# Measures

## Path length

A simple node-counting scheme (path). The relatedness score is inversely proportional to the number of nodes along the shortest path between the synsets. The shortest possible path occurs when the two synsets are the same, in which case the length is 1. Thus, the maximum relatedness value is 1.

## Leacock & Chodorow

The relatedness measure proposed by Leacock and Chodorow (lch) is -log (length / (2 * D)), where length is the length of the shortest path between the two synsets (using node-counting) and D is the maximum depth of the taxonomy.

The fact that the lch measure takes into account the depth of the taxonomy in which the synsets are found means that the behavior of the measure is profoundly affected by the presence or absence of a unique root node. If there is a unique root node, then there are only two taxonomies: one for nouns and one for verbs. All nouns, then, will be in the same taxonomy and all verbs will be in the same taxonomy. D for the noun taxonomy will be somewhere around 18, depending upon the version of WordNet, and for verbs, it will be 14. If the root node is not being used, however, then there are nine different noun taxonomies and over 560 different verb taxonomies, each with a different value for D.

If the root node is not being used, then it is possible for synsets to belong to more than one taxonomy. For example, the synset containing turtledove#n#2 belongs to two taxonomies: one rooted at group#n#1 and one rooted at entity#n#1. In such a case, the relatedness is computed by finding the LCS that results in the shortest path between the synsets. The value of D, then, is the maximum depth of the taxonomy in which the LCS is found. If the LCS belongs to more than one taxonomy, then the taxonomy with the greatest maximum depth is selected (i.e., the largest value for D).

## Wu & Palmer

The Wu & Palmer measure (wup) calculates relatedness by considering the depths of the two synsets in the WordNet taxonomies, along with the depth of the LCS. The formula is score = 2*depth(lcs) / (depth(s1) + depth(s2)). This means that 0 < score <= 1. The score can never be zero because the depth of the LCS is never zero (the depth of the root of a taxonomy is one). The score is one if the two input synsets are the same.

## Resnik

The related value is equal to the information content (IC) of the Least Common Subsumer (LCS) (most informative subsumer). This means that the value will always be greater-than or equal-to zero. The upper bound on the value is generally quite large and varies depending upon the size of the corpus used to determine information content values. To be precise, the upper bound should be ln (N) where N is the number of words in the corpus.

## Jiang & Conrath

The relatedness value returned by the jcn measure is equal to 1 / jcn_distance, where jcn_distance is equal to IC(synset1) + IC(synset2) - 2 * IC(lcs).

There are two special cases that need to be handled carefully when computing relatedness; both of these involve the case when jcn_distance is zero.

In the first case, we have ic(synset1) = ic(synset2) = ic(lcs) = 0. In an ideal world, this would only happen when all three concepts, viz. synset1, synset2, and lcs, are the root node. However, when a synset has a frequency count of zero, we use the value 0 for the information content. In this first case, we return 0 due to lack of data.

In the second case, we have ic(synset1) + ic(synset2) = 2 * ic(ics). This is almost always found when synset1 = synset2 = lcs (i.e., the two input synsets are the same). Intuitively this is the case of maximum relatedness, which would be infinity, but it is impossible to return infinity. Insteady we find the smallest possible distance greater than zero and return the multiplicative inverse of that distance.

## Lin

The relatedness value returned by the lin measure is a number equal to 2 * IC(lcs) / (IC(synset1) + IC(synset2)). Where IC(x) is the information content of x. One can observe, then, that the relatedness value will be greater-than or equal-to zero and less-than or equal-to one.

If the information content of any of either synset1 or synset2 is zero, then zero is returned as the relatedness score, due to lack of data. Ideally, the information content of a synset would be zero only if that synset were the root node, but when the frequency of a synset is zero, we use the value of zero as the information content because of a lack of better alternatives.

## Adapted Lesk (Extended Gloss Overlaps)

The Extended Gloss Overlaps measure (lesk) works by finding overlaps in the glosses of the two synsets. The relatedness score is the sum of the squares of the overlap lengths. For example, a single word overlap results in a score of 1. Two single word overlaps results in a score of 2. A two word overlap (i.e., two consecutive words) results in a score of 4. A three word overlap results in a score of 9.

## Gloss Vector

The Gloss Vector measure (vector) works by forming second-order co-occurrence vectors from the glosses or WordNet definitions of concepts. The relatedness of two concepts is determined as the cosine of the angle between their gloss vectors. In order to get around the data sparsity issues presented by extremely short glosses, this measure augments the glosses of concepts with glosses of adjacent concepts as defined by WordNet relations.

## Gloss Vector (pairwise)

The Gloss Vector (pairwise) measure (vector_pairs) is very similar to the "regular" Gloss Vector measure, except in the way it augments the glosses of concepts with adjacent glosses. The regular Gloss Vector measure first combines the adjacent glosses to form one large "super-gloss" and creates a single vector corresponding to each of the two concepts from the two "super-glosses". The pairwise Gloss Vector measure, on the other hand, forms separate vectors corresponding to each of the adjacent glosses (does not form a single super gloss). For example separate vectors will be created for the hyponyms, the holonyms, the meronyms, etc. of the two concepts. The measure then takes the sum of the individual cosines of the corresponding gloss vectors, i.e. the cosine of the angle between the hyponym vectors is added to the cosine of the angle between the hlonym vectors, and so on. From empirical studies, we have found that the regular Gloss Vector measure performs better than the pairwise Gloss Vector measure.

## Hirst & St-Onge

This measure (hso) works by finding lexical chains linking the two word senses. There are three classes of relations that are considered: extra-strong, strong, and medium-strong. The maximum relatedness score is 16.

## Random

The relatedness values are simply randomly generated numbers. This is intended only to be used as a baseline.