Publications (Books, Patents, Papers)

Books

  1.  M. Kirby (2001), Geometric Data Analysis, Wiley and Sons.
  2.  M. Kirby and G. Dangelmayr, A Comprehensive Introduction to Mathematical Modeling, in preparation.
Patents
  1. Nonlinear function approximation over high-dimensional domains, US8521488 B2, Aug 27, 2013 (with Arta Jamshidi).
  2. Unknown pattern set recognition, US 8,116,566.  Kirby; Michael Joseph, Beveridge, James Ross, Chang; Jen-Mei, Draper; Bruce Anthony, Kley; Holger Philipp, Peterson; Christopher Scott, issued February, 2012.
  3. Nonlinear function approximation over high-dimensional domains, US 8,046,200, issued Oct. 25, 2011, (with Arta Jamshidi.)
  4. Nonlinear set to set pattern recognition US 7,917,540, issued March 29, 2011, (with Chris Peterson.)
  5. Apparatus, System and Method for Interpolating High-Dimensional Non-linear Data}, U.S. Patent Serial No. 11/263,740 Nov. 1, 2005, (with Yue Qiao.)

Refereed Papers

106. Robert Arn, Pradyumna Narayana,Tegan Emerson, Bruce Draper, Michael Kirby and Chris Peterson, Motion Segmentation via Generalized Curvatures, to appear Transactions on Pattern Recognition and Machine Intelligence (2018).

105. H. Kvinge, E.Farnell, M. Kirby and C. Peterson, A GPU-Oriented Algorithm Design for Secant-Based Dimensionality Reduction,  ISPDC 2018 17th IEEE International Symposium on Paralleland Distributed Computing, 6/2018.

104. Javier Alvarez-Vizoso, Michael Kirby, Chris Peterson, Manifold Curvature from Covariance Analysis, (SSP 2018) 2018 IEEE Statistical Signal Processing Workshop, 6/2018.

103. H. Kvinge, E. Farnell, M. Kirby and C. Peterson, Endmember Extraction on the Grassmannian,  (DSW 2018) 2018 IEEE Data Science Workshop, 6/2018.

102. T. Ghosh, X. Ma and M. Kirby, (2018) New Tools for the Visualization of Biological Pathways, Methods, Vol. 132, pages 26 - 33.

101. I. Santamaria, J. Via, M. Kirby, T. Marrinan, C. Peterson, L. Scharf (2017),  Constrained Subspace Estimation via Convex Optimization, EUSIPCO 2017, Kos Island, Greece.

100. Tomojit Ghosh, Michael Kirby, and Xiaofeng Ma (2017), Dantzig-Selector Radial Basis Function Learning with Nonconvex Refinement,  p. 313-327, In: Advances in Time Series Analysis and Forecasting: Selected Contributions from ITISE 2016, Editors Rojas, Ignacio and Pomares, Hector and Valenzuela, Olga, 2017, Springer.


99. M. Kirby and C. Peterson, (2017) Visualizing Data Sets on the Grassmannian Using Self-Organizing Mappings, World Self Organizing Mappings, Nancy, France, 6/2017.
 
98. T. Ghosh, X. Ma and M. Kirby, (2017).  A Sequential  Simplex Algorithm for Automatic Data and Center Selecting Radial Basis Functions, International Joint Conference on Neural Networks 5/17.

97. Lori Ziegelmeier, Michael Kirby, and Chris Peterson (2017), Sparse Local Linear Embeddings, Proceedings International Conference on Computational Science, Z"urich, Switzerland, 6/2017.

96. Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta, Rachel Neville, Chris Peterson, Patrick Shipman, Lori Ziegelmeier, (2017) Persistence Images: A Stable Vector Representation of Persistent Homology, Journal of Machine Learning Research 18, Number 8, 1-35, see also arXiv:1507.06217.2.

95. Chepushtanova, Sofya and Michael Kirby, (2017) Sparse Grassmannian Embeddings for Hyperspectral Data Representation and Classification, IEEE Geoscience and Remote Sensing Letters 14.3: 434-438.

