Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homology groups of filtrations   Such modern applications of topology as data analysis and digital image
analysis have to deal with noise and other uncertainty. In this environment,
topological spaces often appear equipped with a real valued function.
Persistence is a measure of robustness of the homology classes of the
filtration of the lower level sets of this function. In this paper we introduce
the homology group of filtration as the product of the kernels of the homology
maps of the inclusions. This group contains all possible homology classes in
all elements of the filtration so that we can later pick the features that lie
within the user's choice of the acceptable level of noise.

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The categories of this paper are: eess
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The categories of this paper are: econ
21
The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg