Aggregating time-series and image data: functors and double functors
This provides a unified theoretical framework for data aggregation in data science, though it appears incremental as it builds on existing functorial concepts.
The paper tackles the problem of aggregating time-series and image data over subsets of the domain by interpreting known operations as (double) functors, enabling parallel implementation via extensions of Blelloch's parallel scan algorithm and proposing new aggregation operations.
Aggregation of time-series or image data over subsets of the domain is a fundamental task in data science. We show that many known aggregation operations can be interpreted as (double) functors on appropriate (double) categories. Such functorial aggregations are amenable to parallel implementation via straightforward extensions of Blelloch's parallel scan algorithm. In addition to providing a unified viewpoint on existing operations, it allows us to propose new aggregation operations for time-series and image data.