94. Lori Ziegelmeier, Michael Kirby, and Chris Peterson (2017), Stratifying High Dimensional Data Based on Proximity to the Convex Hull Boundary, SIAM Review 59 (2), 346-365,  (preprint http://arxiv.org/abs/1611.01419).

93. Wang, Kun, Langevin, Stanley, O'Hern, Corey, Shattuck, Mark, Ogle, Serenity, Forero, Adriana, Morrison, Juliet, Slayden, Richard, Katze, Michael and Kirby, Michael  (2016),  Anomaly Detection in Host Signaling Pathways for the Early Prognosis of Acute Infection, PloS One, Vol. 11, No. 8., pp. e0160919.

92. Mmanu Chaturvedi, Tomojit Ghosh, Michael Kirby, Xiaoyu Liu, Xiaofeng Ma and Shannon Stiverson, (2016),  Explorations in Very Early Prognosis of the Human Immune Response to Influenza,  Proceedings ACM International Workshop on Big Data in Life Sciences, October, 2016.

91. T. Emerson, M. Kirby, C. Peterson, L. Scharf (2016), Reduced Dimension Estimators in Matched Subspace Detection, accepted 8th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Los Angeles, UCLA. (Won Best Paper Award.)

90. Chepushtanova, Sofya, Michael Kirby, Chris Peterson, and Lori Ziegelmeier (2016),  Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies. In Proceedings (Springer Lecture Notes in Computer Science) 6th International Workshop on Computational Topology in Image Context, pp. 228-239. Springer International Publishing.

89. T. Ghosh, M. Kirby, and X. Ma (2016), Sparse skew radial basis functions for time-series prediction, Proceedings International Work Conference on Time Series Analysis, pp. 296-307, Granada, Spain, June 2016.

88. I. Santamaria, L. L. Scharf,  C. Peterson, M. Kirby and, J. Francos (2016), An Order Fitting Rule for Optimal Subspace Averaging, 2016 IEEE Workshop on Statistical Signal Processing, Palma de Mallorca, Spain, June 2016.   

87. Marrinan, Timothy, J. Ross Beveridge, Bruce Draper, Michael Kirby, and Chris Peterson (2016),  Flag-based detection of weak gas signatures in long-wave infrared hyperspectral image sequences. In SPIE Defense+ Security, pp. 98401N-98401N. International Society for Optics and Photonics, 2016.

86. Sofya Chepushtanova, Michael Kirby, Chris Peterson and Lori Ziegelmeier (2015), An Application of Persistent Homology on Grassmann Manifolds for the Detection of Signals in Hyper-spectral Imagery, In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Milan, Italy.

85. K. Wang, J. Thompson, C. Peterson, and M. Kirby, (2015) Identity maps and their extensions on parameter spaces: Applications to anomaly detection in video, Proceedings Science and Information Conference, pp. 345-351, London, July 28-30, 2015.

84. Michael Kirby, (2015) An Embedding Algorithm Using Whitney’s Theorem, Mathematics Today, Vol. 51, No 3., pp 142-145.

83. Arta Jamshidi and Kirby, Michael, (2015) A Radial Basis Function Algorithm with Automatic Model Order Determination, SIAM Journal of Scientific Computation (SISC), Vol. 37., No.3, ppA1319-A1341.

82. Mai M, Wang K, Huber G, Kirby M, Shattuck MD, OHern CS (2015), Outcome Prediction in Mathematical Models of Immune Response to Infection. PLoS ONE 10(8): e0135861.

81. Julia R. Dupuis, Michael Kirby, and Bogdan R. Cosofret (2015), Longwave infrared compressive hyperspectral imager,

Proc. SPIE 9482, Next-Generation Spectroscopic Technologies VIII, 94820Z (June 3, 2015); doi:10.1117/12.2177893.


80. Daniel Bates and Davis, Brent and Kirby, Michael and Marks, Justin and Peterson, Chris (2015), The max-length-vector line of best fit to a set of vector subspaces and an optimization problem over a set of hyperellipsoids, Numerical Linear Algebra with Applications, Vol. 22 pp 453–464

79. Emerson, Tegan,  Kirby, Michael,  Bethel, Kelly,  Kolatkar, Anand,  Luttgen, Madelyn, OHara, Stephen,  Newton, Paul,  Kuhn, Peter, (2015), Fourier-Ring Descriptor to Characterize Rare Circulating Cells from Images Generated Using Immunofluorescence Microscopy,
Computerized Medical Imaging and Graphics, Vol. 40, pp 70–87.

