Curse of Dimensionality - The "curse of Dimensionality" As Open Problem

The "curse of Dimensionality" As Open Problem

The "curse of dimensionality" is often used as a blanket excuse for not dealing with high-dimensional data. However, the effects are not yet completely understood by the scientific community, and there is ongoing research. On one hand, the notion of intrinsic dimension refers to the fact that any low-dimensional data space can trivially be turned into a higher dimensional space by adding redundant (e.g. duplicate) or randomized dimensions, and in turn many high-dimensional data sets can be reduced to lower dimensional data without significant information loss. This is also reflected by the effectiveness of dimension reduction methods such as principal component analysis in many situations. For distance functions and nearest neighbor search, recent research also showed that data sets that exhibit the curse of dimensionality properties can still be processed unless there are too many irrelevant dimensions, while relevant dimensions can make some problems such as cluster analysis actually easier. Secondly, methods such as Markov chain Monte Carlo or shared nearest neighbor methods often work very well on data that were considered intractable by other methods due to high dimensionality.