a similarity measure to be symmetric by considering \(\mathbf {S}:=(\mathbf {S}+\mathbf {S}^T)/2\) (e.g. [14]).

  13. 13.

    Also known as the Krebs cycle.

  14. 14.

    Protein molecules driving the folding of other protein systems.

  15. 15.

    Indeed, the absolute entity of metabolic rate can vary for a lot of reasons going from anatomical differences among patients to their actual nutrition state.

References

  1. S. Alelyani, J. Tang, H. Liu, Feature selection for clustering: a review. Data Clust. Algorithms Appl. 29, 110–121 (2013)

    Google Scholar 

  2. C. Anderson, The end of theory: the data deluge makes the scientific method obsolete. Wired mag. 16(7), 16–07 (2008)

    Google Scholar 

  3. M. Ankerst, M.M. Breunig, H.P. Kriegel, J. Sander, Optics: ordering points to identify the clustering structure. ACM Sigmod Rec. 28, 49–60 (1999)

    Article  Google Scholar 

  4. A. Bargiela, W. Pedrycz, Granular Computing: An Introduction (Kluwer Academic Publishers, Boston, 2003)

    Book  Google Scholar 

  5. V. Beckers, L.M. Dersch, K. Lotz, G. Melzer, O.E. Bläsing, R. Fuchs, T. Ehrhardt, C. Wittmann, In silico metabolic network analysis of arabidopsis leaves. BMC Syst. Biol. 10(1), 102 (2016)

    Article  Google Scholar 

  6. J. Bergstra, Y. Bengio, Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13, 281–305 (2012)

    MathSciNet  MATH  Google Scholar 

  7. H.M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. Bhat, H. Weissig, I.N. Shindyalov, P.E. Bourne, The protein data bank. Nucleic Acids Res. 28(1), 235–242 (2000)

    Article  Google Scholar 

  8. F.M. Bianchi, L. Livi, A. Rizzi, A. Sadeghian, A granular computing approach to the design of optimized graph classification systems. Soft Comput. 18(2), 393–412 (2014)

    Article  Google Scholar 

  9. F.M. Bianchi, S. Scardapane, A. Rizzi, A. Uncini, A. Sadeghian, Granular computing techniques for classification and semantic characterization of structured data. Cogn. Comput. 8(3), 442–461 (2016)

    Article  Google Scholar 

  10. P.S. Bradley, O.L. Mangasarian, W.N. Street, Clustering via concave minimization, in Advances in Neural Information Processing Systems (1997), pp. 368–374

    Google Scholar 

  11. E. Bullmore, O. Sporns, Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)

    Article  Google Scholar 

  12. G. Carlsson, Topology and data. Bull. Am. Math. Soc. 46(2), 255–308 (2009)

    Article  MathSciNet  Google Scholar 

  13. C. Cellucci, Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method (Springer Science & Business Media, 2013)

    Google Scholar 

  14. Y. Chen, E.K. Garcia, M.R. Gupta, A. Rahimi, L. Cazzanti, Similarity-based classification: concepts and algorithms. J. Mach. Learn. Res. 10, 747–776 (2009)

    Google Scholar 

  15. Y. Chen, M.R. Gupta, B. Recht, Learning kernels from indefinite similarities, in Proceedings of the 26th Annual International Conference on Machine Learning (ACM, 2009), pp. 145–152

    Google Scholar 

  16. A. Colorni, M. Dorigo, V. Maniezzo, Distributed optimization by ant colonies, in Toward a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life (Mit Press, 1992), p. 134

    Google Scholar 

  17. D. Counsell, A review of bioinformatics education in the uk. Brief. Bioinform. 4(1), 7–21 (2003)

    Article  Google Scholar 

  18. J. Damoiseaux, S. Rombouts, F. Barkhof, P. Scheltens, C. Stam, S.M. Smith, C. Beckmann, Consistent resting-state networks across healthy subjects. Proc. Natl. Acad. Sci. 103(37), 13848–13853 (2006)

    Article  Google Scholar 

  19. D.L. Davies, D.W. Bouldin, A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 2, 224–227 (1979)

    Article  Google Scholar 

  20. G. Del Vescovo, L. Livi, F.M. Frattale Mascioli, A. Rizzi, On the problem of modeling structured data with the minsod representative. Int. J. Comput. Theory Eng. 6(1), 9 (2014)

