Scalable topological data analysis

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

• receiving first data associated with data points;
• receiving a lens function selection, a metric function selection, and a resolution function, the metric function identified by the metric function selection being capable of performing functions on data as matrix functions;
• mapping second data based on the first data to a reference space by utilizing matrix vector multiplication for application of selected lens function on second data based on the first data to map the second data to the reference space;
• generating cover of reference space including the second data;
• clustering second data in cover based on the selected metric function to determine each node of a plurality of nodes, each of the nodes of the plurality of nodes comprising members representative of at least one subset of the data points;
• and
• generating a visualization comprising the plurality of nodes and a plurality of edges wherein each of the edges of the plurality of edges connects nodes with shared members.

A system comprising:

• one or more processors;
• and
• memory containing instructions executable by the processor to:
• receive first data associated with data points;
• receive a lens function selection, a metric function selection, and a resolution function, the metric function identified by the metric function selection being capable of performing functions on data as matrix functions;
• map second data based on the first data to a reference space by utilizing matrix vector multiplication for application of selected lens function on second data based on the first data to map the second data to the reference space;
• generate cover of reference space including the second data;
• cluster second data in cover based on the selected metric function to determine each node of a plurality of nodes, each of the nodes of the plurality of nodes comprising members representative of at least one subset of the data points;
• and
• generate a visualization comprising the plurality of nodes and a plurality of edges wherein each of the edges of the plurality of edges connects nodes with shared members.