# The limits of Web metadata, and beyond

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5 The first round of tests was done setting the size n of the Web region to 200, and the number m of Web objects that the users had to classify to 20 (which corresponds to the 10% of the total considered Web objects). Various tests were performed, in order to study the effectiveness of the method with the varying of the parameter p. We run the judgment test for each of the following percentages p of classified Web objects: p=2.5%, p=5%, p=7.5%, p=10%, p=15%, p=20%, p=30%, p=40%, p=50%, p=60%, p=70%, p=80% and p=90%. The final average results are shown in the following table: p: 2.5% 5% 7.5% 10% 15% 20% 30% 40% 50% 60% 70% 80% 90% judgment: Average judgments in the n=200 case. The data are graphically summarized in the following chart, where an interpolated spline is used to better emphasize the dependency between the percentage p of already classified Web objects and the obtained judgment j (here, the diagonal magenta dotted line indicates the average judgment in the original case without back-propagation): As we can see, there is an almost linear dependence roughly from the value of p=20% on, until the value of p=70% where the judgment starts its asymptotic deviation towards the upper bound. The behaviour is also rather clear in the region from p=5% to p=20%: however, since in practice the lower percentages of p are also the more important to study, we run a second round of tests specifically devoted to this zone of p values. This time, the size of the Web region was five times bigger, setting n=1000, and the value m was set to 20 (that is to say, the 2% of the Web objects). Again, various tests were performed, each one with a different value of p. This time, the granularity was increased, so that while in the previous phase we had the values of p=2.5%, p=5%, p=7.5%, p=10%, p=15%, p=20%, in this new phase we also run the tests for the extra cases p=12.5% and p=17.5%, so to perform an even more precise analysis of this important zone. The final average results are shown in the next table:

6 p: 2.5% 5% 7.5% 10% 12.5% 15% 17.5% 20% judgment: Average judgments in the n=1000 case. It can be seen as these new, more precise data essentially confirm the previous analysis performed with the more limited size n=200. In the next chart, we again present an interpolated spline for this second round of tests (represented in green), and also overimpose the curve obtained in the first round (represented as a dashed curve, again in red), so to better show the connections: Therefore, the results we have obtained show that: When employing a particular metadata classification for the Web, even when the percentage of classified Web objects is relatively small, usage of the back-propagation method can significantly help the effectiveness of the classification, thus helping the metadata to get more and more widespread, especially in the initial crucial phases when the number of classified objects will be extremely limited. The experimentation can help to answer the fundamental question: what is the minimum "critical mass" that a general WWW metadata classification needs to reach in order to be really useful? If we fix the level of decency of metadata to a judgment level of 50, then by reverse interpolation we obtain that a reasonable prediction for the critical mass is roughly 16%. Thus, in order for a general WWW metadata classification to be really useful, at least 16% of the WWW (or of the local WWW zone we are considering) should be classified. Note that, without back-propagation, the critical mass would grow up to 50%. Analogously, we can predict what is the percentage metadata needs to have in order to reach an "excellence level": if we fix such a level at 80, then by reverse interpolation we obtain a value of 53%; so, using the back-propagation method we can reach an excellence level when slightly more than half of the WWW (or of the local WWW zone we are considering) has been classified. The interpolations we have given also give an indication on how the situation is in the transitory phase before the

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