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Hoch-dimensionale Datenanalyse

Among different types of data, high-dimensional data is one of the most challenging type. This class of data is also sometimes refered to as "big data". It, for instance, occurs in situations when objects or phenomena are described by thousands of parameters. Think of the application [1] of cancer diagnosis using proteomics data with each possible weight of a protein giving one dimension.

From a mathematical and, in particular, functional analytic standpoint, such high-dimensional data is quite intriguing with one particularly curious and very unintuitive phenomena being the concentration of measure. Citing Talagand, this can be roughly explained by saying that "A random variable that depends in a Lipschitz way on many independent variables (but not too much on any of them) is essentially constant."

The area of geometric functional analysis studies these and many related effects in high dimensions, having direct impact on data science [2].

Some of our Research Topics

  • Analyzing quantization of data modeled via a manifold.
  • Extending techniques from applied harmonic analysis to high-dimensional data.
  • Developing methods for classification of high-dimensional data.
  • Studying reasonable model assumptions for high-dimensional data.
  • Study of the interrelation of machine learning and compressed sensing.
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