Detection of an anomalous cluster in a network

Annals of Statistics

Volumn 39, Issue 1, 2011, Pages 278-304

  Arias Castro, Ery ^a   Cand̀s, Emmanuel J ^b   Durand, Arnaud ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b STANFORD UNIVERSITY   (United States)

^c UNIVERSITÉ PARIS SUD   (France)

Author keywords

Bayesian detection; Cellular automata; Detecting a cluster of nodes in a network; Disease outbreak detection; Generalized likelihood ratio test; Minimax detection; Richardson's model; Scan statistic; Sensor networks

Indexed keywords

EID: 79551611884     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOS839     Document Type: Article

References (75)

1. ADDARIO-BERRY, L., BROUTIN, N.,DEVROYE, L. and LUGOSI, G. (2010). On combinatorial testing problems. Ann. Statist. 38 3063-3092.
2. AGUR, S., DIEKMANN, O., HEESTERBEEK, H., CUSHING, J., GYLLENBERG, M., KIMMEL, M., MILNER, F., JAGERS, P. and KOSTOVA, T., EDS. (1999). Epidemiology, Cellular Automata and Evolution. Elsevier, Oxford. MR1683061
3. AKYILDIZ, I., SU, W., SANKARASUBRAMANIAM, Y. and CAYIRCI, E. (2002). A survey on sensor networks. IEEE Communications Magazine 40 102-114.
4. ALDOSARI, S. andMOURA, J. (2004). Detection in decentralized sensor networks. In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing 2004 (ICASSP'04) 2 277-280.
5. ARIAS-CASTRO, E., CANDÈS, E. J. and DURAND, A. (2009). Detection of an abnormal cluster in a network. In Proc. 57th Session of the International Statistical Institute, Durban, South Africa.
6. ARIAS-CASTRO, E., CANDÈS, E. J. and DURAND, A. (2010). Supplement to "Detection of an anomalous cluster in a network." DOI: 10.1214/10-AOS839SUPP.
7. ARIAS-CASTRO, E., CANDÈS, E. J., HELGASON, H. and ZEITOUNI, O. (2008). Searching for a trail of evidence in a maze. Ann. Statist. 36 1726-1757. MR2435454
8. ARIAS-CASTRO, E., DONOHO, D. and HUO, X. (2005). Near-optimal detection of geometric objects by fast multiscale methods. IEEE Trans. Inform. Theory 51 2402-2425. MR2246369
9. ARIAS-CASTRO, E., DONOHO, D. and HUO, X. (2006). Adaptive multiscale detection of filamentary structures in a background of uniform random points. Ann. Statist. 34 326-349. MR2275244
10. ARIAS-CASTRO, E., EFROS, B. and LEVI, O. (2010). Networks of polynomial pieces with application to the analysis of point clouds and images. J. Approx. Theory 162 94-130. MR2565828
11. ARORA, A., DUTTA, P., BAPAT, S., KULATHUMANI, V., ZHANG, H., NAIK, V., MITTAL, V., CAO, H., DEMIRBAS, M., GOUDA, M., CHOI, Y., HERMAN, T., KULKARNI, S., ARUMUGAM, U., NESTERENKO, M., VORA, A. and MIYASHITA, M. (2004). A line in the sand: A wireless sensor network for target detection, classification and tracking. Comput. Networks 46 605-634.
12. BOHMAN, T. and GRAVNER, J. (1999). Random threshold growth dynamics. Random Structures Algorithms 15 93-111. MR1698409
13. BOUTSIKAS,M. V. and KOUTRAS, M. V. (2006). On the asymptotic distribution of the discrete scan statistic. J. Appl. Probab. 43 1137-1154. MR2274642
14. BRAAMS, J., PRUIM, J., FRELING, N., NIKKELS, P., ROODENBURG, J., BOERING, G., VAALBURG, W. andVERMEY, A. (1995). Detection of lymph node metastases of squamous-cell cancer of the head and neck with FDG-PET and MRI. Journal of Nuclear Medicine 36 211.
15. BRENNAN, S. M., MIELKE, A. M., TORNEY, D. C. and MACCABE, A. B. (2004). Radiation detection with distributed sensor networks. IEEE Computer 37 57-59.
16. BRODSKY, B. and DARKHOVSKY, B. (1993). Nonparametric Methods in Change-Point Problems. Mathematics and Its Applications 243. Kluwer Academic, Dordrecht. MR1228205
17. CANDÈS, E. J., CHARLTON, P. R. and HELGASON, H. (2008). Detecting highly oscillatory signals by chirplet path pursuit. Appl. Comput. Harmon. Anal. 24 14-40. MR2379113
18. CARON, Y.,MAKRIS, P. and VINCENT, N. (2002). A method for detecting artificial objects in natural environments. In Proceedings 16th International Conference on Pattern Recognition 1 10600. IEEE Comput. Soc., New York.
19. CUI, Y.,WEI, Q., PARK, H. and LIEBER, C. (2001). Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species. Science 293 1289-1292.
20. CULLER, D., ESTRIN, D. and SRIVASTAVA, M. (2004). Overview of sensor networks. Computer 37 41-49.
