40. References [1] H. Guo. Diffeomorphic point matching with applications in medical image analysis . PhD thesis, University of Florida, Gainesville, FL, 2005. Ph.D. Thesis. [2] J. Zhang. New information theoretic distance measures and algorithms for multimodality image registration . PhD thesis, University of Florida, Gainesville, FL, 2005. Ph.D. Thesis. [3] A. A. Kumthekar. Affine image registration using minimum spanning tree entropies. Master’s thesis, University of Florida, Gainesville, FL, 2004. M. S. Thesis. [4] A. Rajwade, A. Banerjee, and A. Rangarajan. A new method of probability density estimation with application to mutual information-based image registration. In IEEE Computer Vision and Pattern Recognition (CVPR) , volume 2, pages 1769–1776, 2006. [5] A. Peter and A. Rangarajan. A new closed form information metric for shape analysis. In Medical Image Computing and Computer Assisted Intervention (MICCAI part 1) , Springer LNCS 4190, pages 249–256. 2006. [6] A. S. Roy, A. Gopinath, and A. Rangarajan. Deformable density matching for 3D non-rigid registration of shapes. In Medical Image Computing and Computer Assisted Intervention (MICCAI part 1) , Springer LNCS 4791, pages 942–949. 2007. [7] F.Wang, B. Vemuri, and A. Rangarajan. Groupwise point pattern registration using a novel CDF-based Jensen Shannon divergence. In IEEE Computer Vision and Pattern Recognition (CVPR) , volume 1, pages 1283–1288, 2006. [8] L. Garcin, A. Rangarajan, and L. Younes. Non-rigid registration of shapes via diffeomorphic point matching and clustering. In IEEE Conf. on Image Processing , volume 5, pages 3299–3302, 2004. [9] F. Wang, B.C. Vemuri, A. Rangarajan, I.M. Schmalfuss, and S.J. Eisenschenk. Simultaneous nonrigid registration of multiple point sets and atlas construction. In European Conference on Computer Vision (ECCV) , pages 551–563, 2006. [10] H. Guo, A. Rangarajan, and S. Joshi. 3D diffeomorphic shape registration on hippocampal datasets. In James S. Duncan and Guido Gerig, editors, Medical Image Computing and Computer Assisted Intervention (MICCAI) , pages 984–991. 2005.
41. References [11] A. Rangarajan, J. Coughlan, and A. L. Yuille. A Bayesian network framework for relational shape matching. In IEEE Intl. Conf. Computer Vision (ICCV) , volume 1, pages 671–678, 2003. [12] J. Zhang and A. Rangarajan. Multimodality image registration using an extensible information metric and high dimensional histogramming. In Information Processing in Medical Imaging , pages 725–737, 2005. [13] J. Zhang and A. Rangarajan. Affine image registration using a new information metric. In IEEE Computer Vision and Pattern Recognition (CVPR) , volume 1, pages 848–855, 2004. [14] J. Zhang and A. Rangarajan. A unified feature based registration method for multimodality images. In IEEE International Symposium on Biomedical Imaging (ISBI) , pages 724–727, 2004. [15] A. Peter and A. Rangarajan. Shape matching using the Fisher-Rao Riemannian metric: Unifying shape representation and deformation. In IEEE International Symposium on Biomedical Imaging (ISBI) , pages 1164–1167, 2006. [16] A. Rajwade, A. Banerjee, and A. Rangarajan. Continuous image representations avoid the histogram binning problem in mutual information-based registration. In IEEE International Symposium on Biomedical Imaging (ISBI) , pages 840–844, 2006. [17] H. Guo, A. Rangarajan, S. Joshi, and L. Younes. A new joint clustering and diffeomorphism estimation algorithm for non-rigid shape matching. In Chandra Khambametteu, editor, IEEE CVPR Workshop on Articulated and Non-rigid motion (ANM) , pages 16–22. 2004. [18] H. Guo, A. Rangarajan, S. Joshi, and L. Younes. Non-rigid registration of shapes via diffeomorphic point matching. In IEEE Intl. Symposium on Biomedical Imaging (ISBI) , volume 1, pages 924–927, 2004. [19] H. Guo, A. Rangarajan, and S. Joshi. Diffeomorphic point matching. In N. Paragios, Y. Chen, and O. Faugeras, editors, The Handbook of Mathematical Models in Computer Vision , pages 205–220. 2005. [20] A. Peter and A. Rangarajan. Maximum likelihood wavelet density estimation with applications to image and shape matching. IEEE Trans. Image Processing , 2007. (accepted subject to minor revision).
