## An alternative extension of the k-means algorithm for clustering categorical data (2004)

Venue: | Int. J. Appl. Math. Comput. Sci |

Citations: | 16 - 0 self |

### BibTeX

@ARTICLE{San04analternative,

author = {Ohn Mar San and Van-nam Huynh and Yoshiteru Nakamori},

title = {An alternative extension of the k-means algorithm for clustering categorical data},

journal = {Int. J. Appl. Math. Comput. Sci},

year = {2004},

volume = {14},

pages = {241--247}

}

### OpenURL

### Abstract

Most of the earlier work on clustering has mainly been focused on numerical data whose inherent geometric properties can be exploited to naturally define distance functions between data points. Recently, the problem of clustering categorical data has started drawing interest. However, the computational cost makes most of the previous algorithms unacceptable for clustering very large databases. The k-means algorithm is well known for its efficiency in this respect. At the same time, working only on numerical data prohibits them from being used for clustering categorical data. The main contribution of this paper is to show how to apply the notion of “cluster centers ” on a dataset of categorical objects and how to use this notion for formulating the clustering problem of categorical objects as a partitioning problem. Finally, a k-means-like algorithm for clustering categorical data is introduced. The clustering performance of the algorithm is demonstrated with two well-known data sets, namely, soybean disease and nursery databases.

### Citations

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Citation Context ... functions are not naturally defined (Ganti et al., 1999). Recently, clustering data with categorical attributes have drawn some attention (Ganti et al., 1999; Gibson et al., 1998; Guha et al., 2000; =-=Huang, 1998-=-). As is well known, k-means clustering (MacQueen, 1967) has been a very popular technique for partitioning large data sets with numerical attributes. Ralambondrainy (1995) proposed a hybrid numeric-s... |

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Citation Context ...ce functions between data points. However, data mining applications frequently involve many datasets that also consist of categorical attributes on which distance functions are not naturally defined (=-=Ganti et al., 1999-=-). Recently, clustering data with categorical attributes have drawn some attention (Ganti et al., 1999; Gibson et al., 1998; Guha et al., 2000; Huang, 1998). As is well known, k-means clustering (MacQ... |

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Citation Context ...lem of not well-defined boundaries between clusters, the notion of fuzzy partitions has been applied successfully to the clustering problem resulting in the so-called fuzzy clustering (Ruspini, 1969; =-=Bezdek, 1980-=-; Ismail and Selim, 1986). However, we do not consider this topic in the present paper. As is shown in (Huang, 1998), the k-means algorithm has the following characteristics: • It is efficient in proc... |

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Citation Context ...se into clusters/groups such that objects within the same cluster have a high degree of similarity, while objects belonging to different clusters have a high degree of dissimilarity (Anderberg, 1973; =-=Jain and Dubes, 1988-=-; Kaufman and Rousseeuw, 1990). Traditionally, numerical clustering methods have been viewed in opposition to conceptual clustering methods developed in Artificial Intelligence. Numerical techniques e... |

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Citation Context ...fined as categorical if it is finite and unordered, e.g., that only a comparison operation is allowed in Di. That is, for any a, b ∈ Di either a = b or a �= b. Symbolic data objects as considered in (=-=Gowda and Diday, 1991-=-) are not discussed in the present paper. Logically, each data object X in the dataset is also represented as a conjunction of attribute-value pairs [A1 = x1] ∧ . . . ∧ [Am = xm], where xi ∈ Di for 1 ... |

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Citation Context ...acteristics: • It is efficient in processing large data sets. • It often terminates at a local optimum. • It works only on numerical data. • The clusters have convex shapes. 243 It was also shown in (=-=Huang, 1997-=-; Huang, 1998) that the k-means method can be extended to categorical data by using a simple matching distance measure for categorical objects with a majority-vote strategy to define the “cluster cent... |

33 | A conceptual version of the K-means algorithm - Ralambondrainy - 1995 |

18 |
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(Show Context)
Citation Context ...s such that objects within the same cluster have a high degree of similarity, while objects belonging to different clusters have a high degree of dissimilarity (Anderberg, 1973; Jain and Dubes, 1988; =-=Kaufman and Rousseeuw, 1990-=-). Traditionally, numerical clustering methods have been viewed in opposition to conceptual clustering methods developed in Artificial Intelligence. Numerical techniques emphasize the determination of... |

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Citation Context ...l-defined boundaries between clusters, the notion of fuzzy partitions has been applied successfully to the clustering problem resulting in the so-called fuzzy clustering (Ruspini, 1969; Bezdek, 1980; =-=Ismail and Selim, 1986-=-). However, we do not consider this topic in the present paper. As is shown in (Huang, 1998), the k-means algorithm has the following characteristics: • It is efficient in processing large data sets. ... |

1 | Local convergence of the c-means algorithms - Hathaway, Bezdek - 1986 |