21. DASGUPTA, B., HESPANHA, J. P., RIEHL, J. and SONTAG, E. (2006). Honey-pot constrained searching with local sensory information. Nonlinear Anal. 65 1773-1793. MR2252129
22. DEMBO, A., GANDOLFI, A. and KESTEN, H. (2001). Greedy lattice animals: Negative values and unconstrained maxima. Ann. Probab. 29 205-241. MR1825148
23. DEMIRBAŞ, K. (1987). Maneuvering target tracking with hypothesis testing. IEEE Trans. Aerospace Electron. Systems 23 757-766. MR0926001
24. DESOLNEUX, A., MOISAN, L. and MOREL, J.-M. (2003). Maximal meaningful events and applications to image analysis. Ann. Statist. 31 1822-1851. MR2036391
25. DUCZMAL, L., KULLDORFF, M. and HUANG, L. (2006). Evaluation of spatial scan statistics for irregularly shaped clusters. J. Comput. Graph. Statist. 15 428-442. MR2256152
26. DUDLEY, R. M. (1967). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1 290-330. MR0220340
27. FITCH, J., RABER, E. and IMBRO, D. (2003). Technology challenges in responding to biological or chemical attacks in the civilian sector. Science 302 1350-1354.
28. GEELHOOD, B., ELY, J., HANSEN, R., KOUZES, R., SCHWEPPE, J. andWARNER, R. (2003). Overview of portal monitoring at border crossings. 2003 IEEE Nuclear Science Symposium Conference Record 1 513-517.
29. GEMAN, D. and JEDYNAK, B. (1996). An active testing model for tracking roads in satellite images. IEEE Trans. Pattern Anal. Mach. Intell. 18 1-14.
30. GLAZ, J., NAUS, J. and WALLENSTEIN, S. (2001). Scan Statistics. Springer, New York. MR1869112
31. GRAVNER, J. and GRIFFEATH, D. (2006). Random growth models with polygonal shapes. Ann. Probab. 34 181-218. MR2206346
32. HALL, P. and JIN, J. (2008). Properties of higher criticism under strong dependence. Ann. Statist. 36 381-402. MR2387976
33. HALL, P. and JIN, J. (2010). Innovated higher criticism for detecting sparse signals in correlated noise. Ann. Statist. 38 1686-1732. MR2662357
34. HEFFERNAN, R., MOSTASHARI, F., DAS, D., KARPATI, A., KULLDORFF, M. andWEISS, D. (2004). Syndromic surveillance in public health practice, New York City. Emerging Infectious Diseases 10 858-864.
35. HILLS, R. (2001). Sensing for danger. Sci. Technol. Rev. Available at https://www.llnl.gov/str/ JulAug01/Hills.html.
36. HUSBY, O. and RUE, H. (2004). Estimating blood vessel areas in ultrasound images using a deformable template model. Stat. Model. 4 211-226. MR2062101
37. ILACHINSKI, A. (2001). Cellular Automata: A Discrete Universe.World Scientific, River Edge, NJ. MR1849342
38. JAIN, A., ZHONG, Y. and DUBUISSON-JOLLY, M. (1998). Deformable template models: A review. Signal Processing 71 109-129.
39. JAMES, D., CLYMER, B. D. and SCHMALBROCK, P. (2001). Texture detection of simulated microcalcification susceptibility effects in magnetic resonance imaging of breasts. Journal of Magnetic Resonance Imaging 13 876-881.
40. JIANG, T. (2002). Maxima of partial sums indexed by geometrical structures. Ann. Probab. 30 1854-1892. MR1944008
41. KLARNER, D. (1967). Cell growth problems. Canad. J. Math. 19 851-863. MR0214489
42. KOLMOGOROV, A. N. and TIHOMIROV, V. M. (1961). e-entropy and e-capacity of sets in functional space. Amer. Math. Soc. Transl. (2) 17 277-364. MR0124720
43. KULLDORFF, M. (1997). A spatial scan statistic. Comm. Statist. Theory Methods 26 1481-1496. MR1456844
44. KULLDORFF, M. (2001). Prospective time periodic geographical disease surveillance using a scan statistic. J. Roy. Statist. Soc. Ser. A 164 61-72. MR1819022
45. KULLDORFF, M., FANG, Z. andWALSH, S. J. (2003). A tree-based scan statistic for database disease surveillance. Biometrics 59 323-331. MR1987399
46. KULLDORFF, M., HEFFERNAN, R., HARTMAN, J., ASSUNCAO, R. and MOSTASHARI, F. (2005). A space-time permutation scan statistic for disease outbreak detection. PLOS Medicine 2 216.
47. KULLDORFF, M., HUANG, L., PICKLE, L. and DUCZMAL, L. (2006). An elliptic spatial scan statistic. Stat. Med. 25 3929-43. MR2297401
48. LAWLER, G., BRAMSON, M. and GRIFFEATH, D. (1992). Internal diffusion limited aggregation. Ann. Probab. 20 2117-2140. MR1188055
49. LEXA, M., ROZELL, C., SINANOVIC, S. and JOHNSON, D. (2004). To cooperate or not to cooperate: Detection strategies in sensor networks. In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing 2004 (ICASSP'04) 3 841-844.