42. References [21] F. Wang, B.C. Vemuri, A. Rangarajan, and S.J. Eisenschenk. Simultaneous nonrigid registration of multiple point sets and atlas construction. IEEE Trans. Pattern Analysis and Machine Intelligence , 2007. (in press). [22] A. Peter and A. Rangarajan. Information geometry for landmark shape analysis: Unifying shape representation and deformation. IEEE Trans. Pattern Analysis and Machine Intelligence , 2007. (revised and resubmitted). [23] A. Rajwade, A. Banerjee, and A. Rangarajan. Probability density estimation using isocontours and isosurfaces: Applications to information theoretic image registration. IEEE Trans. Pattern Analysis and Machine Intelligence , 2007. (under revision). [24] A. Peter and A. Rangarajan. Shape L’Ane Rouge: Sliding wavelets for indexing and retrieval. In IEEE Computer Vision and Pattern Recognition (CVPR) , 2008. (submitted). [25] A. Rajwade, A. Banerjee, and A. Rangarajan. Newimage-based density estimators for 3D intermodality image registration. In IEEE Computer Vision and Pattern Recognition (CVPR) , 2008. (submitted). [26] A. Rangarajan and H. Chui. Applications of optimizing neural networks in medical image registration. In Artificial Neural Networks in Medicine and Biology (ANNIMAB) , Perspectives in neural computing, pages 99–104. Springer, 2000. [27] A. Rangarajan and H. Chui. A mixed variable optimization approach to non-rigid image registration. In Discrete Mathematical Problems with Medical Applications , volume 55 of DIMACS series in Discrete Mathematics and Computer Science , pages 105–123. American Mathematical Society, 2000. [28] H. Chui and A. Rangarajan. A new algorithm for non-rigid point matching. In Proceedings of IEEE Conf. on Computer Vision and Pattern Recognition–CVPR 2000 , volume 2, pages 44–51. IEEE Press, 2000. [29] H. Chui and A. Rangarajan. A feature registration framework using mixture models. In IEEEWorkshop on Mathematical Methods in Biomedical Image Analysis (MMBIA) , pages 190–197. IEEE Press, 2000. [30] H. Chui, L. Win, J. Duncan, R. Schultz, and A. Rangarajan. A unified feature registration method for brain mapping. In Information Processing in Medical Imaging (IPMI) , pages 300–314. Springer, 2001
43. References [ [31] A. Rangarajan. Learning matrix space image representations. In Energy Minimization Methods for Computer Vision and Pattern Recognition (EMMCVPR) , Lecture Notes in Computer Science, LNCS 2134, pages 153–168. Springer, New York, 2001. [32] A. Rangarajan, H. Chui, and E.Mjolsness. A relationship between spline-based deformable models and weighted graphs in non-rigid matching. In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR) , pages I:897–904. IEEE Press, 2001. [33] H. Chui and A. Rangarajan. Learning an atlas from unlabeled point-sets. In IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA) , pages 58–65. IEEE Press, 2001. [34] H. Chui and A. Rangarajan. A new joint point clustering and matching algorithm for estimating nonrigid deformations. In Intl. Conf. on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS) , pages I:309–315. CSREA Press, 2002. [35] A. Rangarajan and A. L. Yuille. MIME: Mutual information minimization and entropy maximization for Bayesian belief propagation. In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14 , pages 873–880, Cambridge, MA, 2002. MIT Press. [36] A. L. Yuille and A. Rangarajan. The Concave Convex procedure (CCCP). In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14 , pages 1033–1040, Cambridge, MA, 2002. MIT Press. [37] H. Chui, L. Win, J. Duncan, R. Schultz, and A. Rangarajan. A unified non-rigid feature registration method for brain mapping. Medical Image Analysis , 7(2):113–130, 2003. [38] H. Chui and A. Rangarajan. A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding , 89(2-3):114–141, 2003. [39] A. L. Yuille and A. Rangarajan. The Concave-Convex procedure (CCCP). Neural Computation , 15:915–936, 2003. [40] H. Chui, A. Rangarajan, J. Zhang, and C.M. Leonard. Unsupervised learning of an atlas from unlabeled point-sets. IEEE Trans. Pattern Analysis and Machine Intelligence , 26(2):160–172, 2004. [41] P. Gardenfors. Conceptual spaces: The geometry of thought . MIT Press, 2000. [42] J. C. Platt, N. Cristianini, and J. Shawe-Taylor. Large margin DAGs for multiclass classification. In Advances in Neural Information Processing Systems (NIPS) , volume 12, pages 547–553. MIT Press, 2000.
