Non-Euclidean Dissimilarities: Causes, Embedding and Informativeness

In many pattern recognition applications, object structure is essential for the discrimination purpose. In such cases, researchers often use recognition schemes based on template matching which lead to the design of non-Euclidean dissimilarity measures. A vector space derived from the embedding of the dissimilarities is desirable in order to use general classifiers. An isometric embedding of the symmetric non-Euclidean dissimilarities results in a pseudo-Euclidean space. More and better tools are available for the Euclidean spaces but they are not fully consistent with the given dissimilarities.

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

[2]  Andrew P. Bradley,et al.  Nearest neighbour group-based classification , 2010, Pattern Recognit..

[3]  Klaus Obermayer,et al.  Classi cation on Pairwise Proximity , 2007 .

[4]  Claus Bahlmann,et al.  The writer independent online handwriting recognition system frog on hand and cluster generative statistical dynamic time warping , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Robert P. W. Duin,et al.  On refining dissimilarity matrices for an improved NN learning , 2008, 2008 19th International Conference on Pattern Recognition.

[6]  Thorsten Joachims,et al.  A Probabilistic Analysis of the Rocchio Algorithm with TFIDF for Text Categorization , 1997, ICML.

[7]  Gabriela Andreu,et al.  Selecting the toroidal self-organizing feature maps (TSOFM) best organized to object recognition , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[8]  Robert P. W. Duin,et al.  Dissimilarity representations allow for building good classifiers , 2002, Pattern Recognit. Lett..

[9]  Wan-Jui Lee,et al.  On Euclidean Corrections for Non-Euclidean Dissimilarities , 2008, SSPR/SPR.

[10]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[11]  Robert P. W. Duin,et al.  Feature-Based Dissimilarity Space Classification , 2010, ICPR Contests.

[12]  Anil K. Jain,et al.  Representation and Recognition of Handwritten Digits Using Deformable Templates , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Arnold W. M. Smeulders,et al.  The Distribution Family of Similarity Distances , 2007, NIPS.

[14]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[15]  J. Gower,et al.  Metric and Euclidean properties of dissimilarity coefficients , 1986 .

[16]  Elzbieta Pekalska,et al.  Kernel Discriminant Analysis for Positive Definite and Indefinite Kernels , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Nicu Sebe,et al.  Toward Improved Ranking Metrics , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[19]  Robert P. W. Duin,et al.  Non-Euclidean Problems in Pattern Recognition Related to Human Expert Knowledge , 2010, ICEIS.

[20]  Horst Bunke,et al.  Syntactic and structural pattern recognition : theory and applications , 1990 .

[21]  N. JARDINE,et al.  A New Approach to Pattern Recognition , 1971, Nature.

[22]  Robert P. W. Duin,et al.  The dissimilarity space: Bridging structural and statistical pattern recognition , 2012, Pattern Recognit. Lett..

[23]  Daphna Weinshall,et al.  Classification with Nonmetric Distances: Image Retrieval and Class Representation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Robert P. W. Duin,et al.  Classification of three-way data by the dissimilarity representation , 2011, Signal Process..

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

[26]  Robert P. W. Duin,et al.  Dissimilarity-based classification for vectorial representations , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[27]  Marcel J. T. Reinders,et al.  Sign Language Recognition by Combining Statistical DTW and Independent Classification , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Edwin R. Hancock,et al.  Geometric Characterisation of Graphs , 2005, ICIAP.

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

[30]  Antonio Bellacicco,et al.  Handbook of statistics 2: Classification, pattern recognition and reduction of dimensionality: P.R. KRISHNAIAH and L.N. KANAL (Eds.) North-Holland, Amsterdam, 1982, xxii + 903 pages, Dfl.275.00 , 1984 .

[31]  Robert P. W. Duin,et al.  A Generalized Kernel Approach to Dissimilarity-based Classification , 2002, J. Mach. Learn. Res..

[32]  Chong-Wah Ngo,et al.  Evaluating bag-of-visual-words representations in scene classification , 2007, MIR '07.

[33]  Robert P. W. Duin,et al.  Prototype Selection for Dissimilarity Representation by a Genetic Algorithm , 2010, 2010 20th International Conference on Pattern Recognition.

[34]  Robert P. W. Duin,et al.  The Dissimilarity Representation for Pattern Recognition - Foundations and Applications , 2005, Series in Machine Perception and Artificial Intelligence.

[35]  Edwin R. Hancock,et al.  Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshop, SSPR&SPR 2010, Cesme, Izmir, Turkey, August 18-20, 2010. Proceedings , 2010, SSPR/SPR.

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

[37]  J. A. Anderson,et al.  7 Logistic discrimination , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[38]  Horst Bunke,et al.  Applications of approximate string matching to 2D shape recognition , 1993, Pattern Recognit..

[39]  R. C. Williamson,et al.  Classification on proximity data with LP-machines , 1999 .

[40]  R. Duin,et al.  Dissimilarity representation on functional spectral data for classification , 2011 .

[41]  Tony Jebara,et al.  A Kernel Between Sets of Vectors , 2003, ICML.

[42]  Wan-Jui Lee,et al.  An Inexact Graph Comparison Approach in Joint Eigenspace , 2008, SSPR/SPR.

[43]  Steven Gold,et al.  A Graduated Assignment Algorithm for Graph Matching , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[44]  Robert P. W. Duin,et al.  Experiments with a featureless approach to pattern recognition , 1997, Pattern Recognit. Lett..

[45]  Robert P. W. Duin,et al.  Beyond Traditional Kernels: Classification in Two Dissimilarity-Based Representation Spaces , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[46]  Robert P. W. Duin,et al.  The Dissimilarity Representation for Structural Pattern Recognition , 2011, CIARP.

[47]  Horst Bunke,et al.  A graph distance metric based on the maximal common subgraph , 1998, Pattern Recognit. Lett..

[48]  Wan-Jui Lee,et al.  Bag Dissimilarities for Multiple Instance Learning , 2011, SIMBAD.

[49]  Sameer A. Nene,et al.  Columbia Object Image Library (COIL100) , 1996 .

[50]  Thomas G. Dietterich,et al.  Solving the Multiple Instance Problem with Axis-Parallel Rectangles , 1997, Artif. Intell..

[51]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[52]  Kaspar Riesen,et al.  Graph Classification Based on Dissimilarity Space Embedding , 2008, SSPR/SPR.

[53]  Elzbieta Pekalska,et al.  Indefinite Kernel Fisher Discriminant , 2008, 2008 19th International Conference on Pattern Recognition.

[54]  Azriel Rosenfeld,et al.  Progress in pattern recognition , 1985 .

[55]  Robert P. W. Duin,et al.  Prototype selection for dissimilarity-based classifiers , 2006, Pattern Recognit..