Subsumption Using the Closest KA DG

The closest knowledge anchor

v

_KA is used to subsume new entities and to generate transition narratives in the exploration path. Table 6.1, describes the types of transition narratives and corresponding scripts used between entities of an exploration path.

Table 6.1. Narrative types of transitions between entities in an exploration path

Narrative Type From_ entity To_ entity Description Output script (From_ entity, Narrative

type, To_entity) Illustrative example 1

N

v

s

v

KA s

v

is subclass of KA

v

“You may find it useful to know that vs belongs to a

familiar and well-known class – vKA. Let's explore vKA.” 2

N

v

s

v

KA s

v

is superclass of KA

v

“You may find it useful to know that there is a well-

known class – vKA that

belongs to vs .

Let's explore vKA.”

3

N

v

_s

v

_KA

v

sand _are

v

KA

siblings

“You may find it useful to know that vs is similar to a

well-known class – vKA. Let's explore vKA.” 4

N

v

KA

v

KA KA v is subclass of KA

v

and superclass of s

v

“You may find it useful to know that v′KA belongs to

vKA, and vs belongs to v′KA. Let's explore v′KA.” 5

N

v

_KA

v 

KA KA v  is subclass of KA

v

and not superclass of s

v

“You may find it useful to know that vʺKA belongs to

vKA.

Let's explore vʺKA.”

Algorithm 6.2 describes our approach for generating exploration paths following Ausubels’ subsumption theory for meaningful learning (described in Section 2.7.2), where the closest knowledge anchor is used to subsume subordinate entities (i.e. subclass of

v

_KA). The narrative types (N1, N2, …, N5) used correspond to the narratives types in Table 6.1.

Algorithm 6.2: Subsumption Using the Closest KADG

Input:DGV,E,T, vs ,V vKAKADG, m = length of exploration path, e = rdfs:subClassOf

Output: an exploration path P of length m.

1. P:{}; //empty exploration path P 2. if vs,e,vKA then //vs is subclass of vKA

3. Pvs,script(N₁),vKA; //insert transition narrative from vs to vKA using N1

4.

m

; //reduce length of P by one

5. V _KAis set of all vKA:vs,e,vKAvKA ,e,vKA //intermediate classes between vs and vKA 6. Q:{} ; //list for storing intermediate classes between vs and vKA

7. QsortDepth(VKA ); //sort classes in V KA in ascending order from least depth

8. for (i:1 ; i |Q| m0 ; i) //start subsuming classes that are in Q

9. PvKA,script(N4),Q[i]; //insert transition narrative from vKA toQ[i]using N4 10. m; //reduce length of P by one

11. end for;

12. else if

v

_KA

,e,v

_s



then //vs is superclass of vKA

13. Pvs,script(N2),vKA; //insert transition narrative from vs to vKA using N2

14. m; //reduce length of P by one

15. else ifvs,e,vivKA,e,vi then //vs and vKA are siblings 16. Pvs,script(N3),vKA; //insert transition narrative from vs to vKA using N3

17. m; //reduce length of P by one

18. end if;

19. V KA is set of all

v

KA



:v

KA



,e,v

KA

v

KA



Q

//subclasses of vKA that are not in listQ

20. Q:{} ; //list for storing subclasses of vKA that are not in listQ

21. QsortDepthDensity(V_KA); //sort classes in V _KA based on depth and density

22. for (j:1 ; j |Q| m0 ; j) do //start subsuming classes that are in Q  23.

Pv

_KA

,script(N

₅

),Q[j];

//insert transition narrative from vKA toQ [ j]using N5

24. m; //reduce length of P by one

25. end for;

The algorithm takes a data graph DG, the first entity

v

_s, the closest knowledge anchor

KA

v

, the length of the exploration path (m), and the edge label e = rdfs:subClassOf as an input, and generates an exploration path P of length m. The algorithm starts by initialising

an empty exploration path P (line 1) used to store m transition narratives. Then the algorithm starts identifying the relationship type between

v

_s and v_KA.

If

v

_s is subclass of v_KA (lines 2), then the following steps are conducted:

 The transition narrative

v

_s

,script(N

₁

),v

_KA



from

v

_s to vKA is inserted into P (line 3) where the function script(N1) retrieves the script output for narrative type N1 from Table 6.1. The length of exploration path m is decreased by one (line 4).

 The algorithm in (line 5) identifies the set of intermediate class entities (V _KA) between

s

v

and v_KA, using the following SPARQL query:

SELECT distinct ?intermediate WHERE {

v

s rdfs:subClassOf ?intermediate . ?intermediate rdfs:subClassOf

v

KA .}

 A list Q is created in (line 6), and the functionsortDepth ()sorts the class entities

KA KA

V

v





based on their depths starting from the least depth class entity (i.e. direct subclass of v_KA) to highest depth in ascending order, and inserts the sorted class entities into list

Q

(line 7). The function sortDepth ()identifies the depth of a class entity

v

_KA via the following SPARQL query:

SELECT (count(?intermediate)-1 as ?depth) WHERE {

v

KA rdfs:subClassOf ?intermediate. ?intermediate rdfs:subClassOf r .}

where r is the root entity in the data graph.

 The algorithm in (lines 8 – 11) uses the closest knowledge anchor

v

KAto subsume the class entities

Q

. The transition narrative v_KA,script(N₄),Q[i] from v_KA to

Q[i]

(i.e. v_KA) is inserted into P (line 9) where the function script(N4) retrieves the script output for narrative type N4 from Table 6.1. The length of exploration path m is decreased by one (line 10).

If

v

_s is superclass of vKA (lines 12), then the transition narrative vs,script(N2),vKA from

v

_s to v_KAis inserted into P (line 13) where the function script(N2) retrieves the script output for narrative type N2 from Table 6.1. The length of exploration path m is decreased by one (line 14). If

v

_s and v_KA are siblings (i.e. share same superclass) (line 15), then the

transition narrative

v

_s

,script(N

3

),v

_KA



from

v

s to vKA is inserted into P (line 16) where the function script(N3) retrieves the script output for narrative type N3 from Table 6.1. The length of exploration path m is decreased by one (line 17).

After identifying the relationship between

v

_s and

v

_KA, the following steps are conducted:

 Identify the set of subclass entities (V _KA) of

v

_KA which do not belong to

Q

(line 19). A list

Q

is created in (line 20), and the function sortDepthD ensity() sorts the class entities

v

_KA



V

_KA



based on two their depths and density, as the following steps: (i) Identify the depth of the class entities (similar to function

sortDepth()

described

above).

(ii) Identify the density (using degree centrality) of the class entities based on number of subclasses.

(iii) Sort the class entity starting from the least depth (i.e. direct subclasses of v_KA) to highest depth in ascending order, and from highest density to least density (i.e. first sort using depth, if two or more entities are at the same depth, then sort these entities based on their density from highest to lowest). The sorted class entities are inserted into list Q (line 21).

 The algorithm in (lines 22 – 25) uses the closest knowledge anchor v_KA to subsume the class entities in Q. The transition narrative vKA,script(N5),Q[j] from vKA to Q [ j] (i.e. v _KA) is inserted into P (line 23) where the function script(N5) retrieves the script output for narrative type N5 from Table 6.1. The length of exploration path m is decreased by one (line 24). Implementation example of the algorithm is here57_.

In the next section, we will provide several illustration examples for generating exploration paths in the data graphs of the two application context of this research: MusicPinta and L4All.

In document Intelligent Support for Exploration of Data Graphs (Page 123-126)