Abstract
Theoretical basis of Novelty Detection in Time Series and its relationships with State Space Reconstruction are discussed. It is shown that the methods for estimation of optimal state-space reconstruction parameters may be used for the estimation of immunological novelty detection system’s parameters. This is illustrated with a V-detector system detecting novelties in Mackey-Glass time series.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Markou, M., Singh, S.: Novelty Detection: A Review. Signal Processing 83(12), 2481–2497 (2003)
Kim, J., Bentley, P.: An Evaluation of Negative Selection in an Artificial Immune System for Network Intrusion Detection. In: GECCO 2001, pp. 1330–1337 (2001)
Balthrop, J., Forrest, S., Glickman, M.R.: Revisiting LISYS: Parameters and Normal Behavior. In: CEC 2002, pp. 1045–1050 (2002)
Esponda, F., Forrest, S., Helman, P.: A Formal Framework for Positive and Negative Detection Schemes. IEEE Trans. Syst., Man Cybernet. 34, 357–373 (2004)
Esponda, F., Forrest, S., Helman, P.: The Crossover Closure and Partial Match Detection. In: Timmis, J., Bentley, P.J., Hart, E. (eds.) ICARIS 2003. LNCS, vol. 2787, pp. 249–260. Springer, Heidelberg (2003)
González, F.: A Study of Artificial Immune Systems Applied to Anomaly Detection. Ph.D thesis, USA. The University of Memphis (2003)
Ji, Z., Dasgupta, D.: Real-valued negative selection algorithm with variable-sized detectors. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 287–298. Springer, Heidelberg (2004)
Ji, Z., Dasgupta, D.: Augmented Negative Selection Algorithm with Variable-Coverage Detectors. In: CEC 2004, pp. 1081–1088 (2004)
Forrest, S., Perelson, A., Allen, L., Cherukuri, R.: Self-Nonself Discrimination in a Computer. In: IEEE Symposium on Research in Security and Privacy (1994)
Dasgupta, D., Forrest, S.: Novelty Detection in Time Series Data using Ideas from Immunology. In: 5th International Conference on Intelligent Systems (1996)
Taylor, D., Corne, D.W.: An Investigation of the Negative Selection Algorithm for Fault Detection in Refrigeration Systems. LNCS, vol. 278 (2003)
Dasgupta, D., Forrest, S.: Tool Breakage Detection in Milling Operations using a Negative-Selection Algorithm. Tech. rep. CS95-5, Computer Science, University of New Mexico (1995)
Hofmeyr, S.A.: An Interpretative Introduction to the Immune System. Tech. rep. University of New Mexico (1999)
Dasgupta, D., Gonzalez, F.: An Immunity-Based Technique to Characterize Intrusions in Computer Networks. IEEE Trans. Evol. Comput. 6, 1081–1088 (2002)
González, F., Dasgupta, D.: An Immunogenetic Technique to Detect Anomalies in Network Traffic. In: GECCO 2002 (2002)
Dasgupta, D., Forrest, S.: Artificial Immune Systems in Industrial Applications. In: IPMM 1999 (1999)
Hart, E., Timmis, J.I.: Application areas of AIS: The past, the present and the future. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 483–497. Springer, Heidelberg (2005)
Ji, Z., Dasgupta, D.: Estimating the Detector Coverage in a Negative Selection. In: GECCO 2005 (2005)
Dasgupta, D., Krishnakumar, K.T., Wong, D., Berry, M.: Negative selection algorithm for aircraft fault detection. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 1–13. Springer, Heidelberg (2004)
Kugiumtzis, D.: State Space Reconstruction Parameters in the Analysis of Chaotic Time Series - the Role of the Time Window Length. Physica D 95, 13–28 (1996)
Small, M., Tse, C.K.: Optimal embedding parameters: A modeling paradigm. Physica D 194, 283–296 (2004)
Robinson, J.C.: A topological delay embedding theorem for infinite-dimensional dynamical systems. Nonlinearity 18(5), 2135–2143 (2005)
Packard, N.H., Crutchfield, J.P., Farmer, J.D., Shaw, R.S.: Geometry from a time series. Phys. Rev. Let. 45, 712–716 (1980)
Gibson, J.F., Farmer, J.D., Casdagli, M., Eubank, S.: An analytic approach to practical state space reconstruction. Physica D 57 (1992)
