Similarity Measures for Categorical Data: A Comparative Evaluation

Measuring similarity or distance between two entities is a key step for several data mining and knowledge discovery tasks. The notion of similarity for continuous data is relatively well-understood, but for categorical data, the similarity computation is not straightforward. Several data-driven similarity measures have been proposed in the literature to compute the similarity between two categorical data instances but their relative performance has not been evaluated. In this paper we study the performance of a variety of similarity measures in the context of a specific data mining task: outlier detection. Results on a variety of data sets show that while no one measure dominates others for all types of problems, some measures are able to have consistently high performance.

[1]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .

[2]  Tony R. Martinez,et al.  Improved Heterogeneous Distance Functions , 1996, J. Artif. Intell. Res..

[3]  Yoram Biberman,et al.  A Context Similarity Measure , 1994, ECML.

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

[5]  Usama M. Fayyad,et al.  Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning , 1993, IJCAI.

[6]  Heikki Mannila,et al.  Context-Based Similarity Measures for Categorical Databases , 2000, PKDD.

[7]  Harald Cramér.  The elements of probability theory and some of its applications , 1955 .

[8]  Jon M. Kleinberg,et al.  Clustering categorical data: an approach based on dynamical systems , 2000, The VLDB Journal.

[9]  Johannes Gehrke,et al.  CACTUS—clustering categorical data using summaries , 1999, KDD '99.

[10]  T. P. Burnaby.  On a method for character weighting a similarity coefficient, employing the concept of information , 1970 .

[11]  Lipika Dey,et al.  A method to compute distance between two categorical values of same attribute in unsupervised learning for categorical data set , 2007, Pattern Recognit. Lett..

[12]  Dekang Lin,et al.  An Information-Theoretic Definition of Similarity , 1998, ICML.

[13]  D. W. Goodall.  A New Similarity Index Based on Probability , 1966 .

[14]  Sridhar Ramaswamy,et al.  Efficient algorithms for mining outliers from large data sets , 2000, SIGMOD '00.

[15]  K. Maung,et al.  MEASUREMENT OF ASSOCIATION IN A CONTINGENCY TABLE WITH SPECIAL REFERENCE TO THE PIGMENTATION OF HAIR AND EYE COLOURS OF SCOTTISH SCHOOL CHILDREN , 1941 .

[16]  Sudipto Guha,et al.  ROCK: a robust clustering algorithm for categorical attributes , 1999, Proceedings 15th International Conference on Data Engineering (Cat. No.99CB36337).

[17]  Tu Bao Ho,et al.  for categorical data , 2005 .

[18]  Salvatore J. Stolfo,et al.  A Geometric Framework for Unsupervised Anomaly Detection , 2002, Applications of Data Mining in Computer Security.

[19]  Michael R. Anderberg,et al.  Cluster Analysis for Applications , 1973 .

[20]  David L. Waltz,et al.  Toward memory-based reasoning , 1986, CACM.

[21]  Joshua Zhexue Huang,et al.  Extensions to the k-Means Algorithm for Clustering Large Data Sets with Categorical Values , 1998, Data Mining and Knowledge Discovery.

[22]  Michael McGill,et al.  A performance evaluation of similarity measures, document term weighting schemes and representations in a Boolean environment , 1980, SIGIR '80.

[23]  Peter H. A. Sneath,et al.  Numerical Taxonomy: The Principles and Practice of Numerical Classification , 1973 .

[24]  Karen Spärck Jones.  A statistical interpretation of term specificity and its application in retrieval , 2021, J. Documentation.

[25]  George W. Furnas,et al.  Pictures of relevance: A geometric analysis of similarity measures , 1987, J. Am. Soc. Inf. Sci..

[26]  Karl Pearson,et al.  ON THE GENERAL THEORY OF MULTIPLE CONTINGENCY WITH SPECIAL REFERENCE TO PARTIAL CONTINGENCY , 1916 .

[27]  Vincent Kanade,et al.  Clustering Algorithms , 2021, Wireless RF Energy Transfer in the Massive IoT Era.

[28]  B. Baets,et al.  A comparative study of similarity measures , 1995 .

[29]  E. S. Smirnov.  On Exact Methods in Systematics , 1968 .

[30]  C. Pappis,et al.  A comparative assessment of measures of similarity of fuzzy values , 1993 .

[31]  Rami Zwick,et al.  Measures of similarity among fuzzy concepts: A comparative analysis , 1987, Int. J. Approx. Reason..

[32]  Christos Faloutsos,et al.  Electricity Based External Similarity of Categorical Attributes , 2003, PAKDD.