# NED and Coverage MeasureΒΆ

Many spoken term discovery systems incorporate a step whereby
fragments of speech are realigned and compared. Matching quality
measures the accuraty of this process. Here, we use the *NED/Coverage*
metrics for evaluating that.

*NED* and *Coverage* are quick to compute and give a qualitative
estimate of the matching step. *NED* is the Normalised Edit Distance;
it is equal to zero when a pair of fragments have exactly the same
transcription, and 1 when they differ in all phonemes. *Coverage* is
the fraction of corpus that contain matching pairs that has been
discovered.

where

with - \(P_{all}\): the set of all possible non overlapping matching

fragment pairs. \(P_{all}=\{ \{a,b \}\in F_{all} \times F_{all} | T_{a} = T_{b}, \neg \textrm{overlap}(a,b)\}\).

\(P_{disc}\): the set of non overlapping discovered pairs, \(P_{disc} = \{ \{a,b\} | a \in c, b \in c, \neg \textrm{overlap}(a,b), c \in C_{disc} \}\)

\(P_{disc^*}\): the set of pairwise substring completion of \(P_{disc}\), which mean that we compute all of the possible minimal path realignments of the two strings, and extract all of the substrings pairs along the path (e.g., for fragment pair