A density based algorithm for discovering clusters with varied density

Clustering is a well studied problem in data analysis and data mining. It has many areas of applications and it is used as a preprocessing step before other data mining tasks such as classification and association analysis. Discovering clusters of arbitrary shapes is a challenging task. Even though density based clustering algorithms manage to detect clusters with different shapes and sizes in large data bases with the presence of noise, they fail in handling local density variation within the data. In this paper, we propose a new algorithm based on the well known density based clustering algorithm DBSCAN. Our algorithm approximates the k nearest neighbors curve by spline interpolation and uses mathematic properties of functions to detect automatically points where the function changes concavity. Some of these points corresponds to the different levels of density within the data set. Experimental results on synthetic data sets show the efficiency of the proposed approach.