78. T. Marrinan, R. Beveridge, B. Draper, M. Kirby and C. Peterson, (2015) Flag Manifolds for the Characterization of Geometric Structure in Large Data Sets, A. Abdulle et al. (eds.), Numerical Mathematics and Advanced Applications ENUMATH 2013, Lecture Notes in Computational Science and Engineering 103, Springer International Publishing. 457-464.

77. Kun Wang, V. Bhandari, J.S. Giuliano, C.S. O’Hern M. Shattuck, and Michael Kirby (2014), Angiopoietin-1, Angiopoietin-2 and Bicarbonate as Diagnostic Biomarkers in Children with Severe Sepsis, PloS one, Vol. 9, No. 9, pp. e108461, Public Library of Science.

76. Sofya Chepushtanova and Michael Kirby, (2014) Classification of Hyperspectral Imagery on Embedded Grassmannians, 6th Workshop on Hyper-spectral Image and Signal Processing: Evolution in Remote Sensing, June 2014, Lausanne, Switzerland WHISPERS 2014.

75. B. Draper, M. Kirby, T. Marrinan and C. Peterson, (2014) Finding the Subspace Mean or Median to Fit Your Needs, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1082-1089.

74. Sofya Chepushtanova, Chriss Gittins, and Michael Kirby, (2014) Band selection in hyperspectral imagery using sparse support vector machines, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XX, edited by Miguel Velez-Reyes, Fred A. Kruse, Proc. of SPIE Vol. 9088, 90881F.

73. Draper, B., Kirby, M., Marks, J., Marrinan, T., and Peterson, C. (2014) A flag representation for finite collections of subspaces of mixed dimensions. Linear Algebra and its Applications, 451, 15-32.

72. Stephen O’Hara, Kun Wang, Richard A Slayden, Alan R Schenkel, Greg Huber, Corey S O’Hern, Mark D Shattuck and Michael Kirby, (2013),  Iterative Feature Removal Yields Highly Discriminative Pathways, BMC Genomics 14:832, 2013.

71. Kun Wang, Vineet Bhandari, Sofya Chepustanova, Greg Huber, Stephen OHara, Corey S. OHern, Mark D. Shattuck, Michael Kirby Which Biomarkers Reveal Neonatal Sepsis? PLoS ONE 8(12): e82700. doi:10.1371/journal.pone.0082700, Dec 18, 2013.

70. Rutherford, Blake, Dangelmayr, Gerhard and Kirby, Michael, A time-dependent Lagrangian eyewall, Quarterly Journal of the Royal Meteorological Society, Vol. 138, No. 669, John Wiley & Sons, Ltd., pp 2009–2018, 2012.

69. J. Chang and C. Peterson and M. Kirby, Feature Patch Illumination Spaces and Karcher Compression for Face Recognition via Grassmannians, Advances in Pure Mathematics, Vol. 2, No. 4,226-242, 2012.

68. A. Jamshidi, M. Kirby and D. Broomhead, Geometric Manifold learning using dimension reduction and skew radial basis functions, IEEE Magazine on Signal Processing, Special Issue on Dimensionality Reduction via Subspace and Manifold Learning, Vol 28, No. 2, March 2011.

67. A. Jamshidi and M. Kirby, Modeling Multivariate Time-Series on Manifolds with Skew Radial Basis Functions, Neural Comput. 2011 Jan;23(1):97-123. Epub 2010 Oct 21, 2010.

66. D. Elliott, C.W. Anderson and M. Kirby (2010), Covariance Regularization for Supervised Learning in High Dimensions, Proceedings of ANNIE 2010.

65. B. Rutherford, G. Dangelmayr, J. Persing, M. Kirby, and M. T. Montgomery (2010), Lagrangian mixing in an axisymmetric hurricane model, Atmos. Chem. Phys, 10, 6777-6791.

