Erratum: Criteria-Based Approximate Matching of Large-Scale Ontologies

In our recent paper “Criteria-Based Approximate Matching of Large-Scale Ontologies (Liang et al., 2011)” we had the following corrections. We adjusted part of the article without changing the basic content of the paper. We deleted the improperly cited formulas in Section 3 and added some explanatory text in Section 4.

No.

Change

Addition

1

Deleted from P284 line 29 “The formula of node global density Gden (c) is:” to P285 line “distance effects. dis(c, N) is the length of shortest path from c to N.”

Replaced with “The node global density is depend on the number of node c’s direct subclasses, direct superclass and functional relations. Different types of link play different role in density calculation. The node local density criterion favours the densest concept in a local area, for being potentially the most important for this particular part of the ontology.”

2

Deleted from P285 line 14 “formula (4)” to line 17 “formula (5)”

Correspondingly modified the formula label referenced in the text.

3

Added “[4]” in the end of P285 line 19

4

Deleted from P285 line 20 “We define Coverage( S) as the measure of the level of coverage of a set of concepts” to line 32 “formula (8)”

5

Modified P286 “formula (9)” to “formula (2)”, “formula (10)” to “formula (3)”, “formula (11)” to “formula (4)”

Correspondingly modified the formula labels referenced in the text.

6

After P286 line 18 “4 Ontology Modular Partitioning”, added a new paragraph text: “The objective of ontology partitioning is to partitioning monolithic large ontology into a set of significant and mostly self-contained modules in order to allow its easier maintenance and use. We propose a method for automatically partitioning the set of ontology vertices into a set of disjoint clusters. The structural proximities among the vertices in a cluster are high; while those coupling crossing different clusters are low. Each cluster is a sub-part of ontology and the union of all clusters is semantically equivalent to the original ontology O. The partitioning algorithm proposed in this paper is modelling the ontology corresponding hierarchical concept network to complex electric circuit.”

7

Modified P286 “formula (12)” to “formula (5)”, “formula (13)” to “formula (6)”

Correspondingly modified the formula labels referenced in the text.

8

Modified P287 “formula (14)” to “formula (7)”, “formula (15)” to “formula (8)”, “formula (16)” to “formula (9)”, “formula (17)” to “formula (10)”

Correspondingly modified the formula labels referenced in the text.

9

After P287 line 7, added a new paragraph text: “In general Eq. (9) takes O(n3) time to solve a set of equations. However, we can actually cut the time down to O(V +E). We first set V1 = 1; V2 = …= Vn = 0 in O(V) time. Starting from node 3, we consecutively update a node’s voltage to the average voltage of its neighbours, according to Eq. (6). The updating process ends when we get to the last node n. We call this a round. Because any node i has ki neighbours, one has to spend an amount of O(ki) time calculating its neighbour average, thus the total time spent in one round is

${\rm O}(\sum\limits^{n}_{i=3}k_i)$

= O(E). After repeating the updating process for a finite number of rounds, one reaches an approximate solution within a certain precision, which does not depend on the graph size n but only depends on the number of iteration rounds. So no matter how large the graph is, so the total running time is always O(V + E).”