    Google Scholar 

  21. A. Di Noia, P. Montanari, A. Rizzi, Occupational diseases risk prediction by cluster analysis and genetic optimization, in Proceedings of the International Joint Conference on Computational Intelligence (SCITEPRESS-Science and Technology Publications, Lda, 2014), pp. 68–75

    Google Scholar 

  22. A. Di Noia, P. Montanari, A. Rizzi, Occupational diseases risk prediction by genetic optimization: Towards a non-exclusive classification approach, in Computational Intelligence (Springer, Berlin, 2016), pp. 63–77

    Google Scholar 

  23. L. Di Paola, M. De Ruvo, P. Paci, D. Santoni, A. Giuliani, Protein contact networks: an emerging paradigm in chemistry. Chem. Rev. 113(3), 1598–1613 (2012)

    Article  Google Scholar 

  24. M. Ester, H.P. Kriegel, J. Sander, X. Xu et al., A density-based algorithm for discovering clusters in large spatial databases with noise. Kdd 96, 226–231 (1996)

    Google Scholar 

  25. M.D. Fox, M.E. Raichle, Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nat. Rev. Neurosci. 8(9), 700–711 (2007)

    Article  Google Scholar 

  26. K.J. Friston, C.D. Frith, R.S. Frackowiak, R. Turner, Characterizing dynamic brain responses with fmri: a multivariate approach. Neuroimage 2(2), 166–172 (1995)

    Article  Google Scholar 

  27. J. Gao, B. Barzel, A.L. Barabási, Universal resilience patterns in complex networks. Nature 530(7590), 307–312 (2016)

    Article  Google Scholar 

  28. A. Giuliani, S. Filippi, M. Bertolaso, Why network approach can promote a new way of thinking in biology. Front. Genet. 5 (2014)

    Google Scholar 

  29. A. Giuliani, A. Krishnan, J.P. Zbilut, M. Tomita, Proteins as networks: usefulness of graph theory in protein science. Curr. Protein Peptide Sci. 9(1), 28–38 (2008)

    Article  Google Scholar 

  30. D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, USA, 1989)

    MATH  Google Scholar 

  31. M.D. Greicius, B. Krasnow, A.L. Reiss, V. Menon, Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. Proc. Natl. Acad. Sci. 100(1), 253–258 (2003)

    Article  Google Scholar 

  32. S. Guha, R. Rastogi, K. Shim, Cure: an efficient clustering algorithm for large databases. ACM Sigmod Rec. 27, 73–84 (1998)

    Article  Google Scholar 

  33. R.W. Hamming, Error detecting and error correcting codes. Bell Labs Tech. J. 29(2), 147–160 (1950)

    Article  MathSciNet  Google Scholar 

  34. B. He, K. Wang, Y. Liu, B. Xue, V.N. Uversky, A.K. Dunker, Predicting intrinsic disorder in proteins: an overview. Cell Res. 19(8), 929–949 (2009)

    Article  Google Scholar 

  35. D.R. Hofstadter, I Am a Strange Loop, Basic Books (2007)

    Google Scholar 

  36. J. Horgan, From complexity to perplexity. Sci. Am. 272(6), 104–109 (1995)

    Article  Google Scholar 

  37. A.K. Jain, M.N. Murty, P.J. Flynn, Data clustering: a review. ACM Comput. Surv. (CSUR) 31(3), 264–323 (1999)

    Article  Google Scholar 

  38. G. Jurman, R. Visintainer, C. Furlanello, An introduction to spectral distances in networks. Front. Artif. Intell. Appl. 226, 227–234 (2011)

    Google Scholar 

  39. L. Kaufman, P. Rousseeuw, Clustering by means of medoids. Stat. Data Anal. Based L1-Norm Relat. Methods, 405–416 (1987)

    Google Scholar 

  40. J. Kennedy, R. Eberhart, Particle swarm optimization, in Proceedings of the IEEE International Conference on Neural Networks, vol. 4 (IEEE, 1995), pp. 1942–1948

    Google Scholar 

  41. S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi, Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  42. V.I. Levenshtein, Binary codes capable of correcting deletions, insertions, and reversals. Soviet physics doklady. 10, 707–710 (1966)

    MathSciNet  MATH  Google Scholar 

  43. A.W.C. Liew, H. Yan, M. Yang, Pattern recognition techniques for the emerging field of bioinformatics: A review. Pattern Recognition 38(11), 2055–2073 (2005)