64.  Josh Thompson, David W. Dreisigmeyer, Terry Jones, Michael Kirby, and Josh Ladd (2010), Accurate Fault Prediction of BlueGene/P RAS Logs Via Geometric Methods, Proceedings 1st Workshop on Fault-Tolerance for HPC at Extreme Scale (FTXS 2010) , Chicago, Illinois.

63. Yui Man Lui, J. Ross Beveridge and Michael Kirby (2010), Action Classfication on Product Manifolds, IEEE Conference on Computer Vision and Pattern Recognition.

62. A. Jamshidi and M. Kirby (2009), Skew-Radial Basis Function Expansions for Empirical Modeling, SIAM J. Sci. Comput. Volume 31, Issue 6, pp. 4715–4743.

61. Yui Man Lui, J. Ross Beveridge and Michael Kirby (2009), Canonical Stiefel Quotient and its Application to Illumination Spaces, IEEE International Conference on Biometrics: Theory, Applications and Systems. (received best paper award).

60. J.R. Beveridge, Bruce Draper, Jen-Mei Chang, Michael Kirby, Holger Kley and Chris Peterson (2009), Principal Angles Separate Subject Illumination Spaces in YDB and CMU-PIE, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 31, No. 2, pp 351-363.

59. A. Jamshidi and M. Kirby (2008), Skew-Radial Basis Functions for Modeling Edges and Jumps, Eighth International Conference on Mathematics in Signal Processing Conference Digest, The Royal Agricultural College, Cirencester, Institute for Mathematics and its Applications, December.

58. Yui Man Lui, J. Ross Beveridge, Bruce A. Draper and Michael Kirby (2008), Image-Set Matching using a Geodesic Distance and Cohort Normalization, IEEE International Conference on Automatic Face and Gesture Recognition, Amsterdam, The Netherlands.

57. Fatemeh Emdad, Michael Kirby, and Seyed A. Zekavat (2008), Feature Extraction via Kernelized Signal Fraction Analysis vs Kernelized Principal Component Analysis, in proceedings, World Comp Congress 08, Data Mining Symposium, Las Vegas.

56. Jen-Mei Chang, M. Kirby, H. Kley and C. Peterson, R. Beveridge, B. Draper, Recognition of Digital Images of the Human Face at Ultra Low Resolution via Illumination Spaces, Springer Lecture Notes in Computer Science, Vol. 4844, pg 733-743, (2007).

55. Jen-Mei Chang, Michael Kirby and Chris Peterson, Set-to-Set Face Recognition Under Variations in Pose and Illumination, 2007 Biometrics Symposium, Baltimore, MD, September, 2007.

54. A. Jamshidi and M. Kirby, Towards a Black Box Algorithm for Nonlinear Function Approximation over High-Dimensional Domains, SIAM Journal of Scientific Computing, Vol. 29, 941, May, 2007.

53. Jen-Mei Chang, Michael Kirby, Holger Kley, Chris Peterson, J.R. Beveridge and Bruce Draper, Examples of Set-to-Set Image Classification, In: Seventh International Conference on Mathematics in Signal Processing Conference Digest, The Royal Agricultural College, Cirencester, Institute for Mathematics and its Applications, December, 2006, pp. 102–105.

52. Yue Qiao, Larry Ernst and M. Kirby, Developing a Computational Radial Basis Function (RBF) Architecture for Nonlinear Scattered Color Data, Proceedings NIP22 International Conference on Digital Printing Technologies, Sept. 2006.

51. Anderson, Charles W., James N. Knight, Tim O’Connor, Michael J. Kirby, and Artem Sokolov. Geometric subspace methods and time-delay embedding for EEG artifact removal and classification. Neural Systems and Rehabilitation Engineering, IEEE Transactions on 14, no. 2 (2006): 142-146.

50. C. Anderson, M. Kirby, J.N. Knight, Classification of Time Embedded EEG Using Short Time Principal Component Analysis, (Book Chapter) In Towards Brain Computer Interfacing, edited by G. Dornhege, J. del R. Millan, T. Hinterberger, D.J. McFarland, and K.R. M¨uller, The MIT Press, 2006.

