Metrics Overview

Available metrics, with activity/sequence categorization, frame/event categorization, intuitive (non-complete) explanation in BPM context, definition and codomain. GT means ground truth, DET means detected.

Metrics Overview

Metric Name	Activity/Sequence	Frame/Event	Intuition	Definition	Codomain
Cross-Correlation (CC)	Activity	Frame	When shifting the DET frame time series over the GT time series: At what shift are they maximally similar, and how similar are they at that shift? (relative to complete equality for time series of that length)	Lyon (2010), with zero-padding and input vector mapping to 1 when active and -1 when inactive	\(\mathbb{R}\), \([-1,1]\) for shift of DET at which max CC occurs.
Two-Set (TS)	Activity	Frame	How many frames can be categorized as true positive (tp), true negative (tn), deletions (d), fragmentations (f), mergings (m), insertions (i), over-fillings at the start/end (oa/oo), under-fillings at the start/end(ua/uo)?	Ward et al. (2011)	\(\mathbb{N}\), \(\mathbb{R}\) when aggregated
Two-Set Rates	Activity	Frame	What perc. of the GT true frames are detected as tp, d, f, ua, uo? What perc. of the GT false frames are detected as tn, m, i, oa, oo?	Ward et al. (2011)	\(\mathbb{R}\), \([0,1]\) for all, \(tpr + dr + fr + uar + uor = 1\), \(tnr + mr + ir + oar + oor = 1\)
Event Analysis (EA)	Activity	Event	How many of the GT events can be categorized as correct (c), deleted (d), fragmented (f), merged (m), fragmented and merged (fm); How many of the DET events as correct, inserted (id),fragmenting (fd), merging (md) and fragmenting and merging (fmd).	Ward et al. (2011)	\(\mathbb{N}\), \(\mathbb{R}\) when aggregated
Event Analysis Rates	Activity	Event	What perc. of the GT events are detected as c, d, f, m, fm? What perc. of the DET events are c, id, fd, md, fmd?	Ward et al. (2011)	\(\mathbb{R}\), \([0,1]\) for all, \(cr\_gt + dr + fr + mr + fmr = 1\), \(cr\_det + idr + fdr + mdr + fmdr = 1\)
Levenshtein Distance (LD)	Sequence	Event	Minimum number of single activity instance edits (insertions, deletions, or substitutions) required to change sequence of activity instances in GT to be equal with DET.	Levenshtein (1966)	\(\mathbb{N}\), \(\mathbb{R}\) when aggregated
LD normalized	Sequence	Event	How large is the LD relative to the maximum possible LD for sequences of that length?	Levenshtein (1966), divided by length of longer sequence	\(\mathbb{R}\), \([0,1]\)
Damerau-Levenshtein-Distance (DLD)	Sequence	Event	An extension of the LD, this metric also considers the transposition of two adjacent activity instances as a single edit.	Damerau (1964)	\(\mathbb{N}\), \(\mathbb{R}\) when aggregated
DLD normalized	Sequence	Event	How large is the DLD relative to the maximum possible DLD for sequences of that length?	Damerau (1964), divided by length of longer sequence	\(\mathbb{R}\), \([0,1]\)