A Nonlinear Technique for Analysis of Big Data in Neuroscience

  • Koel Das
  • Zoran Nenadic


Recent technological advances have paved the way for big data analysis in the field of neuroscience. Machine learning techniques can be used effectively to explore the relationship between large-scale neural and behavorial data. In this chapter, we present a computationally efficient nonlinear technique which can be used for big data analysis. We demonstrate the efficacy of our method in the context of brain computer interface. Our technique is piecewise linear and computationally inexpensive and can be used as an analysis tool to explore any generic big data.


Linear Discriminant Analysis Neural Signal Discriminatory Information Common Spatial Pattern Neural Data 
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.
    Focus on big data. Nat Neurosci 17(11):1429
  2. 2.
    Ang KK, Chin ZY, Zhang H, Guan C (2008) Filter bank common spatial pattern (fbcsp) in brain-computer interface. In: IEEE International joint conference on neural networks, 2008. IJCNN 2008 (IEEE World congress on computational intelligence). IEEE, pp 2390–2397Google Scholar
  3. 3.
    Belhumeur P, Hespanha J, Kriegman D (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal 19(7):711–720Google Scholar
  4. 4.
    Birbaumer N, Ghanayim N, Hinterberger T, Iversen I, Kotchoubey B, Kbler A, Perelmouter J, Taub E, Flor H (1999) A spelling device for the paralysed. Nature 398(6725):297–298CrossRefGoogle Scholar
  5. 5.
    Blankertz B, Tomioka R, Lemm S, Kawanabe M, Muller K-R (2008) Optimizing spatial filters for robust eeg single-trial analysis. IEEE Signal Process Mag 25(1):41–56CrossRefGoogle Scholar
  6. 6.
    Chen L-F, Liao H-YM, Ko M-T, Lin J-C, Yu G-J (2000) A new lda-based face recognition system which can solve the small sample size problem. Pattern Recogn 33(10):1713–1726CrossRefGoogle Scholar
  7. 7.
    Cover TM, Campenhout JMV (1977) On the possible ordering in the measurement selection problem. IEEE Trans Syst Man Cybern 7:657–661CrossRefzbMATHGoogle Scholar
  8. 8.
    Daly JJ, Cheng R, Rogers J, Litinas K, Hrovat K, Dohring M (2009) Feasibility of a new application of noninvasive brain computer interface (bci): a case study of training for recovery of volitional motor control after stroke. J Neurol Phys Ther 33(4):203–211Google Scholar
  9. 9.
    Daniels MJ, Kass RE (2001) Shrinkage estimators for covariance matrices. Biometrics 57:1173–1184MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Das K, Meyer J, Nenadic Z (2006) Analysis of large-scale brain data for brain-computer interfaces. In: Proceedings of the 28th Annual international conference of the IEEE engineering in medicine and biology society, pp 5731–5734Google Scholar
  11. 11.
    Das K, Nenadic Z (2009) An efficient discriminant-based solution for small sample size problem. Pattern Recogn 42(5):857–866CrossRefzbMATHGoogle Scholar
  12. 12.
    Das K, Osechinskiy S, Nenadic Z (2007) A classwise pca-based recognition of neural data for brain-computer interfaces. In: Proceedings of the 29th Annual international conference of the IEEE engineering in medicine and biology society, pp 6519–6522Google Scholar
  13. 13.
    Das K, Rizzuto D, Nenadic Z (2009) Estimating mental states for brain-computer interface. IEEE Trans Biomed Eng 56(8):2114–2122CrossRefGoogle Scholar
  14. 14.
    Do AH, Wang PT, King CE, Chun SN, Nenadic Z (2013) Brain-computer interface controlled robotic gait orthosis. J Neuro Eng Rehabil 10(111)Google Scholar
  15. 15.
    Do AH, Wang PT, King CE, Schombs A, Cramer SC, Nenadic Z (2012) Brain-computer interface controlled functional electrical stimulation device for foot drop due to stroke. Conf Proc IEEE Eng Med Biol Soc 6414–6417:2012Google Scholar
  16. 16.
    Duda RO, Hart PE, Stork DG(2001) Pattern classification. Wiley-InterscienceGoogle Scholar
  17. 17.
    Enke H, Partl A, Reinefeld A, Schintke F (2012) Handling big data in astronomy and astrophysics: rich structured queries on replicated cloud data with xtreemfs. Datenbank-Spektrum 12(3):173–181CrossRefGoogle Scholar
  18. 18.
    Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugenics 7:179–188CrossRefGoogle Scholar
  19. 19.