50. LI, D.,WONG, K., HU, Y. H. and SAYEED, A. (2002). Detection, classification and tracking of targets. IEEE Signal Processing Magazine 19 17-29.
51. MCINERNEY, T. and TERZOPOULOS, D. (1996). Deformable models in medical image analysis: A survey. Medical Image Analysis 1 91-108.
52. MEI, Y. (2008). Asymptotic optimality theory for decentralized sequential hypothesis testing in sensor networks. IEEE Trans. Inform. Theory 54 2072-2089. MR2450850
53. MOON, N., BULLITT, E., VAN LEEMPUT, K. and GERIG, G. (2002). Automatic brain and tumor segmentation. In MICCAI'02: Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I 372-379. Springer, London.
54. PATIL, G. P., BALBUS, J., BIGING, G., JAJA, J.,MYERS, W. L. and TAILLIE, C. (2004). Multiscale advanced raster map analysis system: Definition, design and development. Environ. Ecol. Stat. 11 113-138. MR2086391
55. PATWARI, N. and HERO, A. (2003). Hierarchical censoring for distributed detection in wireless sensor networks. In Proceedings of 2003 IEEE International Conference on Acoustics, Speech and Signal Processing 2003 (ICASSP'03) 4 848-851.
56. PENROSE, M. (2003). Random Geometric Graphs. Oxford Studies in Probability 5. Oxford Univ. Press, Oxford. MR1986198
57. PERONE PACIFICO, M., GENOVESE, C., VERDINELLI, I. andWASSERMAN, L. (2004). False discovery control for random fields. J. Amer. Statist. Assoc. 99 1002-1014. MR2109490 (Pubitemid 39665946)
58. POZO, D., OLMO, F. and ALADOS-ARBOLEDAS, L. (1997). Fire detection and growth monitoring using a multitemporal technique on AVHRR mid-infrared and thermal channels. Remote Sensing of Environment 60 111-120.
59. RICHARDSON, D. (1973). Random growth in a tessellation. Proc. Cambridge Philos. Soc. 74 515-528. MR0329079
60. ROTZ, L. and HUGHES, J. (2004). Advances in detecting and responding to threats from bioterrorism and emerging infectious disease. Nature Medicine S130-S136.
61. SCHIFF, J. L. (2008). Cellular Automata. Wiley, Hoboken, NJ. MR2367301
62. ŞENDUR, L., MAXIM, V., WHITCHER, B. and BULLMORE, E. (2005). Multiple hypothesis mapping of functional MRI data in orthogonal and complex wavelet domains. IEEE Trans. Signal Process. 53 3413-3426. MR2213561
63. SHEN, X., HUANG, H.-C. and CRESSIE, N. (2002). Nonparametric hypothesis testing for a spatial signal. J. Amer. Statist. Assoc. 97 1122-1140. MR1951265
64. SIEGMUND, D. (1985). Sequential Analysis: Tests and Confidence Intervals. Springer, New York. MR0799155
65. STRICKLAND, R. and HAHN, H.Wavelet transform methods for object detection and recovery. IEEE Trans. Image Process. 6 724-735.
66. SZOR, P. (2005). The Art of Computer Virus Research and Defense. Addison-Wesley Professional.
67. TALAGRAND, M. (2005). The Generic Chaining. Springer, Berlin. MR2133757
68. TAN, H. and ZHANG, Y. (2006). An energy minimization process for extracting eye feature based on deformable template. Lecture Notes in Computer Science 3852 663. Springer, Berlin.
69. THOMOPOULOS, S., VISWANATHAN, R. and BOUGOULIAS, D. (1989). Optimal distributed decision fusion. IEEE Transactions on Aerospace and Electronic Systems 25 761-765.
70. WAGNER, M., TSUI, F., ESPINO, J., DATO, V., SITTIG, D., CARUANA, R., MCGINNIS, L., DEERFIELD, D., DRUZDZEL, M. and FRIDSMA, D. (2001). The emerging science of very early detection of disease outbreaks. Journal of Public Health Management and Practice 7 51-59.
71. WALTHER, G. (2010). Optimal and fast detection of spatial clusters with scan statistics. Ann. Statist. 38 1010-1033. MR2604703
72. XU, C. and PRINCE, J. (1998). Snakes, shapes and gradient vector flow. IEEE Trans. Image Process. 7 359-369. MR1669528
73. YU, L., YUAN, L., QU, G. and EPHREMIDES, A. (2006). Energy-driven detection scheme with guaranteed accuracy. Processing of the Fifth International Conference on Information in Sensor Networks 2006 (IPSN'2006) 284-291.
74. ZHAO, F. and GUIBAS, L. (2004). Wireless Sensor Networks: An Information Processing Approach. Morgan Kaufmann, San Francisco.
75. ZHONG, Y., JAIN, A. and DUBUISSON-JOLLY, M.-P. (2000). Object tracking using deformable templates. IEEE Trans. Pattern Anal. Mach. Intell. 2 544-549.