Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate Extension of Matrix-based Renyi's \alpha-order Entropy
  Functional   The matrix-based Renyi's \alpha-order entropy functional was recently
introduced using the normalized eigenspectrum of a Hermitian matrix of the
projected data in a reproducing kernel Hilbert space (RKHS). However, the
current theory in the matrix-based Renyi's \alpha-order entropy functional only
defines the entropy of a single variable or mutual information between two
random variables. In information theory and machine learning communities, one
is also frequently interested in multivariate information quantities, such as
the multivariate joint entropy and different interactive quantities among
multiple variables. In this paper, we first define the matrix-based Renyi's
\alpha-order joint entropy among multiple variables. We then show how this
definition can ease the estimation of various information quantities that
measure the interactions among multiple variables, such as interactive
information and total correlation. We finally present an application to feature
selection to show how our definition provides a simple yet powerful way to
estimate a widely-acknowledged intractable quantity from data. A real example
on hyperspectral image (HSI) band selection is also provided.

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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int