    Fukunaga K (1990) Inroduction to statistical pattern recognition, 2nd edn. Academic PressGoogle Scholar
  20. 20.
    He X, Yan S, Hu Y, Niyogi P (2005) Face recognition using laplacian faces. IEEE Trans Pattern Anal 27(3):328–340CrossRefGoogle Scholar
  21. 21.
    Hochberg L, Serruya M, Friehs G, Mukand J, Saleh M, Caplan A, Branner A, Chen D, Penn RD, Donoghue J (2006) Neuronal ensemble control of prosthetic devices by a human with tetraplegia. Nature 442(7099):164–171Google Scholar
  22. 22.
    Hoffbeck JP, Landgrebe DA (1996) Covariance matrix estimation and classification with limited training data. IEEE Trans Pattern Anal 18(7):763–767CrossRefGoogle Scholar
  23. 23.
    Huang R, Liu Q, Lu H, Ma S (2002) Solving the small sample size problem of lda. In: ICPR ’02: Proceedings of the 16th International conference on pattern recognition (ICPR’02), vol 3. IEEE Computer Society, p 30029Google Scholar
  24. 24.
    Huber PJ (1985) Projection pursuit. Ann Stat 13(2):435–475MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Insel TR, Landis SC, Collins FS (2013) The nih brain initiative. Science 340(6133):687–688CrossRefGoogle Scholar
  26. 26.
    Kawanabe M, Samek W, Müller K-R, Vidaurre C (2014) Robust common spatial filters with a maxmin approach. Neural Comput 26(2):349–376MathSciNetCrossRefGoogle Scholar
  27. 27.
    Kesner RP, Farnsworth G, Kametani H (1991) Role of parietal cortex and hippocampus in representing spatial information. Cereb Cortex 1(5):367–373CrossRefGoogle Scholar
  28. 28.
    King CE, Dave KR, Wang PT, Mizuta M, Reinkensmeyer DJ, Do AH, Moromugi S, Nenadic Z (2014) Performance assessment of a brain-computer interface driven hand orthosis. Annals of Biomed Eng 42(10):2095–2105CrossRefGoogle Scholar
  29. 29.
    King CE, Wang PT, McCrimmon CM, Chou CCY, Do AH, Nenadic Z (2014) Brain-computer interface driven functional electrical stimulation system for overground walking in spinal cord injury participant. In: Proceedings of the 36th Annual international conference IEEE engineering and medical biological society, pp 1238–1242Google Scholar
  30. 30.
    Kirby M, Sirovich L (1990) Application of the karhunen-loeve procedure for the characterization of human faces. IEEE Trans Pattern Anal 12:103–108CrossRefGoogle Scholar
  31. 31.
    Kittler J (1978) Feature set search algorithms. In: Chen CH (ed) Pattern recognition and signal processing. Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands, pp 41–60Google Scholar
  32. 32.
    Kohavi R (1995) A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Joint commission international, pp 1137–1145Google Scholar
  33. 33.
    Leuthardt E, Schalk G, Wolpaw J, Ojemann J, Moran D (2004) A brain-computer interface using electrocorticographic signals in humans. J Neural Eng 1(2):63–71Google Scholar
  34. 34.
    Lewis S, Csordas A, Killcoyne S, Hermjakob H, Hoopmann MR, Moritz RL, Deutsch EW, Boyle J (2012) Hydra: a scalable proteomic search engine which utilizes the hadoop distributed computing framework. BMC Bioinform 13(1):324CrossRefGoogle Scholar
  35. 35.
    Loog M, Duin R (2004) Linear dimensionality reduction via a heteroscedastic extension of lda: the chernoff criterion. IEEE Trans Pattern Anal 26:732–739CrossRefGoogle Scholar
  36. 36.
    Markram H (2012) The human brain project. Sci Am 306(6):50–55CrossRefGoogle Scholar
  37. 37.
    Mathé C, Sagot M-F, Schiex T, Rouze P (2002) Current methods of gene prediction, their strengths and weaknesses. Nucleic Acids Res 30(19):4103–4117CrossRefGoogle Scholar
  38. 38.
    McCrimmon CM, King CE, Wang PT, Cramer SC, Nenadic Z, Do AH (2014) Brain-controlled functional electrical stimulation for lower-limb motor recovery in stroke survivors. Conf Proc IEEE Eng Med Biol Soc 2014:1247–1250Google Scholar
  39. 39.
    McFarland DJ, McCane LM, David SV, Wolpaw JR (1997) Spatial filter selection for EEG-based communication. Electroeng Clin Neuro 103(3):386–394CrossRefGoogle Scholar
  40. 40.