    Article  Google Scholar 

  44. L. Livi, A. Giuliani, A. Rizzi, Toward a multilevel representation of protein molecules: comparative approaches to the aggregation/folding propensity problem. Inf. Sci. 326, 134–145 (2016)

    Article  Google Scholar 

  45. L. Livi, A. Giuliani, A. Sadeghian, Characterization of graphs for protein structure modeling and recognition of solubility. Curr. Bioinform. 11(1), 106–114 (2016)

    Article  Google Scholar 

  46. L. Livi, E. Maiorino, A. Giuliani, A. Rizzi, A. Sadeghian, A generative model for protein contact networks. J. Biomol. Struct. Dyn. 34(7), 1441–1454 (2016)

    Article  Google Scholar 

  47. L. Livi, A. Rizzi, The graph matching problem. Pattern Anal. Appl. 16(3), 253–283 (2013)

    Article  MathSciNet  Google Scholar 

  48. L. Livi, A. Rizzi, A. Sadeghian, Optimized dissimilarity space embedding for labeled graphs. Inf. Sci. 266, 47–64 (2014)

    Article  MathSciNet  Google Scholar 

  49. L. Livi, A. Rizzi, A. Sadeghian, Granular modeling and computing approaches for intelligent analysis of non-geometric data. Appl. Soft Comput. 27, 567–574 (2015)

    Article  Google Scholar 

  50. L. Livi, A. Sadeghian, Granular computing, computational intelligence, and the analysis of non-geometric input spaces. Granul. Comput. 1(1), 13–20 (2016)

    Article  Google Scholar 

  51. S. Lloyd, Least squares quantization in pcm. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)

    Article  MathSciNet  Google Scholar 

  52. L. MacQueen, Some methods for classification and analysis of multivariate observations, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1 (Oakland, USA, 1967), pp. 281–297

    Google Scholar 

  53. H.A. Maghawry, M.C. Mostafa, M.H. Abdul-Aziz, T.E. Gharib, A modified cutoff scanning matrix protein representation for enhancing protein function prediction, in 9th International Conference on Informatics and Systems (INFOS) (IEEE, 2014), pp. DEKM–40

    Google Scholar 

  54. E. Maiorino, A. Rizzi, A. Sadeghian, A. Giuliani, Spectral reconstruction of protein contact networks. Phys. A: Stat. Mech. Appl. 471, 804–817 (2017)

    Article  Google Scholar 

  55. A. Martino, E. Maiorino, A. Giuliani, M. Giampieri, A. Rizzi, Supervised approaches for function prediction of proteins contact networks from topological structure information, in Scandinavian Conference on Image Analysis (Springer, Berlin, 2017), pp. 285–296

    Chapter  Google Scholar 

  56. A. Martino, A. Rizzi, F.M. Frattale Mascioli, Efficient approaches for solving the large-scale k-medoids problem, in Proceedings of the 9th International Joint Conference on Computational Intelligence. IJCCI, vol. 1 (INSTICC, 2017), pp. 338–347

    Google Scholar 

  57. J. Mercer, Functions of positive and negative type, and their connection with the theory of integral equations, in Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, vol. 209 (1909), pp. 415–446

    Article  Google Scholar 

  58. D.C. Mikulecky, Network thermodynamics and complexity: a transition to relational systems theory. Comput. Chem. 25(4), 369–391 (2001)

    Article  Google Scholar 

  59. T.M. Mitchell, Machine Learning (McGraw-Hill Boston, MA, 1997)

    MATH  Google Scholar 

  60. M. Neuhaus, H. Bunke, Bridging the Gap Between Graph Edit Distance and Kernel Machines, vol. 68 (World Scientific, 2007)

    Google Scholar 

  61. M. Pagani, A. Giuliani, J. Öberg, A. Chincarini, S. Morbelli, A. Brugnolo, D. Arnaldi, A. Picco, M. Bauckneht, A. Buschiazzo et al., Predicting the transition from normal aging to alzheimer’s disease: a statistical mechanistic evaluation of fdg-pet data. NeuroImage 141, 282–290 (2016)

    Article  Google Scholar 

  62. M. Pagani, A. Giuliani, J. Öberg, F. De Carli, S. Morbelli, N. Girtler, F. Bongioanni, D. Arnaldi, J. Accardo, M. Bauckneht et al., Progressive disgregation of brain networking from normal aging to alzheimer’s disease. independent component analysis on fdg-pet data. J. Nucl. Med. jnumed–116 (2017)

