Optimal Grid-Clustering: Towards Breaking the Curse of Dimensionality in High-Dimensional Clustering Alexander Hinneburg Daniel A. Keim
[email protected] [email protected] Institute of Computer Science, UniversityofHalle Kurt-Mothes-Str.1, 06120 Halle (Saale), Germany Abstract 1 Intro duction Because of the fast technological progress, the amount Many applications require the clustering of large amounts of data which is stored in databases increases very fast. of high-dimensional data. Most clustering algorithms, This is true for traditional relational databases but however, do not work e ectively and eciently in high- also for databases of complex 2D and 3D multimedia dimensional space, which is due to the so-called "curse of data such as image, CAD, geographic, and molecular dimensionality". In addition, the high-dimensional data biology data. It is obvious that relational databases often contains a signi cant amount of noise which causes can be seen as high-dimensional databases (the at- additional e ectiveness problems. In this pap er, we review tributes corresp ond to the dimensions of the data set), and compare the existing algorithms for clustering high- butitisalsotrueformultimedia data which - for an dimensional data and show the impact of the curse of di- ecient retrieval - is usually transformed into high- mensionality on their e ectiveness and eciency.Thecom- dimensional feature vectors such as color histograms parison reveals that condensation-based approaches (such [SH94], shap e descriptors [Jag91, MG95], Fourier vec- as BIRCH or STING) are the most promising candidates tors [WW80], and text descriptors [Kuk92]. In many for achieving the necessary eciency, but it also shows of the mentioned applications, the databases are very that basically all condensation-based approaches havese- large and consist of millions of data ob jects with sev- vere weaknesses with resp ect to their e ectiveness in high- eral tens to a few hundreds of dimensions.