    Müller-Gerking J, Pfurtscheller G, Flyvbjerg H (1999) Designing optimal spatial filters for single-trial eeg classification in a movement task. Clin Neurophysiol 110(5):787–798CrossRefGoogle Scholar
  41. 41.
    Musallam S, Corneil BD, Greger B, Scherberger H, Andersen RA (2004) Cognitive control signals for neural prosthetics. Science 305(5681):258–262CrossRefGoogle Scholar
  42. 42.
    Nenadic Z (2007) Information discriminant analysis: Feature extraction with an information-theoretic objective. IEEE Trans Pattern Anal 29(8):1394–1407CrossRefGoogle Scholar
  43. 43.
    Nenadic Z, Rizzuto D, Andersen R, Burdick J (2007) Advances in cognitive neural prosthesis: recognition of neural data with an information-theoretic objective. In: Dornhege G, Millan J, Hinterberger T, McFarland D, Muller KR (eds) Toward brain computer interfacing, Chap 11. The MIT Press, pp 175–190Google Scholar
  44. 44.
    Nilsson T, Mann M, Aebersold R, Yates JR III, Bairoch A, Bergeron JJ (2010) Mass spectrometry in high-throughput proteomics: ready for the big time. Nat Methods 7(9):681–685CrossRefGoogle Scholar
  45. 45.
    ODriscoll A, Daugelaite J, Sleator RD (2013) Big data, hadoop and cloud computing in genomics. J Biomed Inf 46(5):774–781Google Scholar
  46. 46.
    Parzen E (1962) On the estimation of a probability density function and mode. Ann Math Stat 33:1065–1076MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Pfurtscheller G, Neuper C, Flotzinger D, Pregenzer M (1997) EEG-based discrimination between imagination of right and left hand movement. Electroeng Clin Neuro 103(6):642–651CrossRefGoogle Scholar
  48. 48.
    Pfurtscheller G, Neuper C, Muller GR, Obermaier B, Krausz G, Schlogl A, Scherer R, Graimann B, Keinrath C, Skliris D, Wortz GSM, Schrank C (2003) Graz-BCI: state of the art and clinical applications. IEEE Trans Neural Syst Rehabil 11(2):177–180CrossRefGoogle Scholar
  49. 49.
    Ramos-Murguialday A, Broetz D, Rea M, Ler L, Yilmaz O, Brasil FL, Liberati G, Curado MR, Garcia-Cossio E, Vyziotis A, Cho W, Agostini M, Soares E, Soekadar S, Caria A, Cohen LG, Birbaumer N (2013) Brain-machine interface in chronic stroke rehabilitation: a controlled study. Ann Neurol 74(1):100–108Google Scholar
  50. 50.
    Ramoser H, Muller-Gerking J, Pfurtscheller G (2000) Optimal spatial filtering of single trial eeg during imagined hand movement. IEEE Trans Rehabil Eng 8(4):441–446CrossRefGoogle Scholar
  51. 51.
    Rao CR (1948) The utilization of multiple measurements in problems of biological classification. J R Stat Soc B Methods 10(2):159–203MathSciNetzbMATHGoogle Scholar
  52. 52.
    Rizzuto D, Mamelak A, Sutherling W, Fineman I, Andersen R (2005) Spatial selectivity in human ventrolateral prefrontal cortex. Nat Neurosci 8:415–417Google Scholar
  53. 53.
    Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323–2326CrossRefGoogle Scholar
  54. 54.
    Santhanam G, Ryu SI, Yu1 BM, Afshar A, Shenoy KV (2006) A high-performance brain-computer interface. Nature 442:195–198Google Scholar
  55. 55.
    Saon G, Padmanabhan M (2000) Minimum Bayes error feature selection for continuous speech recognition. In: NIPS, pp 800–806Google Scholar
  56. 56.
    Schäfer J, Strimmer K (2005) A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat Appl Genet Mol Biol 4(1):Article 32Google Scholar
  57. 57.
    Schölkopf B, Smola A, Müller KR (1997) Kernel principal component analysis. In: Artificial neural networks ICANN’97. Springer, pp 583–588Google Scholar
  58. 58.
    Serruya MD, Hatsopoulos NG, Paninski L, Fellows MR, Donoghue JP (2002) Instant neural control of a movement signal. Nature 416(6877):141–142CrossRefzbMATHGoogle Scholar
  59. 59.
    Shenoy P, Miller K, Ojemann J, Rao R (2007) Finger movement classification for an electrocorticographic bci. In: 3rd International IEEE/EMBS conference on neural engineering, 2007. CNE ’07, pp 192–195, 2–5 May 2007Google Scholar
  60. 60.
