Scalable topological data analysis using topological summaries of subsets

A non-transitory computer readable medium comprising instructions executable by a processor to perform a method, the 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.

A system comprising:

• 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.