These functions implement a distance scaling method based on density-ratio for discovering clusters with varying densities, proposed by Ye Zhu, Kai Ming Ting, and Maia Angelova: "A Distance Scaling Method to Improve Density-based Clustering" published on PAKDD 2018 https://doi.org/10.1007/978-3-319-93040-4_31 Written by Ye Zhu and Xiaoyu Qin, Deakin University, Sep 2018, version 2.0 This software is under GNU General Public License version 3.0 (GPLv3) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Abstract of the paper Density-based clustering is able to find clusters of arbitrary sizes and shapes while effectively separating noise. Despite its advantage over other types of clustering, it is well-known that most density-based algorithms face the same challenge of finding clusters with varied densities. Recently, ReScale, a principled density-ratio preprocessing technique, enables a density-based clustering algorithm to identify clusters with varied densities. However, because the technique is based on one-dimensional scaling, it does not do well in datasets which require multi-dimensional scaling. In this paper, we propose a multi-dimensional scaling method, named DScale, which rescales based on the computed distance. It overcomes the key weakness of ReScale and requires one less parameter while maintaining the simplicity of the implementation. Our empirical evaluation shows that DScale has better clustering performance than ReScale for three existing density-based algorithms, i.e., DBSCAN, OPTICS and DP, on synthetic and real-world datasets. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This code was used for the following publication (Bibtex format): @InProceedings{DScale2018Zhu, author="Zhu, Ye and Ting, Kai Ming and Angelova, Maia", editor="Phung, Dinh and Tseng, Vincent S. and Webb, Geoffrey I. and Ho, Bao and Ganji, Mohadeseh and Rashidi, Lida", title="A Distance Scaling Method to Improve Density-Based Clustering", booktitle="Advances in Knowledge Discovery and Data Mining", year="2018", publisher="Springer International Publishing", address="Cham", pages="389--400", isbn="978-3-319-93040-4" } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% References: [1] M. Ester, H. peter Kriegel, J. S, X. Xu, A density-based algorithm for discovering clusters in large spatial databases with noise, in: Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96), AAAI Press, 1996, pp. 226-231. [2] Zhu, Y., Ting, K.M., Carman, M.J.: Density-ratio based clustering for discovering clusters with varying densities. Pattern Recognition 60, 983-997 (2016)