Query capabilities of topological data analysis graphs

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

• receiving a data set from any number of data sources;
• receiving a lens function identifier, a metric function identifier, and a resolution function identifier;
• mapping data points from the data set to a reference space utilizing a lens function identified by the lens function identifier;
• generating a cover of the reference space using a resolution function identified by the resolution identifier;
• clustering the data points mapped to the reference space using the cover and a metric function identified by the metric function identifier to determine each node of a plurality of nodes of a graph, each node including at least one data point;
• generating a graph including the plurality of nodes, the graph including an edge between every two nodes that share at least one data point as a member;
• and
• generating a first data structure and a second data structure, the first data structure identifying membership of each node of the plurality of nodes, the membership including one or more of the data points, the second data structure identifying each edge between two nodes of the plurality of nodes, the second data structure further identifying the nodes of the plurality of nodes that are connected by each edge, the first and second data structure being capable of being queryable using a query language.

A system comprising:

• one or more processors;
• and
• memory containing instructions executable by at least one of the one or more processors to:
• receive a data set from any number of data sources;
• receive a lens function identifier, a metric function identifier, and a resolution function identifier;
• map data points from the data set to a reference space utilizing a lens function identified by the lens function identifier;
• generate a cover of the reference space using a resolution function identified by the resolution identifier;
• cluster the data points mapped to the reference space using the cover and a metric function identified by the metric function identifier to determine each node of a plurality of nodes of a graph, each node including at least one data point;
• generate a graph including the plurality of nodes, the graph including an edge between every two nodes that share at least one data point as a member;
• and
• generate a first data structure and a second data structure, the first data structure identifying membership of each node of the plurality of nodes, the membership including one or more of the data points, the second data structure identifying each edge between two nodes of the plurality of nodes, the second data structure further identifying the nodes of the plurality of nodes that are connected by each edge, the first and second data structure being capable of being queryable using a query language.