# Multiple retrievals across varying queries

The next step of our construction is to go beyond a single query to consider the performance of a system across a set of queries. It should come as no surprise, given the wide range of activities in which FOA is a crucial component that there is enormous variability among the kinds of queries produced by users.

One obvious dimension to this variability concerns the breadth'' of the query: How general is it? If the set for a query is known, this can be quantified by GENERALITY , comparing the size of \Rel to the total number of documents in the corpus: \beq \mathname{Generality}_q \equiv {\left|\mathname{Rel}_q\right|\over\mathname{NDoc}} \eeq There are many other ways in which queries can vary, and the fact that different retrieval techniques seem to be much more effective on some types of queries than others makes this a critical issue for further research. For now, however, we will treat all queries interchangeably but consider average performance across a set of them.

Figure (figure) juxtaposes two Re/Pre curves, corresponding to two queries. Query 1 is as before while Query 2 is a more specific query, as evidenced by its lower asymptote. Even with these two queries, we can see that in general there is no guarantee that we will have Re/Pre data points at the desired recall level. This necessitates INTERPOLATION of data points at required recall levels. The typical interpolation is done at pre-specified recall levels, for example ${0, 0.25, 0.5, 0.75, 1.0}$. As \vanR{152} discusses, a number of interpolation techniques are available, each with their own biases. Since each new relevant document added to our retrieved set will produce an increase in precision (causing the saw-tooth pattern observed in the graph), simply using the next available data point above a desired recall level will produce an over-estimate, while using the prior data point will produce an under-estimate.

With pre-established recall levels, we can now juxtapose an arbitrary number of queries, and average over them at these levels. For 30 years the most typical presentation of results within the IR community is the 11-POINT AVERAGE curves, like those shown in Figure (figure) [REF563] [Salton68] . (This data happens to show performance on the ADI corpus of Boolean versus weighted retrieval methods, include only the last 10 data points.)

It is not uncommon to see research data reduced even further. For if queries are averaged at fixed recall levels, and then all of these recall levels are averaged together, we can produce a single number that measures retrieval system performance. Note the even more serious bias this last averaging produces, however. It says that we are as interested in how well the system did at the 90% percent recall level as at 10\%!? Virtually all users care more about the first screen full of hits they retrieve than the last.

This motivates another way to use the same basic Re/Pre data. Rather than measuring at fixed recall levels, statistics are collected at the 10, 25, 50 document retrieval levels. Precision within the first 10 or 15 documents is arguably a much closer measure of standard browser effectiveness than any other single number.

All such atempts to boil the full Re/Pre plot are bound to introduce artifacts of their own. In most cases the full Re/Pre curve picture is certainly worth a thousand words. Plotting the entire curve is straight-forward and immediately interpretable, and lets the viewer draw more of their own conclusions.

We must guard against taking our intuitions based on this tiny example (with only 25 documents in the entire corpus) too seriously when considering results from standard corpora and queries. For example, our first query had fully twenty percent of the corpus as relevant; even our second query had eight percent. In a corpus of a million documents, this would mean eighty thousand of them were relevant!? Much more typical are queries with a tiny fraction, perhaps .001% relevant. This will mean that the precision asymptote is very nearly zero. Also, we are likely to have many, many more relevant documents, resulting in a much smoother curve.

FOA © R. K. Belew - 00-09-21