    Google Scholar 

  63. E. Parzen, On estimation of a probability density function and mode. Ann. Math. Stat. 33(3), 1065–1076 (1962)

    Article  MathSciNet  Google Scholar 

  64. M. Pascual, S.A. Levin, From individuals to population densities: searching for the intermediate scale of nontrivial determinism. Ecology 80(7), 2225–2236 (1999)

    Article  Google Scholar 

  65. K. Pearson, Mathematical contributions to the theory of evolution. iii. regression, heredity, and panmixia, in Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, vol. 187 (1896), pp. 253–318

    Article  Google Scholar 

  66. E. Pękalska, R.P. Duin, The Dissimilarity Representation for Pattern Recognition: Foundations and Applications (World Scientific, 2005)

    Google Scholar 

  67. K. Peng, P. Radivojac, S. Vucetic, A.K. Dunker, Z. Obradovic, Length-dependent prediction of protein intrinsic disorder. BMC Bioinform. 7(1), 208 (2006)

    Article  Google Scholar 

  68. J.B. Pereira, M. Mijalkov, E. Kakaei, P. Mecocci, B. Vellas, M. Tsolaki, I. Kłoszewska, H. Soininen, C. Spenger, S. Lovestone et al., Disrupted network topology in patients with stable and progressive mild cognitive impairment and alzheimer’s disease. Cereb. Cortex 26(8), 3476–3493 (2016)

    Article  Google Scholar 

  69. F. Possemato, A. Rizzi, Automatic text categorization by a granular computing approach: facing unbalanced data sets, in The International Joint Conference on Neural Networks (IJCNN) (IEEE, 2013), pp. 1–8

    Google Scholar 

  70. J.S. Richardson, The anatomy and taxonomy of protein structure. Adv. Protein Chem. 34, 167–339 (1981)

    Article  Google Scholar 

  71. D. de Ridder, J. de Ridder, M.J. Reinders, Pattern recognition in bioinformatics. Brief. Bioinform. 14(5), 633–647 (2013)

    Article  Google Scholar 

  72. A. Rizzi, F. Possemato, L. Livi, A. Sebastiani, A. Giuliani, F.M. Frattale Mascioli, A dissimilarity-based classifier for generalized sequences by a granular computing approach, in The International Joint Conference on Neural Networks (IJCNN) (IEEE, 2013), pp. 1–8

    Google Scholar 

  73. P. Romero, Z. Obradovic, X. Li, E.C. Garner, C.J. Brown, A.K. Dunker, Sequence complexity of disordered protein. Proteins Struct. Funct. Bioinform. 42(1), 38–48 (2001)

    Article  Google Scholar 

  74. P.J. Rousseeuw, Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)

    Article  Google Scholar 

  75. M. Rubinov, O. Sporns, Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3), 1059–1069 (2010)

    Article  Google Scholar 

  76. H. Sakoe, S. Chiba, Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. Acoust. Speech Signal Process. 26(1), 43–49 (1978)

    Article  Google Scholar 

  77. B. Schölkopf, A.J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (MIT press, 2002)

    Google Scholar 

  78. J. Shawe-Taylor, N. Cristianini, Kernel Methods for Pattern Analysis (Cambridge university press, Cambridge, 2004)

    Google Scholar 

  79. D.H. Silverman, G.W. Small, C.Y. Chang, C.S. Lu, M.A.K. de Aburto, W. Chen, J. Czernin, S.I. Rapoport, P. Pietrini, G.E. Alexander et al., Positron emission tomography in evaluation of dementia: regional brain metabolism and long-term outcome. Jama 286(17), 2120–2127 (2001)

    Article  Google Scholar 

  80. G.P. Singh, M. Ganapathi, D. Dash, Role of intrinsic disorder in transient interactions of hub proteins. Proteins Struct. Funct. Bioinform. 66(4), 761–765 (2007)

    Article  Google Scholar 

  81. J. Smucny, K.P. Wylie, J.R. Tregellas, Functional magnetic resonance imaging of intrinsic brain networks for translational drug discovery. Trends Pharmacol. Sci. 35(8), 397–403 (2014)

    Article  Google Scholar 

  82. C. Soguero-Ruiz, K. Hindberg, J.L. Rojo-Álvarez, S.O. Skrøvseth, F. Godtliebsen, K. Mortensen, A. Revhaug, R.O. Lindsetmo, K.M. Augestad, R. Jenssen, Support vector feature selection for early detection of anastomosis leakage from bag-of-words in electronic health records. IEEE J. Biomed. Health Inf. 20(5), 1404–1415 (2016)

