Challenges for Cluster Analysis in a Virtual Observatory

There has been an unprecedented and continuing growth in the volume, quality, and complexity of astronomical data sets over the past few years, mainly through large digital sky surveys. Virtual Observatory (VO) concept represents a scientific and technological framework needed to cope with this data flood. We review some of the applied statistics and computing challenges posed by the analysis of large and complex data sets expected in the VO-based research. The challenges are driven both by the size and the complexity of the data sets (billions of data vectors in parameter spaces of tens or hundreds of dimensions), by the heterogeneity of the data and measurement errors, the selection effects and censored data, and by the intrinsic clustering properties (functional form, topology) of the data distribution in the parameter space of observed attributes. Examples of scientific questions one may wish to address include: objective determination of the numbers of object classes present in the data, and the membership probabilities for each source; searches for unusual, rare, or even new types of objects and phenomena; discovery of physically interesting multivariate correlations which may be present in some of the clusters; etc.