Abstract

A general method is presented to construct ordered similarity measures (OS-measures), i.e., similarity measures for ordered sets of documents (as, e.g., being the result of an IR-process), based on classical, well-known similarity measures for ordinary sets (measures such as Jaccard, Dice, Cosine or overlap measures). To this extent, we first present a review of these measures and their relationships.

The method given here to construct OS-measures extends the one given by Michel in a previous paper so that it becomes applicable on any pair of ordered sets. Concrete expressions of this method, applied to the classical similarity measures, are given.

Some of these measures are then tested in the IR-system Profil-Doc. The engine SPIRIT^© extracts ranked document sets in three different contexts, each for 550 requests. The practical usability of the OS-measures is then discussed based on these experiments.

Article Outline

1. Introduction

1.1. General note on the interpretation of these similarity measures for the comparison of vectors

2. General properties of similarity measures (on ordinary sets)

3. Ordered similarity measures (OS-measures)

3.1. Statement of the problem

3.2. General theorem on the construction of strong OS-measures

3.3. Strong OS-measures derived from strong similarity measures for ordinary sets

3.3.1. Jaccard

3.3.2. Dice

3.3.3. Generalized Dice

3.3.4. Cosine

3.3.5. The measure N

3.3.6. The overlap measure O₂

4. Experimentation

4.1. Presentation of the context

4.2. Tested OS-measures

4.3. Analysis

4.4. Results

4.4.1. Impact of weight function

4.4.2. Impact of the classical similarity indicator

4.4.3. Impact of the query type

5. Conclusion

Appendix A

References