Sauer, T., Yorke, J.A., Casdagli, M.: Embedology. Journal of Stat. Phys. 65, 579–616 (1991)
Ruelle, D., Takens, F.: On the nature of turbulence. Comm. Math. Phys. 20, 167–192 (1971)
Broomhead, D.S., King, G.P.: Extracting qualitative dynamics from experimental data. Physica D 20, 217–236 (1986)
Rosenstein, M.T., Collins, J.J., De Luca, C.J.: Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica D 73, 82–98 (1993)
Tsonis, A.A.: Chaos: From Theory to Applications. Plenum Press, New York (1992)
Takens, F.: Detecting strange attractors in turbulence, Dynamical Systems and Turbulence. Lecturer Notes in Mathematics, vol. 898, pp. 366–381 (1981)
Mane, R.: On the dimension of the compact invariant sets of certain nonlinear maps. In: Dynamical systems and turbulence, Warwick (1981)
Bünner, M.J., Ciofini, M., Giaquinta, A., Hegger, R., Kantz, H., Meucci, R., Politi, A.: Recons-truction of systems with delayed feedback: I. Theory. EPJ D 10(2) (2000)
Sharif, S.S., Taylor, J.H.: Chaos in Nonlinear Dynamical Systems. Interim Report on Vibration Mechanisms of the EH101 Helicopter (2001)
Cao, L.: Practical method for determining the minimum embedding dimension of a scalar time series. Phys. Rev. A 45, 3403–3411 (1992)
Ataei, M., Lohmann, B., Khaki-Sedigh, A., Lucas, C.: Model based method for estimating an attractor dimension from uni/multivariate chaotic time series with application to Bremen climatic dynamics. Chaos, Solutons and Fractals 19, 1131–1139 (2004)
Froehling, H., Crutchfield, J.P., Farmer, D., Packard, N.H., Show, R.: On determining the dimension of chaotic flows. Physica D 3(3), 605–617 (1981)
Kennel, M.B., Brown, R., Abarbanel, H.D.I.: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys.Rev. A 45, 3403–3411 (1992)
Kennel, M.B., Abarbanel, H.D.I.: False neighbors and false strands: A reliable minimum embedding dimension algorithm. Tech.rep., Institute for Nonlinear Science and Department of Physics, University of California, San Diego, Mail Code 0402, La Jolla, CA 92093-0402
Liebert, W., Pawelzik, K., Schuster, H.G.: Optimal embeddings of chaotic attractors from topological considerations. Europhys. Lett. 14, 521 (1991)
Aleksic, Z.: Estimating the embedding dimension. Physica D 52 (1991)
Buzug, T., Pfister, G.: Comparison of algorithms calculating optimal embedding parameters for delay time coordinates. Physica D 58, 127–137 (1992)
Grassberger, P., Procaccia, I.: Measuring the strangeness of strange attractors. Phys. D (1983)
Kugiumtzis, D., Christophersen, N.: State Space Reconstruction: Method of Delays vs Singular Spectrum Approach. Report No 236, Dept. of Informatics, Univ. of Oslo (1997)
Casdagli, M., Eubank, S., Farmer, J.D., Gibson, J.: State space reconstruction in the presence of noise. Physica D 51, 52–98 (1991)
Mackey, M.C., Glass, L.: Oscillations and chaos in physiological control systems. Science 197, 287–289 (1977)
Lorenz, E.N.: Deterministic non-periodic flow. J. of Atmospheric Science 357 (1963)
Stibor, T., Timmis, J.I., Eckert, C.: A comparative study of real-valued negative selection to statistical anomaly detection techniques. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 262–275. Springer, Heidelberg (2005)
Ebner, M., Breunig, H.G., Albert, J.: On the Use of Negative Selection in an Artificial Immune System. In: GECCO 2002 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pasek, R. (2006). Theoretical Basis of Novelty Detection in Time Series Using Negative Selection Algorithms. In: Bersini, H., Carneiro, J. (eds) Artificial Immune Systems. ICARIS 2006. Lecture Notes in Computer Science, vol 4163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11823940_29
Download citation
DOI: https://doi.org/10.1007/11823940_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37749-8
Online ISBN: 978-3-540-37751-1
eBook Packages: Computer ScienceComputer Science (R0)