Abstract
Information theoretic learning (ITL) was initiated in the late 1990s at CNEL [126]. It uses descriptors from information theory (entropy and divergences) estimated directly from the data to substitute the conventional statistical descriptors of variance and covariance. It can be used in the adaptation of linear or nonlinear filters and also in unsupervised and supervised machine learning applications. In this chapter, we introduce two commonly used differential entropies for data understanding and information theoretic measures (ITMs) for evaluations in abstaining classifications.
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References
Ahna, J., Oha, J., Choib, S.: Learning principal directions: Integrated-squared-error minimization. Neurocomputing 70, 1372–1381 (2007)
Belhumeur, P.N., Hespanha, J., Kriegman, D.J.: Eigenfaces vs. fisherfaces: Recognition using class specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(7), 711–720 (1997)
Belkin, M., Niyogi, P., Sindhwani, V.: Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. Journal of Machine Learning Research pp. 2399–2434 (2006)
Boyd, S., Vandenberghe, L.: Convex optimization. Cambridge University Press (2004)
Cai, D., He, X., Han, J.: Spectral regression for efficient regularized subspace learning. In: International Conference on Computer Vision, pp. 1–7 (2007)
Chartrand, R.: Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Processing Letters 14(10), 707–710 (2007)
Combettes, P.L., Pesquet, J.C.: Proximal thresholding algorithm for minimization over orthonormal bases. SIAM Journal on Optimization 18(4), 1531–1376 (2007)
Cover, T.M., Thomas, J.A.: Elements of information theory, 2nd edition. NewYork: John Wiley (2005)
Donoho, D.L.: Compressed sensing. IEEE Transactions on Information Theory 52(4), 1289–1306 (2006)
Feng, Y., Huang, X., Shi, L., Yang, Y., Suykens, J.A.K.: Learning with the maximum correntropy criterion induced losses for regression. Tech. rep., K.U.Leuven (Leuven, Belgium) (2013)
Fornasier, M.: Theoretical foundations and numerical methods for sparse recovery. Radon Series on Computational and Applied Mathematics 9, 1–121 (2010)
Guyon, I., Elissee, A.: An introduction to variable and feature selection. Journal of Machine Learning Research 3, 1157–1182 (2003)
He, R., Ao, M., Xiang, S., Li, S.: nearest feature line: a tangent approximation. In: Chinese Conference on Pattern Recognition (2008)
He, R., Hu, B.G., Yuan, X., Zheng, W.S.: Principal component analysis based on nonparametric maximum entropy. Neurocomputing 73, 1840–1952 (2010)
He, R., Hu, B.G., Zheng, W.S., Guo, Y.Q.: Two-stage sparse representation for robust recognition on large-scale database. In: AAAI Conference on Artificial Intelligence, pp. 475–480 (2010)
Hellier, P., Barillot, C., Memin, E., Perez, P.: An energy-based framework for dense 3D registration of volumetric brain images. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2000)
Hou, L., He, R.: Minimum entropy linear embedding based on gaussian mixture model. In: Asian Conference on Pattern Recognition, pp. 362–366 (2011)
Hu, B.G., He, R., Yuan, X.: Information-theoretic measures for objective evaluation of classifications. Acta Automatica Sinica 38(7), 1169–1182 (2012)
Hu, B.G., Wang, Y.: Evaluation criteria based on mutual information for classifications including rejected class. Acta Automatica Sinica 34, 1396–1403 (2008)
Huber, P.: Robust statistics. Wiley (1981)
Hyvarinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks 10, 626–634 (1999)
Hyvärinen, A.: Survey on independent component analysis. Neural Computing Surveys 2, 94–128 (1999)
Idier, J.: Convex half-quadratic criteria and interacting auxiliary variables for image restoration. IEEE Transactions on Image Processing 10(7), 1001–1009 (2001)
Jeonga, K.H., Liu, W.F., Han, S., Hasanbelliu, E., Principe, J.C.: The correntropy mace filter. Pattern Recognition 42(5), 871–885 (2009)
