Over a decade ago, Stanford statistician David Donoho predicted that the 21st century will be the century of data. "We can say with complete confidence that in the coming century, high-dimensional data analysis will be a very significant activity, and completely new methods of high-dimensional data analysis will be developed; we just don't know what they are yet." -- D. Donoho, 2000.

Unprecedented technological advances lead to increasingly high dimensional data sets in all areas of science, engineering and businesses. These include genomics and proteomics, biomedical imaging, signal processing, astrophysics, finance, web and market basket analysis, among many others. The number of features in such data is often of the order of thousands or millions - that is much larger than the available sample size.

For a number of reasons, classical data analysis methods inadequate, questionable, or inefficient at best when faced with high dimensional data spaces:
1. High dimensional geometry defeats our intuition rooted in low dimensional experiences, and this makes data presentation and visualisation particularly challenging.
2. Phenomena that occur in high dimensional probability spaces, such as the concentration of measure, are counter-intuitive for the data mining practitioner. For instance, distance concentration is the phenomenon that the contrast between pair-wise distances may vanish as the dimensionality increases.
3. Bogus correlations and misleading estimates may result when trying to fit complex models for which the effective dimensionality is too large compared to the number of data points available.
4. The accumulation of noise may confound our ability to find low dimensional intrinsic structure hidden in the high dimensional data.
5. The computation cost of processing high dimensional data or carrying out optimisation over a high dimensional parameter spaces is often prohibiting.