Hello,
I am looking for a suitable estimate of semantic similarity (between two words) which is based on comparison of two binary vectors (each word has a vector of "0s" and "1s" where each 0 or 1 represents association or dissociation with/from a semantic feature).
E.g. (the 10 columns represent 10 semantic features)
Word A: 0-0-0-0-0-1-1-1-1-1
Word B: 0-1-1-0-0-0-0-1-1-1
The problem with the common metrics (such a correlation) is that if the both words are dissociated from a feature (e.g. first column = 0 for both), this is counted as "match", so the similarity is increased. An extreme case, if the two vectors are composed of 0s only, the correlation is r = 1 even thou there is no overlapping semantic feature.
So, I would need a measure of similarity that increases with matching features (a column for both words is 1),decreases with mismatching features (one word has 1 and the other 0 in a column or vice versa), and does nothing when both words do not match to a semantic feature (two 0s).
Thank you for any advice!
Martin
Dear Chris,
I would really appreciate that, thank you!
However, I thought this could actually be done with following formulas:
1) compute "similarity" = sum of products of the two vectors (thus 1*1 = 1, 0*1 = 0 etc, sum it for each column). This satisfies the first condition.
2) compute "dissimilarity" = absolute value of the sum of differences between the two vectors = Sum(Abs(col_wordA_1 - col_wordB_1)). Thus only 01 or 10 gives nonzero value.
3) Compute contrast = "similarity - dissimilarity"
In case of the example in the first post, contrast would be 3 - 4 = -1
Does it make sense?
M.
Hi Martin,
It looks like you're describing the dot product (or inner product) of binary vectors as the measure of similarity (in your answer to Chris), and that the Manhattan distance (aka l_1 distance) could serve as the measure of dissimilarity.
--John
The problem as I see it is providing a definition of "semantic feature". Reducing these features to "present/not present" would also be a difficult project.
The shared absence of a feature would definitely be a problem. Given any reasonable assessment of what might or might not be a semantic feature, the set of shared absent features is likely to be roughly infinite.
Another major problem is that attributes that may be considered "semantic" in one language are considered "inflectional" or "syntactic" in another. Consider the genitive or possessive language attribute. Is belonging to someone a semantic feature? Does this determination change based on whether the indicator of possession is indicated by a change of an internal sound, by the attachment of additional sounds, or by the presence of an additional word that indicates that entity represented by the word preceding the added possessive-marker word belongs to the entity represented by the following word?
Are size, shape, and location semantic features? Does it matter whether location is fully or partially represented by whether an entity is the direct object or indirect object of the statement? If one language distinguishes by inflection whether an object is able to be held in a person's hands and by another inflection that the object is too large to be held in a person's hands while in another language the size is expressed by an separate adjective, but one that doesn't explicitly make the distinction between "able to be held/not able to be held"?
These are issues that have been worked on, in modern scholarly form, for several hundred years, and by various intellectual exchanges for at least as long as language has existed. Finding a semantic feature that can't be decomposed into smaller semantic features, and therefore indicated by a single binary choice independent of the rest of the contents of the universe and human mind, would be quite remarkable.