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XML Data Clustering: An Overview · 27
integer a > 0. The level similarity, Sim L1,L 2
, between two level representations is:
Sim L1,L 2
= 0.5 × ∑ M−1
i=0 c1 i × aM−i−1 + 0.5 × ∑ M−1
∑ M−1
k=0 t k × a M−k−1
j=0 c2 j × aM−j−1
where c 1 i denotes the number of common elements in level i of L 1 and some level of
L 2 , where c 2 j denotes the number of common elements in level j of L 2 and some level
of L 1 during the matching process, t k denotes the total number of distinct elements in
the level k of L 1 , and M is the number of levels in the first level structure. Since the
level similarity measure is not transitive, XCLS determines the structural similarity from
the first XML document to the second one and viceversa and chooses the highest value
between the two.
—Clustering/Grouping. In this phase, an incremental clustering algorithm is used to group
the XML documents within various XML sources considering the level similarity. The
clustering algorithm progressively places each coming XML document into a new cluster
or into an existing cluster that has the maximum level similarity with it.
—Evaluation Criteria. The quality of XCLS is evaluated using the standard criteria, such
as the intra- and inter-cluster similarity, purity, entropy, and FScore. The scalability
of the XCLS system is also evaluated to validate its space and time complexity. Since
XSLC uses an incremental clustering algorithm that avoids the need of pairwise comparison,
it has a time complexity of O(NKdc), where c is the number of distinct elements
in clusters. Experimental evaluation indicates that XCLS achieves a similar quality result
as the pairwise clustering algorithms in much less time. However, XCLS lacks a
unified clustering framework that can be applied efficiently both to homogeneous and
heterogenous collections of XML documents.
6.1.2 XEdge. XML documents Clustering using Edge Level Summaries (XEdge) [Antonellis
et al. 2008] represents a unified clustering algorithm for both homogeneous and
heterogenous XML documents. Based on the type of the XML documents, the proposed
method modifies its distance metric in order to adapt to the special structure features of
homogeneous and heterogeneous documents.
—Data Representation. Like XCLS, XEdge represents XML documents as ordered data
trees where leaf nodes represent content values. Instead of summarizing the distinct
nodes as XCLS, XEdge introduces the LevelEdge representation, which summarizes all
distinct parent/child relationships (distinguished by a number associated to each edge as
shown in Fig. 11(a)) in each level of the XML document, as shown in Fig. 11(c). The
distinct edges are first encoded as integers and those integers are used to construct the
LevelEdge representation.
—Similarity Computation. In order to compute the similarity among XML documents,
XEdge proposes two similarity measures to distinguish between similarity computation
among homogeneous XML documents and similarity computation among heterogeneous
ones. Assuming that homogeneous XML documents are derived from sub-
DTDs of the same DTD, XEdge only searches for common edges in the same levels in
both documents. To measure the similarity between two homogeneous XML documents
represented as LevelEdge L 1 and L 2 , it uses the following similarity function:
ACM Computing Surveys, Vol. , No. , 2009.