49. J.M. Chang, R. Beveridge, B. Draper, M. Kirby, H. Kley and C. Peterson, Illumination Face Spaces are Idiosyncratic, IPCV’06, Vol 2., 390-396, 2006, CSREA Press.

48. Anderson, C.W., Knight, J.N., O’Connor, T., Kirby, M.J., and Sokolov, A. (2006) Geomeric Subspace Methods and Time-Delay Embedding for EEG Artifact Removal and Classification, IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 14, no. 2, pp. 142–146, June 2006.

47. A. A. Jamshidi and M. J. Kirby, Examples of Compactly Supported Functions for Radial Basis Approximations, Proceedings of The 2006 International Conference on Machine learning; Models, Technologies and Applications, Editors H. R. Arabnia, E. Kozerenko and S. Shaumy, 155-160, 2006.

46. Anderson, C.W., Knight, J.N., Kirby, M.J. (2005) An Inexpensive Brain-Computer Interface Based on Spatial and Temporal Analysis of EEG. Proceedings of HCI International, (HCI-I) 2005, Las Vegas, NV, (CD-ROM).

45. David A. Peterson, James N. Knight, Michael J. Kirby, Charles W. Anderson and Michael H. Thaut, Feature selection and blind source separation in an EEG-based brain-computer interface, EURASIP Journal on Applied Signal Processing, vol. 2005, issue 19, pp. 3128-3140.

44. D. Broomhead and M. Kirby, Large Dimensionality Reduction using Secant-based Projection Methods: The Induced Dynamics in Projected Systems, Nonlinear Dynamics 41(1-3)  (August 2005), pp. 47-67.

43. M. Kirby, Nonlinear Signal Processing, Encyclopedia of Nonlinear Science, ed. Alwyn Scott. New York and London: Routledge, 2004.

42. A. Fox, M. Kirby, M. Montgomery, J. Persing, A Comparison of Optimal Low Dimensional Projections of a Hurricane Simulation. In: Dynamics and Bifurcation of Patterns in Dissipative Systems, G. Dangelmayr and I. Oprea (eds.), World Scientific Series on Nonlinear Science, Vol. 12, pages 292-308, World Scientific, Singapore, 2004
 
41. Fatemeh Emdad, Seyed A. Zekavat, Michael Kirby: Adaptive Antenna Beam Forming Via Maximum Noise Fraction for Multi Carrier CDMA Systems. International Conference on Wireless Networks 2003: 431-437.

40. Seyed A Zekavat, Fatemeh Emdad and Michael Kirby, A Merger of Maximum Noise Fraction Beam Forming and MC-CDMA Systems: Perturbation Analysis in Dispersive Channels, Proceedings IEEE 37th Asilomar conference on Signals, Systems and Computers, Nov. 9-12, 2003.

39. Charles Anderson and Michael Kirby, EEG Subspace Representation and Feature Selection for Brain Computer Interface, 1st IEEE Workshop on Computer Vision and Pattern Recognition for Human Computer Interaction (CVPRHCI), Madison, WI, June 17, 2003.

38. D. Hundley and M. Kirby, Estimation of Topological Dimension, Proceedings of the Third SIAM International Conference on Data Mining, D. Barbara and C. Kamath (editors), SIAM 2003, pgs. 194-202

37. Michael Kirby and Charles Anderson, Geometric Analysis for the Characterization of Nonstationary Time Series, in Perspectives and Problems in Nonlinear Science: A Celebratory Volume in Honor of Larry Sirovich, Editors: Ehud Kaplan, Jerrold E. Marsden, Katepalli R. Sreenivasan, March 2003.

36. Douglas R. Hundley, Michael J. Kirby, and Markus Anderle, Blind source separation using the maximum signal fraction approach, Douglas R. Hundley, Michael J. Kirby, and Markus Anderle, Signal Processing Volume 82, Issue 10, October 2002, Pages 1505-1508
 
35. M. Anderle, D. Hundley and M. Kirby, The Bilipschitz criterion for mapping design in data analysis, Intelligent Data Analysis, Volume 6, Number 1, 2002, pages 85–104.

