High-dimensional clustering
Résumé
High-dimensional (HD) data sets are now frequent, mostly motivated by technological reasons which concern automation in variable acquisition, cheaper availability of data storage and more powerful standard computers for quick data management possibility. All fields are impacted by this general phenomenon of variable number inflation, only the definition of ``high'' being domain dependent. In marketing, this number can be of order 10e2, in microarray gene expression between 10e2 and 10e4, in text mining 10e3 or more, of order 10e6 for single nucleotide polymorphism (SNP) data, etc. Note also that sometimes much more variables can be involved, what can be typically the case with discretized curves, for instance curves coming from temporal sequences.
Such a technological revolution has a huge impact in other scientific fields, as societal or also mathematical ones. In particular, high-dimensional data management brings some new challenges to statisticians since standard (low-dimensional) data analysis methods struggle to directly apply to the new (high-dimensional) data sets. The reason can be twofold, sometimes linked, involving either combinatorial difficulties or disastrously large estimate variance increase. Data analysis methods are essential for providing a synthetic view of data sets, allowing data summary and data exploratory for future decision making for instance. This need is even more acute in the high-dimensional setting since on the one hand the large number of variables suggests that a lot of information is conveyed by data but, in the other hand, such information may be hidden behind their volume.
Domaines
Méthodologie [stat.ME]
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