Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularized Tensor Factorizations and Higher-Order Principal Components
  Analysis   High-dimensional tensors or multi-way data are becoming prevalent in areas
such as biomedical imaging, chemometrics, networking and bibliometrics.
Traditional approaches to finding lower dimensional representations of tensor
data include flattening the data and applying matrix factorizations such as
principal components analysis (PCA) or employing tensor decompositions such as
the CANDECOMP / PARAFAC (CP) and Tucker decompositions. The former can lose
important structure in the data, while the latter Higher-Order PCA (HOPCA)
methods can be problematic in high-dimensions with many irrelevant features. We
introduce frameworks for sparse tensor factorizations or Sparse HOPCA based on
heuristic algorithmic approaches and by solving penalized optimization problems
related to the CP decomposition. Extensions of these approaches lead to methods
for general regularized tensor factorizations, multi-way Functional HOPCA and
generalizations of HOPCA for structured data. We illustrate the utility of our
methods for dimension reduction, feature selection, and signal recovery on
simulated data and multi-dimensional microarrays and functional MRIs.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: physics