Paper:

# Landmark FN-DBSCAN: An Efficient Density-Based Clustering Algorithm with Fuzzy Neighborhood

## Hao Liu, Satoshi Oyama, Masahito Kurihara,

and Haruhiko Sato

Division of Synergetic Information Science in Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo 060-0814, Japan

Clustering is an important tool for data analysis and many clustering techniques have been proposed over the past years. Among them are density-based clustering methods, which have several benefits such as the number of clusters is not required before carrying out clustering; the detected clusters can be represented in an arbitrary shape and outliers can be detected and removed. Recently, the density-based algorithms were extended with the fuzzy set theory, which has made these algorithm more robust. However, the density-based clustering algorithms usually require a time complexity of *O*(*n*^{2}) where *n* is the number of data in the data set, implying that they are not suitable to work with large scale data sets. In this paper, a novel clustering algorithm called landmark fuzzy neighborhood DBSCAN (landmark FN-DBSCAN) is proposed. The concept, landmark, is used to represent a subset of the input data set which makes the algorithm efficient on large scale data sets. We give a theoretical analysis on time complexity and space complexity, which shows both of them are linear to the size of the data set. The experiments show that the landmark FN-DBSCAN is much faster than FN-DBSCAN and provides a very good quality of clustering.

and Haruhiko Sato, “Landmark FN-DBSCAN: An Efficient Density-Based Clustering Algorithm with Fuzzy Neighborhood,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.17, No.1, pp. 60-73, 2013.

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