Abstract
In some application areas, similarities and distances are used to calculate how similar two objects are in order to use these measurements to find related objects, to cluster a set of objects, to make classifications or to perform an approximate search guided by the distance. In many other application areas, we require patterns to describe similarities in the data. These patterns are usually constructed through generalisation (or specialisation) operators. For every data structure, we can define distances. In fact, we may find different distances for sets, lists, atoms, numbers, ontologies, web pages, etc. We can also define pattern languages and use generalisation operators over them. However, for many data structures, distances and generalisation operators are not consistent. For instance, for lists (or sequences), edit distances are not consistent with regular languages, since, for a regular pattern such as *a, the covered set of lists might be far away in terms of the edit distance (e.g. bbbbbba and aa). In this paper we investigate the way in which, given a pattern language, we can define a pair of generalisation operator and distance which are consistent. We define the notion of (minimal) distance-based generalisation operators for lists. We illustrate positive results with two different pattern languages.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bowers, A.F., Giraud-Carrier, C.G., Lloyd, J.W.: Classification of individuals with complex structure. In: Proc. of the 17th International Conference on Machine Learning (ICML 2000), pp. 81–88. Morgan Kaufmann, San Francisco (2000)
Edgar, G.A.: Measure, Topology and Fractal Geometry. Springer, Heidelberg (1990)
Estruch, V.: Bridging the gap between distance and generalisation: Symbolic learning in metric spaces. PhD Thesis, DSIC-UPV (2008), http://www.dsic.upv.es/~vestruch/thesis.pdf
Estruch, V., Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J.: Distance based generalisation. In: Kramer, S., Pfahringer, B. (eds.) ILP 2005. LNCS (LNAI), vol. 3625, pp. 87–102. Springer, Heidelberg (2005)
Estruch, V., Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J.: Distance based generalisation for graphs. In: Proc. Work. of Machine and Learning with Graphs, pp. 133–140 (2006)
Estruch, V., Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J.: Minimal distance-based generalisation operators for first-order objects. In: Muggleton, S.H., Otero, R., Tamaddoni-Nezhad, A. (eds.) ILP 2006. LNCS (LNAI), vol. 4455, pp. 169–183. Springer, Heidelberg (2007)
Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J.: Incremental learning of functional logic programs. In: Kuchen, H., Ueda, K. (eds.) FLOPS 2001. LNCS, vol. 2024, pp. 233–247. Springer, Heidelberg (2001)
Hamming, R.W.: Error detecting and error correcting codes. Bell System Technical Journal 26(2), 147–160 (1950)
Hernández-Orallo, J., Ramírez-Quintana, M.J.: Inverse narrowing for the induction of functional logic programs. In: 1998 Joint Conference on Declarative Programming, APPIA-GULP-PRODE 1998, A Coruña, Spain, July 20-23, pp. 379–392 (1998)
Hernández-Orallo, J., Ramírez-Quintana, M.J.: A strong complete schema for inductive functional logic programming. In: Džeroski, S., Flach, P.A. (eds.) ILP 1999. LNCS (LNAI), vol. 1634, pp. 116–127. Springer, Heidelberg (1999)
Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Doklady 10, 707–710 (1966)
Lloyd, J.W.: Learning comprehensible theories from structured data. In: Mendelson, S., Smola, A.J. (eds.) Advanced Lectures on Machine Learning. LNCS (LNAI), vol. 2600, pp. 203–225. Springer, Heidelberg (2003)
Muggleton, S.H.: Inductive logic programming: Issues, results, and the challenge of learning language in logic. Artificial Intelligence 114(1-2), 283–296 (1999)
Olsson, R.: Inductive functional programming using incremental program transformation. Artifificial Intelligence 74(1), 55–81 (1995)
Rissanen, J.: Hypothesis selection and testing by the MDL principle. The Computer Journal 42(4), 260–269 (1999)
Schmid, U.: Inductive synthesis of Functional Programs-Universal Planning, Folding of Finite Programs, and Schema Abstraction by Analogical Reasoning. Springer, Heidelberg (2003)
Swamidass, S.H., Chen, J., Bruand, J., Phung, P., Ralaivola, L., Baldi, P.: Kernels for small molecules and the prediction of mutagenecity, toxicity and anti-cancer activity. Bioinformatics 21, 359–368 (2005)
Rivest, R., Cormen, T.H., Leiserson, C., Stein, C. (eds.): Introduction to Algorithms. MIT Press, Cambridge (2000)
Wallace, C.S., Dowe, D.L.: Minimum Message Length and Kolmogorov Complexity. Computer Journal 42(4), 270–283 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Estruch, V., Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J. (2010). Generalisation Operators for Lists Embedded in a Metric Space. In: Schmid, U., Kitzelmann, E., Plasmeijer, R. (eds) Approaches and Applications of Inductive Programming. AAIP 2009. Lecture Notes in Computer Science, vol 5812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11931-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-11931-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11930-9
Online ISBN: 978-3-642-11931-6
eBook Packages: Computer ScienceComputer Science (R0)