Similarity Measures

With complex multimedia data, we see the emergence of database systems in which the fundamental operation is similarity assessment. Before database issues can be addressed, it is necessary to give a definition of similarity as an operation. We develop a similarity measure, based on fuzzy logic, that exhibits several features that match experimental findings in humans. The model is dubbed fuzzy feature contrast (FFC) and is an extension to a more general domain of the feature contrast model due to Tversky (1977). We show how the FFC model can be used to model similarity assessment from fuzzy judgment of properties, and we address the use of fuzzy measures to deal with dependencies among the properties.

[1]  Christos Faloutsos,et al.  Efficient Similarity Search In Sequence Databases , 1993, FODO.

[2]  W. Torgerson,et al.  Multidimensional scaling of similarity , 1965, Psychometrika.

[3]  Gregory Ashby,et al.  Toward a Unified Theory of Similarity and Recognition , 1988 .

[4]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[5]  A. Tversky.  Features of Similarity , 1977 .

[6]  A. Tversky,et al.  Similarity, separability, and the triangle inequality. , 1982, Psychological review.

[7]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[8]  Dragutin Petkovic,et al.  Content-Based Representation and Retrieval of Visual Media: A State-of-the-Art Review , 1996 .

[9]  F ATTNEAVE,et al.  Dimensions of similarity. , 1950, The American journal of psychology.

[10]  Kenneth Mullen,et al.  A multidimensional stochastic theory of similiarity , 1988 .

[11]  Anca L. Ralescu,et al.  Modeling of natural objects including fuzziness and application to image understanding , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[12]  F. Gregory Ashby,et al.  Toward a Unified Theory of Similarity and Recognition , 1988 .

[13]  E. Rothkopf.  A measure of stimulus similarity and errors in some paired-associate learning tasks. , 1957, Journal of experimental psychology.

[14]  Rangachar Kasturi,et al.  Machine vision , 1995 .

[15]  P. Jaccard,et al.  Etude comparative de la distribution florale dans une portion des Alpes et des Jura , 1901 .

[16]  D. Ennis.  Toward a Universal Law of Generalization , 1988, Science.

[17]  Roger N. Shepard,et al.  Toward a Universal Law of Generalization , 1988, Science.

[18]  Julius T. Tou,et al.  Pattern Recognition Principles , 1974 .

[19]  Fang Liu,et al.  Periodicity, directionality, and randomness: Wold features for perceptual pattern recognition , 1994, Proceedings of the 12th IAPR International Conference on Pattern Recognition, Vol. 3 - Conference C: Signal Processing (Cat. No.94CH3440-5).

[20]  E. Brunswik.  Perception and the Representative Design of Psychological Experiments , 1957 .

[21]  R. Shepard,et al.  Toward a universal law of generalization for psychological science. , 1987, Science.

[22]  Andrew R. Webb,et al.  Statistical Pattern Recognition , 1999 .

[23]  R. Shepard.  The analysis of proximities: Multidimensional scaling with an unknown distance function. I. , 1962 .

[24]  Dragutin Petkovic,et al.  Representation and Retrieval of Visual Media in Multimedia Systems , 1996, Springer US.

[25]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[26]  Brian Everitt,et al.  Graphical Techniques for Multivariate Data. , 1978 .

[27]  R. Shepard.  The analysis of proximities: Multidimensional scaling with an unknown distance function. II , 1962 .

[28]  L. Thurstone.  A law of comparative judgment. , 1994 .

[29]  E. Rosch.  Cognitive reference points , 1975, Cognitive Psychology.

[30]  Richard P. Runyon.  Fundamentals of behavioral statistics , 1968 .

[31]  J. T. Curtis,et al.  An Ordination of the Upland Forest Communities of Southern Wisconsin , 1957 .

[32]  Simone Santini,et al.  The use of psychological similarity measure for queries in image databases , 1996 .

[33]  G. Debreu.  Topological Methods in Cardinal Utility Theory , 1959 .

[34]  C. Krumhansl.  Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. , 1978 .

[35]  J. Marden.  Analyzing and Modeling Rank Data , 1996 .

[36]  B. S. Manjunath,et al.  Texture Features for Browsing and Retrieval of Image Data , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  David H. Krantz,et al.  The dimensional representation and the metric structure of similarity data , 1970 .