Semantic Similarity based on Weighted Ontology - Geographical Information Systems: Trends and Technologies - page 313

measures; they were essentially concerned to study the relationship between
similarity of context and similarity of meaning (synonyms). In fact, only
a part of these experiments was dedicated to ask humans to judge the
similarity between words, and this later became the basis for similarity
measures evaluation.
In general, a qualitative assessment of similarity measures is achieved
in terms of calculating correlation between two sets of rating, i.e., estimated
similarity measures and human judgment. The correlation refl ects the
noisiness in the linear relationship between human judgment and estimated
similarity measures and essentially means that higher scores on human
judgment tend to be paired with higher scores on estimated values and
analogously for lower scores. It varies in the interval [-1,1]. The formal
defi nition of the correlation ( r ) between human judgment ( HJ ) and estimated
similarity values ( v ) is given as follows:

ே

തതതത
ߪ ு௃ ቇ ܰെͳ ෍ቆ ܪܬ ௜ െܪܬ

ͳ

൬ ݒ ௜ െݒ ҧ

ߪ ௩ ൰
where N is the total number of pairs of words (or concepts), HJ , v are the
means of HJ , and v , respectively, and U HJ , U v are the standard deviation as
follows:

ݎൌ

௜ୀଵ

ߪ ு௃ ൌඨ ͳ

ே

തതതത ሻ ଶ

ܰ ෍ ሺܪܬ ௜ െܪܬ

௜ୀଵ

ߪ ௩ ൌ ඨ ͳ

ே

ܰ ෍ ሺݒ ௜ െݒҧሻ ଶ

௜ୀଵ

In the following analysis, we refer to the set of human judgment rates
indicated in our previous work (Formica and Pourabbas 2009) . This set of
values has been established by asking 24 students to assess the similarity
among all pairs of geographic classes (shown in Fig. 2). They were asked
to assign a similarity score, on a scale of 0 to 1, to each 42 pairs of classes.
In Table 3, second column, for each pair the average of values of human
judgment ( HJ ) is shown.
In the same table the similarity values obtained according to Lin ,
Dice , MDSM v , MDSM c , tSim , GSim v , and GSim c are illustrated. Note that as
anticipated, MDSM and GSim are based on the variability and commonality
measures. Hence, in this experiment, the weights are w part =0.474 ( w att =0.526),
and w c part =0.558 ( w c att =0.442). Note that these weights are computed by
applying Eq. (5) and Eq. (6) and the number of occurrences of attributes
and parts are 25, and 17, respectively.