44. References [43] Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines, theory, and application to the classification of microarray data and satellite radiance data. Journal of the American Statistical Association , 99:67–81, 2004. [44] C.-W. Hsu and C.-J. Lin. A comparison of methods for multiclass support vector machines. IEEE Trans. Neural Networks , 13(2):415–425, 2002. [45] T. Kolb. Music theory for guitarists: Everything you ever wanted to know but were afraid to ask . Hal Leonard, 2005. [46] K. Fukunaga. Introduction to Statistical Pattern Recognition . Academic Press (second edition), 1990. [47] S. Mika, G. Ratsch, and K.-R. Muller. A mathematical programming approach to the kernel fisher algorithm. In T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Advances in Neural Information Processing Systems 13 , pages 591–597. MIT Press, 2001. [48] D. Widdows. Geometry and Meaning . Center for the Study of Language and Information, 2004. [49] T. Jebara. Machine Learning: Discriminative and Generative . Kluwer Academic Publishers, 2003. [50] V. Vapnik. Statistical Learning Theory . Wiley Interscience, 1998. [51] B. Scholkopf, A. Smola, R. C. Williamson, and P. L. Bartlett. New support vector algorithms. Neural Computation , 12(5):1207–1245, 2000. [52] M. E. Tipping. Sparse Bayesian learning and the relevance vector machine. Journal of Machine Learning Research , 1:211–244, 2001. [53] U. Kressel. Pairwise classification and support vector machines. In Advances in Kernel Methods - Support Vector Learning , pages 255–268. MIT Press, 1999. [54] C. M. Bishop. Pattern recognition and machine learning . Springer, 2006. [55] J. Weston and C. Watkins. Multi-class support vector machines. Technical Report CSD-TR-98-04, Department of Computer Science, Royal Holloway, University of London, 1998. [56] E. L. Allwein, R. E. Schapire, and Y. Singer. Reducing multiclass to binary: a unifying approach for margin classifiers. Journal of Machine Learning Research , 1:113–141, 2001. [57] J. C. Platt. Fast training of support vector machines using sequential minimal optimization. In Advances in Kernel Methods - Support Vector Learning , pages 185–208. MIT Press, 1999.
45. References [58] L. Kaufman. Solving the quadratic programming problem arising in support vector classification. In B. Schölkopf, C. Burges, and A. Smola, editors, Advances in Kernel Methods - Support Vector Learning , pages 147–168. MIT Press, 1999. [59] O. L. Mangasarian and D. R. Musicant. Lagrangian support vector machines. Journal of Machine Learning Research , 1(3):161–177, 2001. [60] G. M. Fung and O. L. Mangasarian. A feature selection Newton method for support vector machine classification. Computational Optimization and Applications , 28:185–2002, 2004. [61] T. Joachims. Making large-scale SVM learning practical. In B. Schölkopf, C. Burges, and A. Smola, editors, Advances in Kernel Methods - Support Vector Learning , pages 169–184. MIT Press, 1999. [62] K. Crammer and Y. Singer. On the algorithmic implementation of multiclass kernel-based vector machine. Journal of Machine Learning Research , 2(2):265–292, Springer 2002. [63] J. A. K. Suykens and J. Vandewalle. Multiclass least squares support vector machines. In International Joint Conference on Neural Networks , volume 2, pages 900–903, 1999. [64] T. Joachims. Training linear SVMs in linear time. In Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining , volume 12, pages 217–226, 2006. [65] G. B. Huang, M. Ramesh, T. Berg, and E. Learned-Miller. Labeled faces in the wild: A database for studying face recognition in unconstrained environments. Technical Report 07-49, University of Massachusetts, Amherst, October 2007. Available at http://vis-www.cs.umass.edu/lfw . [66] P. Viola and M. Jones. Rapid object detection using a boosted cascade of simple features. In IEEE Computer Vision and Pattern Recognition (CVPR) , volume 1, pages 511–518, 2001. [67] G. Wahba. Spline models for observational data . SIAM, Philadelphia, PA, 1990. [68] F. L. Bookstein. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans. Patt. Anal. Mach. Intell. , 11(6):567–585, June 1989. [69] S. Ramaswamy, P. Tamayo, R. Rifkin, S. Mukherjee, C.-H. Yeang, M. Angelo, C. Ladd, M. Reich, E. Latulippe, J. P. Mesirov, T. Poggio, W. Gerald, M. Lodadagger, E. S. Lander, and T. R. Golub. Multiclass cancer diagnosis using tumor gene expression signatures. Proceedings of the National Academy of Sciences (PNAS) , 98(26):15149–15154, 2001.