34. M. Anderle and M. Kirby, An Application of the Maximum Noise Fraction Method to Filtering Noisy Time-Series, in Mathematics in Signal Processing V, Editors: J. G. McWhirter and I. K. Proudler, Oxford University Press, June 2002.

33. D. Hundley, M. Kirby and Markus Anderle, A Solution Procedure for Blind Signal Separation using the Maximum Noise Fraction Approach: Algorithms and Examples, Proceedings of the Conference on Independent Component Analysis, San Diego, CA, pages 337–342., December, 2001.

32. M. Anderle and M. Kirby, Correlation Feedback Resource Allocation RBF, Proceedings of the International Joint conference on neural Networks, vol 3., pages 1949-1953, 2001.

31. D.S. Broomhead and M. Kirby, The Whitney Reduction Network: a method for computing autoassociative graphs, Neural Computation 13:2595-2616, 2001.

30. M. Anderle, M. Kirby, and A. Todd. Identifying Structure in High-Dimensional Data Sets using Connectivity Matrices. SIAM Workshop on Mining Scientific Datasets. Chicago, pages 29-36. April 7, 2001.

29. A. Todd and M. Kirby. Data Visualization via Structured Voronoi Cell Refinement. SIAM Workshop on Mining Scientific Datasets. Chicago, pages 45-52. April 7, 2001.

28. D.S. Broomhead and M. Kirby, A New Approach for Dimensionality Reduction: Theory and Algorithms, SIAM J. of Applied Mathematics, vol. 60, no. 6, pp. 2114–2142, 2000.

27. M. Anderle and M. Kirby, Filtering Noisy Time Series: Keeping the Baby and Most of the Bathwater, Conference Digest, Fifth IMA International Conference on Mathematics in Signal Processing, Univeristy of Warwick, 200060. Shawn Martin, Michael Kirby and Rick Miranda, Symmetric Veronese Classifiers with Application to Materials Design, Engineering Applications of Artifical Intelligence, 13:513-520, 2000.

26. Shawn Martin, Michael Kirby and Rick Miranda, Symmetric Veronese Classifiers with Application to Materials Design, Engineering Applications of Artificial Intelligence, 13:513-520, 2000.

25. Shawn Martin, Michael Kirby and Rick Miranda, Kernel/Feature selection for support vector machines applied to materials design, In IFAC Symposium on Artificial Intelligence in Real Time Control AIRTC-2000, Budapest, Hungary, pp 29-34, Elsevier Science, 2000.

24. Empirical Dynamical System Reduction I: Global Nonlinear Transformations, (with R. Miranda), Editor K. Coughlin, In Semi-Analytic Methods for the Navier-Stokes Equations (Montreal, 1995), Vol.20, 41-64, CRM Proc. Lecture Notes, Amer. Math. Soc., Providence, RI. 1999

23. Empirical Dynamical System Reduction II:Neural Charts, (with D.Hundley and R.Miranda) Editor K. Coughlin, In Semi-Analytic Methods for the Navier-Stokes Equations (Montreal, 1995), Vol.20, 65-83, CRM Proc. Lecture Notes, Amer. Math. Soc., Providence, RI. 1999

22. Adaptive Clustering Based on Local Neighborhood Interactions, (with Markus Anderle), Proc. SPIE Vol. 3807, Advanced Signal Processing Algorithms,Architectures, and Implementations IX, Editor Franklin T. Luk, 1999

21. A New Optimal Basis for Image Representation, (with D. Dreisigmeyer), Proc. SPIE Vol. 3814,Mathematics of Data/Image Coding, Compression and Encryption II,Editor M. Schmalz, 1999

20. Time series prediction by estimating Markov probabilities through topology preserving maps, (with G. Dangelmayr and S.Gadaleta and D. Hundley), Proc. SPIE Vol. 3812, In:Applications and Science of Neural Networks, Fuzzy Systems,and Evolutionary Computation II, 86–93, Editors B. Bosacchi and D. B. Fogel and J.C. Bezdek, 1999.

