Learning in indefinite proximity spaces - recent trends

Efficient learning of a data analysis task strongly depends on the data representation. Many methods rely on symmetric similarity or dissimilarity representations by means of metric inner products or distances, providing easy access to powerful mathematical formalisms like kernel approaches. Similarities and dissimilarities are however often naturally obtained by non-metric proximity measures which can not easily be handled by classical learning algorithms. Major efforts have been undertaken to provide approaches which can either directly be used for such data or to make standard methods available for these type of data. We provide an overview about recent achievements in the field of learning with indefinite proximities.

[1]  Jing Yang,et al.  A Novel Indefinite Kernel Dimensionality Reduction Algorithm: Weighted Generalized Indefinite Kernel Discriminant Analysis , 2013, Neural Processing Letters.

[2]  Thomas Gärtner,et al.  Kernels and Distances for Structured Data , 2004, Machine Learning.

[3]  Craig K. Abbey,et al.  Objective Assessment of Sonographic: Quality II Acquisition Information Spectrum , 2013, IEEE Transactions on Medical Imaging.

[4]  Prateek Jain,et al.  Supervised Learning with Similarity Functions , 2012, NIPS.

[5]  F. Meer.  The effectiveness of spectral similarity measures for the analysis of hyperspectral imagery , 2006 .

[6]  Shiyong Cui,et al.  Building Change Detection Based on Satellite Stereo Imagery and Digital Surface Models , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Maya R. Gupta,et al.  Similarity-based Classification: Concepts and Algorithms , 2009, J. Mach. Learn. Res..

[8]  E.E. Pissaloux,et al.  Image Processing , 1994, Proceedings. Second Euromicro Workshop on Parallel and Distributed Processing.

[9]  Anil K. Jain,et al.  A modified Hausdorff distance for object matching , 1994, Proceedings of 12th International Conference on Pattern Recognition.

[10]  Aleksandar Poleksic,et al.  Optimal Pairwise Alignment of Fixed protein Structures in Subquadratic Time , 2011, J. Bioinform. Comput. Biol..

[11]  Ulrike Hahn,et al.  Similarity-based asymmetries in perceptual matching. , 2012, Acta psychologica.

[12]  Haibin Ling,et al.  Using the inner-distance for classification of articulated shapes , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[13]  Alexander J. Smola,et al.  Learning with non-positive kernels , 2004, ICML.

[14]  Stéphane Canu,et al.  Non positive SVM , 2010 .

[15]  Paul M. B. Vitányi,et al.  Clustering by compression , 2003, IEEE Transactions on Information Theory.

[16]  Elena Deza,et al.  Encyclopedia of Distances , 2014 .

[17]  Vladimir Cherkassky,et al.  The Nature Of Statistical Learning Theory , 1997, IEEE Trans. Neural Networks.

[18]  R. Duin,et al.  The dissimilarity representation for pattern recognition , a tutorial , 2009 .

[19]  Liwei Wang,et al.  Theory and Algorithm for Learning with Dissimilarity Functions , 2009, Neural Computation.

[20]  Gaëlle Loosli.  Study on the loss of information caused by the "positivation" of graph kernels for 3D shapes , 2016, ESANN.

[21]  Bernard Haasdonk,et al.  Feature space interpretation of SVMs with indefinite kernels , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Peter Tiño,et al.  Incremental probabilistic classification vector machine with linear costs , 2015, 2015 International Joint Conference on Neural Networks (IJCNN).

[23]  Horst Bunke,et al.  On Not Making Dissimilarities Euclidean , 2004, SSPR/SPR.

[24]  Peter Tiño,et al.  Indefinite Proximity Learning: A Review , 2015, Neural Computation.

[25]  Bernard Haasdonk,et al.  Tangent distance kernels for support vector machines , 2002, Object recognition supported by user interaction for service robots.

[26]  S. Chiba,et al.  Dynamic programming algorithm optimization for spoken word recognition , 1978 .

[27]  Andrzej Cichocki,et al.  Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities , 2010, Entropy.

[28]  James T. Kwok,et al.  Making Large-Scale Nyström Approximation Possible , 2010, ICML.

[29]  Cheng Soon Ong,et al.  Learning SVM in Kreĭn Spaces , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  Edwin R. Hancock,et al.  Determining the Cause of Negative Dissimilarity Eigenvalues , 2011, CAIP.

[31]  Frank-Michael Schleif,et al.  Metric and non-metric proximity transformations at linear costs , 2014, Neurocomputing.

[32]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[33]  Barbara Hammer,et al.  Discriminative dimensionality reduction in kernel space , 2016, ESANN.

[34]  Giorgio Gnecco,et al.  Approximation and Estimation Bounds for Subsets of Reproducing Kernel Kreǐn Spaces , 2013, Neural Processing Letters.

[35]  Stefanos Zafeiriou.  Subspace Learning in Krein Spaces: Complete Kernel Fisher Discriminant Analysis with Indefinite Kernels , 2012, ECCV.

[36]  Thomas Villmann,et al.  Divergence-based classification in learning vector quantization , 2011, Neurocomputing.

[37]  Maria-Florina Balcan,et al.  A theory of learning with similarity functions , 2008, Machine Learning.

[38]  Lev Goldfarb,et al.  A unified approach to pattern recognition , 1984, Pattern Recognit..

[39]  Huanhuan Chen,et al.  Probabilistic Classification Vector Machines , 2009, IEEE Transactions on Neural Networks.

[40]  Peter Tiño,et al.  Large Scale Indefinite Kernel Fisher Discriminant , 2015, SIMBAD.

[41]  Hsuan-Tien Lin.  A Study on Sigmoid Kernels for SVM and the Training of non-PSD Kernels by SMO-type Methods , 2005 .

[42]  T. Kinsman,et al.  Color is not a metric space implications for pattern recognition, machine learning, and computer vision , 2012, 2012 Western New York Image Processing Workshop.

[43]  Stefanos Zafeiriou,et al.  Incremental Slow Feature Analysis with Indefinite Kernel for Online Temporal Video Segmentation , 2012, ACCV.

[44]  Robert P. W. Duin,et al.  Non-Euclidean Dissimilarities: Causes and Informativeness , 2010, SSPR/SPR.

[45]  Alexandre d'Aspremont,et al.  Support vector machine classification with indefinite kernels , 2007, Math. Program. Comput..

[46]  Dan Gusfield,et al.  Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology , 1997 .

[47]  Horst Bunke,et al.  Edit distance-based kernel functions for structural pattern classification , 2006, Pattern Recognit..

[48]  Thomas Villmann,et al.  Adaptive dissimilarity weighting for prototype-based classification optimizing mixtures of dissimilarities , 2016, ESANN.

[49]  Yuhong Guo,et al.  Learning SVM Classifiers with Indefinite Kernels , 2012, AAAI.

[50]  Panu Somervuo,et al.  How to make large self-organizing maps for nonvectorial data , 2002, Neural Networks.

[51]  Frank-Michael Schleif,et al.  Data Analysis of (Non-)Metric Proximities at Linear Costs , 2013, SIMBAD.

[52]  Huanhuan Chen,et al.  Efficient Probabilistic Classification Vector Machine With Incremental Basis Function Selection , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[53]  M S Waterman,et al.  Identification of common molecular subsequences. , 1981, Journal of molecular biology.