I am reading up on distance and dissimilarity measures for my class on natural language processing and could not understand this slide. Why does the dissimilarity measure not satisfy item 3 ? What would an example be ?

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  • $\begingroup$ To me, it seems point 1 implies point 3. Not sure how you could have a metric that satisfies 1 and not 3. $\endgroup$ – colorlace May 29 '18 at 18:51
  • $\begingroup$ These are the three axioms of metricity (en.wikipedia.org/wiki/Metric_(mathematics)). #3 is the "triangular inequality" axiom. $\endgroup$ – ttnphns May 29 '18 at 19:01
  • $\begingroup$ A note on terminology. Some authors define "distances" as metric dissimilarities. Thence, there are metric dissimilarities (=distances) and nonmetric dissimilarities. Other authors equate "distances" and "dissimilarities" to be synonyms. Thence, for them there are metric and nonmetric dissimilarities (= distances) $\endgroup$ – ttnphns May 29 '18 at 19:06
  • $\begingroup$ Thanks guys. Do you know if there is a page online where I get to see which distance satisfies / does not satisfy the 3 inequalities ? Im trying to select one for my project. So far I have seen that the KL and chi square do not satisfy the triangle inequality. $\endgroup$ – Kong May 29 '18 at 20:52

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