19. M. Kirby 1998, Ill-Conditioning and Gradient Based Optimization of Multi-Layer Perceptrons, Eds. J.G. McWhirter and I.K. Proudler, Mathematics in Signal Processing IV, pp223-237, Oxford University Press, The Institute of Mathematics and Its Applications Conference Series: No. 67”,

18. M. Kirby and R. Miranda (1996), Circular Nodes in Neural Networks, Neural Computation, Vol. 8, No. 2, p. 390-402.

17. M. Kirby (1996), Optimal Empirical Transformations with Applications: A Summary, Conference Digest, Fourth International Conference on Mathematics in Signal Processing, 1996.

16. D. Hundley M. Kirby and R. Miranda (1995), Spherical Nodes in Neural Networks, Intelligent Engineering Through Artificial Neural Networks, Vol. 5, Eds. S.H. Dagli, B.R. Fernandez, J. Ghosh and R.T. Soundar Kumara.

15. M. Kirby and R. Miranda (1994), Nonlinear reduction of high-dimensional dynamical systems via neural networks, Phys. Rev. Letters, Vol. 72, No. 12, p. 1822.

14. M. Kirby and R. Miranda (1994), The Remodeling of Chaotic Dynamical Systems, Intelligent Engineering Through Artificial Neural Networks, Vol. 4, Eds. S.H. Dagli, B.R. Fernandez, J. Ghosh and R.T. Soundar Kumara.

13. E. Stone and M. Kirby (1993), Dependence of bifurcation structures on the approximation of O(2) symmetry in minimal ODEs, in Exploiting Symmetry in Applied and Numerical Analysis, Lectures in Applied Mathematics, Eds. E.L. Allgower, K. Georg and R. Miranda, Vol. 29, p. 389-404.

12. M. Kirby, F. Weisser and G. Dangelmayr (1993), Speaking with images: a model problem in the representation of digital image sequences, Pattern Recognition, 26 No. 1, 63.

11. M. Kirby and D. Armbruster (1992), Reconstructing phase-space from PDE simulations, Z. angew. Math. Phys., 43, 999.

10. G. Dangelmayr and M. Kirby (1992), On Diffusively Coupled Oscillators, Intl. Ser. of Num. Math., Vol. 104 p. 85-97.

9. M. Kirby (1992), Minimal dynamical systems from partial differential equations using Sobolev eigenfunctions, Physica D 57 p. 466-475.

8. M. Kirby (1992), Low-Dimensional Techniques for Processing Still and Moving Images, IEEE proceedings on Signal Processing, Asilomar 1026.

7. M. Kirby, F. Weisser and G. Dangelmayr (1991) , A problem in facial animation: analysis and synthesis of lip motion, Proc. of the 7th Scandinavian Conf. on Image Analysis, Aalborg, Denmark, ed: P. Johansen and S. Olsen p. 529.

6. M. Kirby, D. Armbruster and W. Guettinger (1991), An approach for the analysis of spatially localized oscillations, Bifurcations and Chaos: Analysis, Algorithms and Applications, Intl. Ser. of Num. Math., Vol. 97, ed: R. Seydel, F.W. Schneider, T. K¨upper, H. Troger, Birkh¨auser Verlag Basel p. 183.

5. M. Kirby, J.P. Boris and L. Sirovich (1990), An eigenfunction analysis of axisymmetric jet flow, J. of Computational Physics Vol. 90, No. 1 p. 98.

4. M. Kirby, J.P. Boris and L. Sirovich (1990), A proper orthogonal decomposition of a simulated supersonic shear layer, Intl. J. for Numerical Methods in Fluids Vol. 10, p. 411-428.

3. L. Sirovich, M. Kirby and M. Winter (1990), An eigenfunction approach to large-scale structures in transitional jet flow, Phys. Fluids A 2(2) p.127.

2. M. Kirby and L. Sirovich (1990), Application of the Karhunen-Lo`eve procedure for the characterization of human faces, IEEE trans. PAMI Vol. 12, No. 1 p. 103.

1. L. Sirovich and M. Kirby (1987), A low dimensional procedure for the characterization of human faces, J. of the Optical Society of America A, Vol. 4., p. 519.