finercount

Finercount is a term used in data analysis and computational geometry to quantify granularity by counting fine-grained elements within a region or window. In its common form, the space is first partitioned into fine units (for example, grid cells or time bins) and into coarser aggregates. The finercount of a region R is the number of fine units that intersect R, or, in some definitions, the number of fine units contained entirely within R. The term is not universally standardized and definitions may vary by field.

Computation and variants: Finercount(R) = the cardinality of the set of fine units that intersect R. Variants exist where only fully contained cells are counted, or where bins with at least one event are counted in a time-series context. In practice, the choice of the fine-scale partition and boundary rules directly influences the finercount value.

Applications: It is used to assess granularity, perform multiscale analysis, density estimation, and anonymization, and to benchmark algorithms across different scales. In spatial analysis, finercount helps compare how much detail a region carries at a given resolution. In time-series, it measures activity within a time window by counting fine-time bins with events.

Examples: In a spatial domain subdivided into a fine grid, the finercount of a region equals the number of grid cells overlapping the region. In a time-series, a 1-second interval with a 100 ms bin size yields up to 10 fine bins; finercount equals the number of those bins containing events.

Limitations: Finercount depends on the chosen fine scale and alignment of the partition, and edge effects can alter counts. It should be used alongside scale parameters and other measures to avoid misinterpretation.

See also: granularity, multiscale analysis, coarse-graining, density estimation, spatial indexing.