    Shenoy P, Miller K, Ojemann J, Rao R (2008) Generalized features for electrocorticographic bcis. IEEE Trans Biomed Eng 55(1):273–280CrossRefGoogle Scholar
  61. 61.
    Shenoy P, Rao R (2004) Dynamic bayes networks for brain-computer interfacing. In: Advances in neural information processing systems, pp 1265–1272Google Scholar
  62. 62.
    Taylor D, Tillery S, Schwartz A (2002) Direct cortical control of 3D neuroprosthetic devices. Science 296(5574):1829–1832CrossRefGoogle Scholar
  63. 63.
    Thomaz CE, Gillies DF, Feitosa RQ (2001) Small sample problem in bayes plug-in classifier for image recognition. In: International conference on image and vision computing, New Zealand, pp 295–300Google Scholar
  64. 64.
    Thorpe S, Fize D, Marlot C (1995) Speed of processing in the human visual system. Nature 381(6582):520–522CrossRefGoogle Scholar
  65. 65.
    Torkkola K (2002) Discriminative features for document classification. In: Proceedings 16th international conference on pattern recognition, vol 1, pp 472–475Google Scholar
  66. 66.
    Townsend G, Graimann B, Pfurtscheller G (2006) A comparison of common spatial patterns with complex band power features in a four-class bci experiment. IEEE Trans Biomed Eng 53(4):642–651Google Scholar
  67. 67.
    Turk M, Pentland A (1991) Eigenfaces for recognition. J Cognit Neurosci 3(1):71–86Google Scholar
  68. 68.
    Wang W, Collinger JL, Degenhart AD, Tyler-Kabara EC, Schwartz AB, Moran DW, Weber DJ, Wodlinger B, Vinjamuri RK, Ashmore RC et al (2013) An electrocorticographic brain interface in an individual with tetraplegia. PloS ONE 8(2):e55344CrossRefGoogle Scholar
  69. 69.
    Wang X, Tang X (2004) Dual-space linear discriminant analysis for face recognition. In: 2004 IEEE Computer society conference on computer vision and pattern recognition (CVPR’04), vol 02, pp 564–569, 2004Google Scholar
  70. 70.
    Wang Y, Gao S, Gao X (2006) Common spatial pattern method for channel selelction in motor imagery based brain-computer interface. In: 27th Annual international conference of the engineering in medicine and biology society, 2005. IEEE-EMBS 2005. IEEE, pp 5392–5395Google Scholar
  71. 71.
    Wessberg J, Stambaugh C, Kralik J, Beck P, Laubach M, Chapin J, Kim J, Biggs S, Srinivasan MA, Nicolelis MA (2000) Real-time prediction of hand trajectory by ensembles of cortical neurons in primates. Nature 408(6810):361–365CrossRefGoogle Scholar
  72. 72.
    Wolpaw J, Birbaumer N, McFarland D, Pfurtscheller G, Vaughan T (2002) Brain-computer interfaces for communication and control. Clin Neurophysiol 6(113):767–791CrossRefGoogle Scholar
  73. 73.
    Wolpaw J, Wolpaw EW (2011) Brain-computer interfaces: principles and practice. Oxford University PressGoogle Scholar
  74. 74.
    Wolpaw JR, McFarland DJ (2004) Control of a two-dimensional movement signal by a noninvasive brain-computer interface in humans. Proc Natl Acad Sci USA 101(51):17849–17854CrossRefGoogle Scholar
  75. 75.
    Yang J, Frangi AF, Yang J-Y, Zhang D, Jin Z (2005) Kpca plus lda: a complete kernel fisher discriminant framework for feature extraction and recognition. IEEE Trans Pattern Anal Mach Intell 27(2):230–244CrossRefGoogle Scholar
  76. 76.
    Yu H, Yang H (2001) A direct lda algorithm for high-dimensional data with application to face recognition. Pattern Recogn Lett 34(10):2067–2070CrossRefzbMATHGoogle Scholar
  77. 77.
    Zhang S, Sim T (2007) Discriminant subspace analysis: a fukunaga-koontz approach. IEEE Trans Pattern Anal 29(10):1732–1745Google Scholar
  78. 78.
    Zhu M, Martinez AM (2006) Subclass discriminant analysis. IEEE Trans Pattern Anal 28(8):1274–1286CrossRefGoogle Scholar

Copyright information

© Springer India 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIISER KolkataMohanpurIndia
  2. 2.Department of Biomedical EngineeringUniversity of CaliforniaIrvineUSA

Personalised recommendations