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Resolving power

Zipf observed that the frequency of words' occurrence varies dramatically, and Poisson models explore deviations of these occurrence patterns from purely random processes. We now make the first important move towards a theory of why some words occur more frequently and how such statistics can be exploited when building an index automatically. Luhn, as far back as 1957, said clearly: It is hereby proposed that the frequency of word occurrence in an article furnishes a useful measurement of word significance. [Luhn57] That is, if a word occurs frequently, more frequently than we would expect it to within a corpus, then it is reflecting emphasis on the part of the author about that topic. But the raw frequency of occurrence in a document is only one of two critical statistics recommending good keywords.

Consider a document taken from our AIT corpus, and imagine using the keyword with it. By construction, virtually every document in the AIT is about \term{ARTIFICIAL INTELLIGENCE}!? Assigning the keyword \term{ARTIFICIAL INTELLIGENCE} to any document in AIT would be a mistake, not because this document isn't about \term{ARTIFICIAL INTELLIGENCE}, but because this term can not help us {\em discriminate} one subset of our corpus as relevant to any query. If we change our search task to looking not only in our AIT corpus but through a much larger collection (for example, all computer industry newsletters) then associating \term{ARTIFICIAL INTELLIGENCE} with those articles in our AIT subcorpus becomes a good idea. This term helps to distinguish AI documents from others.

The second critical characteristic of good indices now becomes clear - a good index term not only characterizes a document {absolutely}, as a feature of a document in isolation, but also allows us to discriminate it {\em relative} to other documents in the corpus. Hence keywords are not strictly properties of any single document, but reflect a relationship between an individual document and the collection from which it might be selected.

These two, countervailing considerations suggest that the best keywords will not be the most ubiquitous, frequently occurring terms, nor those that occur only once or twice, but rather those occurring a moderate number of times. Using Zipf's rank ordering of words as a baseline, Luhn hypothesized a modal function of a word's rank he called RESOLVING POWER centered exactly at the middle of this rank ordering. If resolving power is defined as a word's ability to {\em discriminate} content, Luhn assumed that this quantity is maximal at the middle and then falls off at either very high or very low frequency extremes, as shown in Figure (figure) . The next step is then to establish maximal and minimal occurrence thresholds defining useful, mid-frequency index terms. Unfortunately, Luhn's view does not provide theoretical grounds for selecting these bounds, and so we are reduced to the engineering task of tuning them for optimal performance.

We'll begin with the maximal-frequency threshold, used to exclude words that occur too frequently. For any particular corpus, it is interesting to contrast this set of most-common words with the negative dictionary of noise words, defined in Section §2.3.2 . While there may often be great overlap, the negative dictionary list is typically a list that has proven itself to be practically useful across many different corpora, while the most frequent tokens in a particular corpus may be quite specific to it.

Establishing the other, low-frequency threshold is less intuitive. Assuming that our index is to be of limited size, including a certain keyword means we must exclude some other. This suggests that a word that occurs in exactly one document can't possibly be used to help discriminate that document from others regularly. For example, imagine a word -- suppose it is -- that occurs exactly once, in a single document. If we took out that word \term{DERIVATIVE} and put in any other word, for example \term{FOOBAR}, in terms of the word frequency co-occurrence statistics that are the basis of all our indexing techniques, the relationship between that document and all the other documents in the collection will remain unchanged! In terms of overlap between what the word \term{DERIVATIVE} \means, in the FOA sense of what this and other documents are \about, a single word occurrence has no rd occurrence has no ce has no \rikmeaning!

The most useful words will be those that are not used so often as to be roughly common to all of the documents, and not so rare so as to be (nearly) unique to any one (or small set) of documents. We seek those keywords whose combinatorial properties, when used in concert with one another as part of queries, help to compare and contrast topical areas of interest against one another.


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