IEEE Systems, Man and Cybernetics Magazine - April 2022 - 37

knowledge graphs. Without loss
of generality, we do not specify
any specific entity and relation,
but represent them by e and r. In
the illustrated example, the reasoning
task is set to reason about
the relationship between entities
e1
and e .3
Tensor-Based Knowledge
Representation and Fusion
First, according to the proposed
method in the " Tensor Representation "
section, the knowledge graph
G1
and G2
G1
!
in Figure 4(a) and Figure
4(b) are represented by tensors
XR332
##
and XR .333
##
G2
!
Then, the fused knowledge graph is obtained by graph
tensor operations according to the " Intragraph Operations "
section. In this example, we conduct graph tensor
union operation between XG1
fused representation tensor XG
and XG2
with size
55 .3## The relation slices are shown in
Figure 4(d).
E
Tensor-Based Knowledge Reasoning
The entity representation tensor of e1
is shown in Figure 5(a). In our example,
e1
is contained in the triple ,,
,,
.
^h
er e11 2
and acts as subject; thus, the ele -
ment
E 12 11=^h After performing
XE :, :,1
G 1# ^h according to (1), we obtain
the 2-hop relation path tensor P with size
35 ,3## which is presented in Figure 5(b).
The first order denotes the 1-hop relation
and the third denotes the 2-hop relation
as marked in Figure 5(b). Therefore, the
element
P ,,
tion path
ee .13
12
""
13 21=
rr
r4
e2
r1
×
^h indicates the relaThe
more detailed
calculation process about the relation
path can be seen in the first example in
Figure 6. We also show more examples in
Figure 6 to make the computation of
relation paths easier to understand.
We take the r1
and r2
basis of the relation path
the knowledge graph tensor XG
rr
ee .13
12
""
trated in Figure 7, RR R12
P
relation slices of
on the
As illus=
# and the entity
pairs in the matrix have the same
relation path, which implies that these
ent ity pairs are most
l ikely to have
t he same relationship. Specifical ly,
R ,13 1
P^h= and R ,
and e3
and e .5 Finally, from X 35 31,
,,
P 35 1=^h mean that we
can infer the relationship between the target
entities e1
through the entities e3
G^h= we
r4
e4
e4
×
(e4, r3, e2)
r3
(e4, r1, e2)
r1
e2
×
(e2, r2, e3)
r2
r1
=
e2
= r4
e2
r3
Figure 6. Some examples of calculation of relation paths.
r e11
e1
e2
e3
e4
e5
e2 e3 e4 e5
1
×
1
r2 e e e e4321
e4
e3
e2
e1
e5
R1 = XG (:, :, 1)
R1 = XG (:, :, 2)
Figure 7. The multiplication of relation slices.
April 2022 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 37
1
1
e5
=
e4
e3
e2
e1
e5
RP
e e e e4321
1
e5
r1
r1
×
(e2, r2, e3)
r2
XG
r1
=
e3
= r4
e3
r2
e1 → e4 → e2
r1
r1
r2
e1 → e2 → e3
r4
r2
P
Relation Path
r1
r2
e1 → e2 → e3
and obtain the
Knowledge graphs
are directed graphs,
and the relationship
direction between
entities has specific
semantic information,
so the relationship
direction cannot
be ignored.
infer that the relation between
entities e1
and e2
may be .r3
Conclusion
With the in-depth integration of
cyber, physical, and social spaces,
the data in the CPSS are growing
explosively at unprecedented
speed, and the relat ionship
between entities has also changed
from a traditional single view to
multiple views, which further
accelerates the formation of highorder
knowledge graphs with complex
association relationships.
How to effectively manage and
process the knowledge from multisource-related
data to further promote artificial intelligence
decision making has become an important research
task. This article proposes a set of integrated tensorbased
knowledge analysis methods, including the
e1 → e4 → e3
r4
r3
1
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