Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Searching for Topological Symmetry in Data Haystack   Finding interesting symmetrical topological structures in high-dimensional
systems is an important problem in statistical machine learning. Limited amount
of available high-dimensional data and its sensitivity to noise pose
computational challenges to find symmetry. Our paper presents a new method to
find local symmetries in a low-dimensional 2-D grid structure which is embedded
in high-dimensional structure. To compute the symmetry in a grid structure, we
introduce three legal grid moves (i) Commutation (ii) Cyclic Permutation (iii)
Stabilization on sets of local grid squares, grid blocks. The three grid moves
are legal transformations as they preserve the statistical distribution of
hamming distances in each grid block. We propose and coin the term of grid
symmetry of data on the 2-D data grid as the invariance of statistical
distributions of hamming distance are preserved after a sequence of grid moves.
We have computed and analyzed the grid symmetry of data on multivariate
Gaussian distributions and Gamma distributions with noise.

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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph