Transformation (function) | EPFL Graph Search

In mathematics, a transformation is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations. While it is common to use the term transformation for any function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections. When such a narrow notion of transformation is generalized to partial functions, then a partial transformation is a function f: A → B, where both A and B are subsets of some set X. The set of all transformations on a given base set, together with function composition, forms a regular semigroup. For a finite set of cardinality n, there are nn transformations and (n+1)n partial transformations.

Schema matching for structured document transformations

Aïda Boukottaya

This dissertation studies structured document content reuse problem. In structured document content reuse, a document (or a part of document) structured under one schema must be restructured and translated into an instance of a different schema. Thus, a notion tied to structured document reuse problem is that of structure transformations. This is typically attained in real world by writing translators encoded on a case-by-case basis using specific transformation languages. Writing and managing complex transformations programs is time consuming and generally requires programming skills. Many solutions to simplify and automate as much as possible the task of structured document transformation specification and execution have been proposed. Several simpler and highly declarative transformation languages and graphical tools for transformation specifications have been introduced as solutions to avoid programming. These languages and tools are very useful in describing and specifying transformations. However, they still require developers to manually indicate mappings for each source and target pair. The manual generation of mappings is an extremely labor-intensive and error-prone process. To shield users from manually performing this task, we advocate the use of a schema matching process which (semi) automatically finds semantic correspondences, so called mappings, between two heterogeneous schemas. Based on such mappings a transformation generator generates automatically the translation program. In this dissertation, we propose a framework for solving XML schema matching problem. We rely on the extraction of semantic information nested within XML structures. Semantics is first captured by making explicit element names meanings, exploiting several element characteristics including the analysis of XML Schema's designer point of view expressed by the logical organisation of XML content and additional semantic information given by means of features such as datatypes, element constraints and inheritance mechanisms. The proposed framework provides a generic view and formalizes the overall matching process. Our proposed solutions allows to (1) discover semi-automatically an efficient sequence of operations for transforming a source XML schema into a target XML schema using schema matching techniques (2) model discovered mappings and (3) generate automatically the transformation script. Note that the purpose of our work is not to replace the programming languages for XML data translations, but rather to complement them. Experiments we have conducted show that we have been able to achieve good performance for the generation of source-to-target mappings.

EPFL2004

Schema matching for structured document transformations

Aïda Boukottaya

EPFL2004