Laaksonen, J.: Local subspace classifier. In: International Conference on Artificial Neural Networks (1997)
Li, S.Z.: Face recognition based on nearest linear combinations. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 839–844 (1998)
Luenberger, D.: Optimization by vector space methods. Wiley (1969)
Mairal, J., Elad, M., Sapiro, G.: Sparse representation for color image restoration. IEEE Transactions on Image Processing 17(1), 53–69 (2008)
Mazeta, V., Carteretb, C., Briea, D., Idierc, J., Humbert, B.: Background removal from spectra by designing and minimising a non-quadratic cost function. Chemometrics and Intelligent Laboratory Systems 76(2), 121–133 (2005)
Nishii, R., Tanaka, S.: Accuracy and inaccuracy assessments in land-cover classification. IEEE Transactions Geoscience and Remote Sensing 37, 491–498 (1999)
Niu, G., Jitkrittum, W., Dai, B., Hachiya, H., Sugiyama, M.: Squared-loss mutual information regularization: A novel information-theoretic approach to semi-supervised learning. In: International Conference on Machine Learning (2013)
Pearson, K.: On lines and planes of closest fit to systems of points in space. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, Sixth Series 2, 559–572 (1901)
Plumbley, M.: Recovery of sparse representations by polytope faces pursuit. In: Proceedings of International Conference on Independent Component Analysis and Blind Source Separation, pp. 206–213 (2006)
Principe, J.C., Xu, D., Fisher, J.W.: Information-theoretic learning. In: S. Haykin, editor, Unsupervised Adaptive Filtering, Volume 1: Blind-Source Separation. Wiley (2000)
Rao, S., Liu, W., Principe, J.C., de Medeiros Martins, A.: Information theoretic mean shift algorithm. In: Machine Learning for Signal Processing (2006)
Renyi, A.: On measures of entropy and information. Selected Papers of Alfred Renyi 2, 565–580 (1976)
Roullot, E., Herment, A., Bloch, I., de Cesare, A., Nikolova, M., Mousseaux, E.: Modeling anisotropic undersampling of magnetic resonance angiographies and reconstruction of a high-resolution isotropic volume using half-quadratic regularization techniques. Signal Processing 84(4), 743–762 (2004)
Rousseeuw, P.J.: Least median of squares regression. Journal of the American Statistical Association 79(388), 871–880 (1984)
Shannon, C.: A mathematical theory of communication. Bell System Technical Journal 27, 623–653 (1948)
Shi, Y., Sha, F.: Information-theoretical learning of discriminative clusters for unsupervised domain adaptation. In: International Conference on Machine Learning (2012)
Siegel, A.F.: Robust regression using repeated medians. Biometrika 69(1), 242–244 (1982)
Vincent, P., Bengio, Y.: K-local hyperplane and convex distance nearest neighbor algorithms. In: Advances in Neural Information Processing Systems, vol. 14, pp. 985–992 (2001)
Vinh, N.X., Epps, J., Bailey, J.: Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research 11, 2837–2854 (2010)
Yang, S., Zha, H., Zhou, S., Hu, B.G.: Variational graph embedding for globally and locally consistent feature extraction. In: Europe Conference on Machine Learning (ECML), pp. 538–553 (2009)
Zhang, T.: Multi-stage convex relaxation for learning with sparse regularization. In: Proceedings of Neural Information Processing Systems, pp. 16–21 (2008)
Zhang, Z.: Parameter estimation techniques: A tutorial with application to conic fitting. Image and Vision Computing 15(1), 59–76 (1997)
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He, R., Hu, B., Yuan, X., Wang, L. (2014). Information Measures. In: Robust Recognition via Information Theoretic Learning. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-07416-0_3
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DOI: https://doi.org/10.1007/978-3-319-07416-0_3
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