    Article  Google Scholar 

  83. P.G. Spetsieris, J.H. Ko, C.C. Tang, A. Nazem, W. Sako, S. Peng, Y. Ma, V. Dhawan, D. Eidelberg, Metabolic resting-state brain networks in health and disease. Proc. Natl. Acad. Sci. 112(8), 2563–2568 (2015)

    Article  Google Scholar 

  84. J.M. Stanton, Galton, pearson, and the peas: A brief history of linear regression for statistics instructors. J. Stat. Education 9(3), 1–16 (2001)

    Article  Google Scholar 

  85. S. Theodoridis, K. Koutroumbas, Pattern Recognition, 4th edn. (Academic Press, 2008)

    Google Scholar 

  86. M.K. Transtrum, B.B. Machta, K.S. Brown, B.C. Daniels, C.R. Myers, J.P. Sethna, Perspective: sloppiness and emergent theories in physics, biology, and beyond. J. Chem. Phys. 143(1), 07B201_1 (2015)

    Google Scholar 

  87. V.N. Uversky, Natively unfolded proteins: a point where biology waits for physics. Protein Sci. 11(4), 739–756 (2002)

    Article  Google Scholar 

  88. B.C. Van Wijk, C.J. Stam, A. Daffertshofer, Comparing brain networks of different size and connectivity density using graph theory. PloS one 5(10), e13701 (2010)

    Article  Google Scholar 

  89. J.P. Vert, K. Tsuda, B. Schölkopf, Kernel Methods in Computational Biology, A primer on kernel methods (2004), pp. 35–70

    Google Scholar 

  90. Y.C. Wang, Y. Wang, Z.X. Yang, N.Y. Deng, Support vector machine prediction of enzyme function with conjoint triad feature and hierarchical context. BMC Syst. Biol. 5(1), S6 (2011)

    Article  Google Scholar 

  91. L. Wasserman, Topological data analysis. Ann. Rev. Stat. Appl. 5(1) (2018)

    Article  Google Scholar 

  92. W. Weaver, Science and complexity. Am. Sci. 36(4), 536 (1948)

    Google Scholar 

  93. A. Wright, A.B. McCoy, S. Henkin, A. Kale, D.F. Sittig, Use of a support vector machine for categorizing free-text notes: assessment of accuracy across two institutions. J. Am. Med. Inf. Assoc. 20(5), 887–890 (2013)

    Article  Google Scholar 

  94. Y. Yang, L. Han, Y. Yuan, J. Li, N. Hei, H. Liang, Gene co-expression network analysis reveals common system-level properties of prognostic genes across cancer types. Nat. Commun. 5, 3231 (2014)

    Google Scholar 

  95. F. Yates, K. Mather, Ronald aylmer fisher, 1890–1962. Biogr. Mem. Fellows R. Soc. 9, 91–129 (1963)

    Article  Google Scholar 

  96. L.A. Zadeh, Soft computing and fuzzy logic. IEEE Softw. 11(6), 48–56 (1994)

    Article  Google Scholar 

  97. T. Zhang, R. Ramakrishnan, M. Livny, Birch: an efficient data clustering method for very large databases. ACM Sigmod Rec. 25, 103–114 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Engineering, Electronics and Telecommunications, University of Rome “La Sapienza”, Via Eudossiana 18, 00184, Rome, Italy

    Alessio Martino & Antonello Rizzi

  2. Department of Environment and Health, Istituto Superiore di Sanità, Via Regina Elena 299, 00161, Rome, Italy

    Alessandro Giuliani

Authors
  1. Alessio Martino
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alessandro Giuliani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antonello Rizzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessio Martino .

Editor information

Editors and Affiliations

  1. University of Alberta, Edmonton, Alberta, Canada

    Witold Pedrycz

  2. National Taiwan University of Science and Technology, Taipei, Taiwan

    Shyi-Ming Chen

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Martino, A., Giuliani, A., Rizzi, A. (2018). Granular Computing Techniques for Bioinformatics Pattern Recognition Problems in Non-metric Spaces. In: Pedrycz, W., Chen, SM. (eds) Computational Intelligence for Pattern Recognition. Studies in Computational Intelligence, vol 777. Springer, Cham. https://doi.org/10.1007/978-3-319-89629-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-89629-8_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-89628-1

  • Online ISBN: 978-3-319-89629-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation