SCALABLE TOPOLOGICAL DATA ANALYSIS USING TOPOLOGICAL SUMMARIES OF SUBSETS
First Claim
1. A method comprising:
- dividing a set of data points into a structure subset and a plurality of boost subsets;
adding the data points in the structure subset into each of the plurality of boost subsets to create a plurality of combination subsets;
receiving a lens function identifier, a metric function identifier, and a resolution function identifier;
mapping data points of the structure subset to a reference space utilizing a lens function identified by the lens function identifier;
generating a cover of reference space using a resolution function identified by the resolution identifier;
clustering the data points of the structure subset using the cover and a metric function identified by the metric function identifier to determine each node of a plurality of nodes of a structure graph;
generating a plurality of nodes for a modified graph, each of the plurality of nodes of the modified graph corresponding to each of the plurality of nodes in the structure graph;
for each of the plurality of combination subsets;
mapping data points of a particular combination subset to the reference space utilizing the lens function;
generating the cover of reference space using the resolution function; and
clustering the data points of the particular combination subset using the cover and the metric function to determine each node of a plurality of nodes to add to a particular boost graph of the plurality of boost graphs; and
for each node in each of the plurality of boost graphs that do not share at least one data point with a node in the structure graph, adding the node of a particular boost subset including data points that are members of the node, to the modified graph; and
generating report indicating relationships between data points of the set of data points based on the nodes of the modified graph.
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Accused Products
Abstract
A method comprises dividing a set of data points into a structure subset and boost subsets, adding the data points in structure subset into each boost subset, analyzing the structure subset using topological data analysis (TDA) to identify nodes of a structure graph, boost graph, and modified graph, analyze each of the boost subsets using the TDA to identify additional nodes of boost graph, for each node in each of the plurality of boost graphs that do not share at least one data point with a node in the structure graph, adding the node of a particular boost subset including data points that are members of the node, to the modified graph, and generating report indicating relationships between data points of the set of data points based on the nodes of the modified graph.
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Citations
21 Claims
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1. A method comprising:
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dividing a set of data points into a structure subset and a plurality of boost subsets; adding the data points in the structure subset into each of the plurality of boost subsets to create a plurality of combination subsets; receiving a lens function identifier, a metric function identifier, and a resolution function identifier; mapping data points of the structure subset to a reference space utilizing a lens function identified by the lens function identifier; generating a cover of reference space using a resolution function identified by the resolution identifier; clustering the data points of the structure subset using the cover and a metric function identified by the metric function identifier to determine each node of a plurality of nodes of a structure graph; generating a plurality of nodes for a modified graph, each of the plurality of nodes of the modified graph corresponding to each of the plurality of nodes in the structure graph; for each of the plurality of combination subsets; mapping data points of a particular combination subset to the reference space utilizing the lens function; generating the cover of reference space using the resolution function; and clustering the data points of the particular combination subset using the cover and the metric function to determine each node of a plurality of nodes to add to a particular boost graph of the plurality of boost graphs; and for each node in each of the plurality of boost graphs that do not share at least one data point with a node in the structure graph, adding the node of a particular boost subset including data points that are members of the node, to the modified graph; and generating report indicating relationships between data points of the set of data points based on the nodes of the modified graph. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A non-transitory computer readable medium comprising instructions executable by a processor to perform a method, the method comprising:
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dividing a set of data points into a structure subset and a plurality of boost subsets; adding the data points in the structure subset into each of the plurality of boost subsets to create a plurality of combination subsets; receiving a lens function identifier, a metric function identifier, and a resolution function identifier; mapping data points of the structure subset to a reference space utilizing a lens function identified by the lens function identifier; generating a cover of reference space using a resolution function identified by the resolution identifier; clustering the data points of the structure subset using the cover and a metric function identified by the metric function identifier to determine each node of a plurality of nodes of a structure graph; generating a plurality of nodes for a modified graph, each of the plurality of nodes of the modified graph corresponding to each of the plurality of nodes in the structure graph; for each of the plurality of combination subsets; mapping data points of a particular combination subset to the reference space utilizing the lens function; generating the cover of reference space using the resolution function; and clustering the data points of the particular combination subset using the cover and the metric function to determine each node of a plurality of nodes to add to a particular boost graph of the plurality of boost graphs; and for each node in each of the plurality of boost graphs that do not share at least one data point with a node in the structure graph, adding the node of a particular boost subset including data points that are members of the node, to the modified graph; and generating report indicating relationships between data points of the set of data points based on the nodes of the modified graph. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20)
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21. A system comprising:
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one or more processors; and memory containing instructions executable by at least one of the one or more processors to; divide a set of data points into a structure subset and a plurality of boost subsets; add the data points in the structure subset into each of the plurality of boost subsets to create a plurality of combination subsets; receive a lens function identifier, a metric function identifier, and a resolution function identifier; map data points of the structure subset to a reference space utilizing a lens function identified by the lens function identifier; generate a cover of reference space using a resolution function identified by the resolution identifier; cluster the data points of the structure subset using the cover and a metric function identified by the metric function identifier to determine each node of a plurality of nodes of a structure graph; generate a plurality of nodes for a modified graph, each of the plurality of nodes of the modified graph corresponding to each of the plurality of nodes in the structure graph; for each of the plurality of combination subsets; map data points of a particular combination subset to the reference space utilizing the lens function; generate the cover of reference space using the resolution function; and cluster the data points of the particular combination subset using the cover and the metric function to determine each node of a plurality of nodes to add to a particular boost graph of the plurality of boost graphs; and for each node in each of the plurality of boost graphs that do not share at least one data point with a node in the structure graph, add the node of a particular boost subset including data points that are members of the node, to the modified graph; and generate report indicating relationships between data points of the set of data points based on the nodes of the modified graph.
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Specification