46. References [70] D. Lowe. Object recognition from local scale-invariant features. In IEEE International Conference on Computer Vision (ICCV) , volume 2, pages 1150–1157, 1999. [71] M. E. Tipping and C. M. Bishop. Mixtures of probabilistic principal component analyzers. Neural Computation , 11(2):443–482, 1999. [72] M. A. O. Vasilescu and D. Terzopoulos. Multilinear Image Analysis for Facial Recognition. In ICPR (2) , pages 511–514, 2002. [73] X. He, D. Cai, H. Liu, and J. Han. Image clustering with tensor representation. In Zhang H., Chua T., Steinmetz R., Kankanhalli M. S., and Wilcox L., editors, ACM Multimedia , pages 132–140. ACM, 2005. [74] J. B. MacQueen. Some Methods for classification and Analysis of Multivariate Observations. In Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability , volume 1, pages 281–297. University of California Press, 1967. [75] D. Titterington, A. Smith, and U. Makov. Statistical Analysis of Finite Mixture Distributions . John Wiley & Sons, 1985. [76] J. Pearl. Probabilistic Reasoning in Intelligent Systems : Networks of Plausible Inference . Morgan Kaufmann, September 1988. [77] X. He, D. Cai, and P. Niyogi. Tensor Subspace Analysis. InWeiss Y., Schölkopf B., and Platt J., editors, Advances in Neural Information Processing Systems 18 , pages 499–506. MIT Press, Cambridge, MA, 2006. [78] R. J. Hathaway. Another interpretation of the EM algorithm for mixture distributions. Statistics and Probability Letters , 4:53–56, 1986. [79] R. M. Neal and G. E. Hinton. A view of the EM algorithm that justifies incremental, sparse, and other variants. In Jordan M. I., editor, Learning in Graphical Models , pages 355–370. Kluwer, 1998. [80] A. L. Yuille and J. J. Kosowsky. Statistical physics algorithms that converge. Neural Computation , 6(3):341–356, May 1994. [81] A. L. Yuille, P. Stolorz, and J. Utans. Statistical physics, mixtures of distributions, and the EM algorithm. Neural Computation , 6(2):334–340, March 1994.
47. References [82] B. Leibe and B. Schiele. Analyzing appearance and contour based methods for object categorization. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , volume 2, pages 409–415, Madison, WI, June 2003. [83] G. Griffin, A. Holub, and P. Perona. CalTech 256 object category dataset. Technical Report CNS-TR- 2007-001, Calif. Inst. of Tech., 2007.
Hinweis der Redaktion
Mapping in such a way that the system has reasonable learning and generalization properties; Training and test set errors are low. Regardless of what features are extracted.
Instead of getting musical time samples containing just a single note. For example, to represent the fact that we have patterns belonging to basic categories {C,D, etc.} and patterns corresponding to compound categories such as certain tritones (highly dissonant intervals in a scale), chords etc. Tritone is not represented in the set of labels. Unstable since it could potentially lead to an exponentially large label space. If the set of labels is truncated because of exponential size considerations, then the intolerance to ambiguity returns in the form of un-represented intervals and chords.
Rather than conceive of categories as nominal labels. Returning to our music sequence classification example. To achieve this, we would have to first map the raw musical sequences to the 12 dimensional vector space and then (if a support vector machine approach is used), maximize the margin of the mapped vectors in the category space.
Attempt at taking categories or labels and building a vector space out of them with one intriguing exception: the multiple class Fisher linear discriminant (MCFLD)
Actually, these are merely hypercone-like since cutting them with a hyperplane need not necessarily be hyperspheres. However, we will continue to call the decision boundaries hypercones for the sake of simplicity. The extension to the case of compound categories is straightforward with the hypercone surrounding the axis of the compound category vector.
After we have learned a mapping from the original feature space to the category vector space If there are compound categories, such as intervals and chords in the music sequence example and mixed races in the race classification example, and we have expert information regarding the compound categories, then these patterns can be directly represented in the category space and if necessary, we can maximize the compound category margin as well as the margins for the basic categories.
Zi is unknown. For a compound category—say a chord, it does not have to be a category basis vector. Since the mapped patterns zi are unknown, this immediately suggests that the classification and regression problems are linked Given a set of patterns xi and their counterpart mapped patterns zi we can fit a regression function. Given a set of mapped patterns zi and their associated label vectors y (which will not all be unique), we can maximize their margins and learn a classification. These problems are coupled Consequently, we combine problems one and two above into an integrated classification and regression objective function.
Illustration of SVM regression, showing the regression curve. Also shown are examples of the slack variables. Illustration of the slack variables >=0. Data points with circles around them are support vectors Standard L1 norm-based SVR objective function
The principal advantage in adopting the SVR formulation is that it can be well integrated with the SVM multi-category objective function