An effective dissimilarity measure for clustering of high-dimensional categorical data (original) (raw)

Abstract

Clustering is to group similar data and find out hidden information about the characteristics of dataset for the further analysis. The concept of dissimilarity of objects is a decisive factor for good quality of results in clustering. When attributes of data are not just numerical but categorical and high dimensional, it is not simple to discriminate the dissimilarity of objects which have synonymous values or unimportant attributes. We suggest a method to quantify the level of difference between categorical values and to weigh the implicit influence of each attribute on constructing a particular cluster. Our method exploits distributional information of data correlated with each categorical value so that intrinsic relationship of values can be discovered. In addition, it measures significance of each attribute in constructing respective cluster dynamically. Experiments on real datasets show the propriety and effectiveness of the method, which improves the results considerably even with simple clustering algorithms. Our approach does not couple with a clustering algorithm tightly and can also be applied to various algorithms flexibly.

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Notes

  1. An object is referred as an item in the whole dataset.
  2. In this paper, the dissimilarity is considered as the opposite concept of similarity.
  3. In representation of data vector, an attribute is considered as a dimension of space.
  4. The distance between two objects \(x=(x_{1},x_{2},\ldots ,x_{n})\) and \(y=(y_{1},y_{2},\ldots ,y_{n})\) is defined with norm, \(r\), as \(\left(\sum _{i=1}^{n}\mid x_{i}-y_{i}\mid ^{r}\right)^{\frac{1}{r}}\), especially, 2-norm distance is known as Euclidean distance.
  5. The Chi-square test is a statistical test procedure to understand if a relationship exists between two categorical variables.
  6. Simple matching coefficient is defined as \(\frac{\text{ the} \text{ number} \text{ of} \text{ attributes} \text{ with} \text{ matching} \text{ values}}{\text{ the} \text{ number} \text{ of} \text{ total} \text{ attributes}}\).
  7. Jaccard coefficient is defined as \(\frac{\text{ the} \text{ number} \text{ of} \text{ matching} \text{ presences}}{\text{ the} \text{ number} \text{ of} \text{ attributes} \text{ not} \text{ involved} \text{ in} \text{ null} \text{ matches}}\).
  8. The values are the model numbers of the 2012 Mercedes \(\text{ Benz}^{(\mathrm TM )}\). CL550 and G550 are available at about 110,000whileE550andML550areatabout110,000 while E550 and ML550 are at about 110,000whileE550andML550areatabout60,000 in 2012 (http://www.mbusa.com/mercedes/).

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Authors and Affiliations

  1. Applied Mathematics and Systems (HPC Team), Ecole Centrale Paris, Châtenay Malabry, France
    Jeonghoon Lee
  2. Department of Computer Science, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea
    Yoon-Joon Lee

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  1. Jeonghoon Lee
  2. Yoon-Joon Lee

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Correspondence toJeonghoon Lee.

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Lee, J., Lee, YJ. An effective dissimilarity measure for clustering of high-dimensional categorical data.Knowl Inf Syst 38, 743–757 (2014). https://doi.org/10.1007/s10115-012-0599-1

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