zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Network traffic analysis using singular value decomposition and multiscale transforms. (English) Zbl 1126.68010
Summary: The present work integrates the multiscale transform provided by the wavelets and Singular Value Decomposition (SVD) for the detection of anomaly in self-similar network data. The algorithm proposed in this paper uses the properties of SVD of a matrix whose elements are local energies of wavelet coefficients at different scales. Unlike existing techniques, our method determines both the presence (i.e., the time intervals in which anomaly occurs) and the nature of anomaly (i.e., anomaly of bursty type, long or short duration, etc.) in network data. It uses the diagonal, left and right singular matrices obtained in SVD to determine the number of scales of self-similarity, location and scales of anomaly in data, respectively. Our simulation work on different data sets demonstrates that the method performs better than the existing anomaly detection methods proposed for self-similar data.

68M10Network design and communication of computer systems
Full Text: DOI
[1] Abry, P.; Veitch, D.: Wavelet analysis of long-range dependent traffic. IEEE transactions on information theory 44, 2-15 (1998) · Zbl 0905.94006
[2] Abry, P.; Flandrin, P.; Taqqu, M. S.; Veitch, D.: Self-similarity and long-range dependence through the wavelet Lens. Theory and applications of long-range dependence, 526-556 (2003) · Zbl 1029.60028
[3] W.H. Allen, G.A. Marin, The LoSS technique for detecting new denial of service attacks, in: Proceedings of IEEE South East Conference, Greensboro, NC, 2004, pp. 302 -- 309.
[4] P. Barford, D. Plonka, Characteristics of network traffic flow anomalies, in: Proceedings of ACM SIGCOMM Internet Measurement Workshop IMW, 2002, pp. 71 -- 82.
[5] Crovella, M.; Bestavros, A.: Self-similarity in world wide web traffic: evidence and possible causes. IEEE-ACM transactions on networking 5, 835-846 (2001)
[6] Daubechies, I.: Ten lectures on wavelets. CBMS-NSF series in appl. Math. 61 (1992) · Zbl 0776.42018
[7] Gilbert, A. C.: Multiscale analysis and data networks. Applied and computational harmonic analysis 10, 185-202 (1992) · Zbl 0986.68004
[8] P. Huang, A. Feldmann, W. Willinger, A non-intrusive, wavelet-based approach to detect network performance problems, in: Proceedings of First ACM SIGCOMM Workshop on Internet Measurement IMW’01, San Francisco, California, USA, 2001, pp. 213 -- 227.
[9] Indian Financial Network (InFiNet). URL: http://www.idrbt.ac.in/infinet/infinet.html. · Zbl 1107.68324
[10] Jung, J.; Krishnamurthy, B.; Robinovich, M.: Flash crowds and denial of service attacks: characterization and implications for CDNs and web sites. Proceedings of WWW’2002, 1-12 (2002)
[11] KDD 1999 data set, Available from: <http://kdd.ics.uci.edu/databases/kddcup99/kddcup99.html>.
[12] Lang, M.; Guo, H.; Odegard, J. E.; Burrus, C. S.: Noise reduction using an undecimated discrete wavelet transform. IEEE signal processing letters 3, No. 1, 10-12 (1996)
[13] Labib, K.; Vemuri, V. R.: An application of principal component analysis to the detection and visualization of computer network attacks. Annals of telecommunications 61, No. 1 -- 2, 218-234 (2006)
[14] W. Lee, S. Stolfo, K. Mok, Mining in a data-flow environment: Experience in network intrusion detection, in: Proceedings of 5th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD’99), San Diego, CA, 1999, pp. 114 -- 124.
[15] Mallat, S.: A wavelet tour of signal processing. (1998) · Zbl 0937.94001
[16] Nash, D. A.; Ragsdale, D. J.: Simulation of self-similarity in network utilization patterns. Transactions of the IEEE systems man and cybernetics part-A 31, No. 4, 327-331 (2001)
[17] K. Pong Chan, A.W.C. Fu, Efficient time series matching by wavelets, in: Proceedings of ICDE, 1999, pp. 126 -- 133.
[18] Rawat, S.; Sastry, C. S.: Network intrusion detection using wavelet analysis. Lecture notes in computer science 3356, 224-232 (2004)
[19] Sastry, C. S.; Pujari, A. K.; Deekshatulu, B. L.; Bhagvati, C.: A wavelet based multiresolution algorithm for rotation invariant feature extraction. Pattern recognition letters 25, 1845-1855 (2004)
[20] Sastry, C. S.; Rawat, S.: Application of wavelets in network security. Enhancing computer security with smart technology, 209-228 (2005)
[21] Stoev, S.; Taqqu, M.; Park, C.; Marron, J. S.: On the wavelet spectrum diagnostic for Hurst parameter estimation in the analysis of Internet traffic. Computer networks 48, 423-445 (2005)
[22] Willinger, W.; Taqqu, M.; Erramilli, A.: A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks. Stochastic networks, 339-366 (1996) · Zbl 0855.60086
[23] Xia, X.; Lazarou, G. Y.; Butler, T.: Automatic scaling range selection for long-range dependent network traffic. IEEE communications letters 9, No. 10, 954-956 (2005)