Dimensionality reduction in Hilbert spaces

نویسنده

  • Maxim Raginsky
چکیده

Dimensionality reduction is a generic name for any procedure that takes a complicated object living in a high-dimensional (or possibly even infinite-dimensional) space and approximates it in some sense by a finite-dimensional vector. We are interested in a particular class of dimensionality reduction methods. Consider a data source that generates vectors in some Hilbert space H , which is either infinite-dimensional or has a finite but extremely large dimension (think Rd with the usual Euclidean norm, where d is huge). We will assume that the vectors of interest lie in the unit ball of H ,

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تاریخ انتشار 2013