One of the strongest problems afflicting current machine learning techniques is dataset dimensionality. In many applications to real world problems, we deal with data with anywhere from a few dozen to many thousands of dimensions. Such high-dimensional data spaces are often encountered in areas such as medicine or biology, where DNA microarray technology can produce a large number of measurements at once, the clustering of text documents, where, if a word-frequency vector is used, the number of dimensions equals the size of the dictionary, and many others, including data integration and management, and social network analysis. In all these cases, the dimensionality of data makes learning problems hardly tractable.

In particular, the high dimensionality of data is a highly critical factor for the clustering task. The following problems need to be faced for clustering high-dimensional data:

• When the dimensionality is high, the volume of the space increases so fast that the available data becomes sparse, and we cannot find reliable clusters, as clusters are data aggregations (curse of dimensionality).
• The concept of distance becomes less precise as the number of dimensions grows, since the distance between any two points in a given dataset converges (concentration effects).
• Different clusters might be found in different subspaces, so a global filtering of attributes is not sufficient (local feature relevance problem).
• Given a large number of attributes, it is likely that some attributes are correlated. Hence, clusters might exist in arbitrarily oriented affine subspaces.
• High-dimensional data could likely include irrelevant features, which may obscure the effect of the relevant ones.

The project is aimed to the study the current approaches for clustering high-dimensional data with particular stress on relational clustering, data reduction using rough and fuzzy sets, biclustering/co-clustering and related methods for intrinsic dimension estimation and for clustering comparison.