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10 · Alsayed Algergawy et al.
—parent-child (induced) relationships, that is the relationship between each element node
and its direct subelement/attribute/text node;
—ancestor-descendant (embedded) relationships, that is the relationship between each element
node and its direct or indirect subelement/attribute/text nodes;
—order relationships among siblings.
The tree-based representation of XML data introduces some limitations for the presentation
of these relationships. For example, association relationships that are structural relationships
specifying that two nodes are conceptually at the same level, are not included in
the tree representation. Association relationships essentially model key/keyref and substitution
group mechanisms. As a result, another tree like structure, such as directed acyclic
graphs, is used [Boukottaya and Vanoirbeek 2005]. Fig. 4(a) represents a substitution
group mechanism, which allows customer names to be in an English or a German style.
This type of relationship can not be represented using the tree representation. It needs a
bi-directional edge, as shown in Fig. 4(b).
(a) Substitution group example.
(b) Data graph.
Fig. 4: Graph representation of an XML schema part.
3.2 Vector-based representation
The Vector Space Model (VSM) model [Salton et al. 1975] is a widely used data representation
for text documents. In this model each document is represented as a feature vector
of the words that appear in documents of the data set. The term weights (usually term
frequencies) of the words are also contained in each feature vector. VSM represents a text
document, doc x , using the document feature vector, d x , as [Yang et al. 2009]
d x = [d x(1) , d x(2) , ..., d x(n) ] T , d x(i) = TF(ρ i , dox x ).IDF(ρ i )
where TF(ρ i , doc x ) is the frequency of the term ρ i of doc x , IDF(ρ i ) = log(
DF(ρ ) i)
is the inverse document frequency of the term ρ i for discounting the importance of the
frequently appearing terms, |D| is the total number of documents, DF(ρ i ) is the number
of documents containing ρ i , and n is the number of distinct terms in the document set.
Applying VSM directly to represent semi-structured documents is not desirable, as the
document syntactic structure tagged by their XML elements will be ignored.
XML data generally can be represented as vectors in an abstract n-dimensional feature
space. A set of objects can be extracted from an XML data. Each object has a set of
features, where each feature is associated with a domain to define its allowed values. The
ACM Computing Surveys, Vol. , No. , 2009.
|D|