IEEE Systems, Man and Cybernetics Magazine - April 2022 - 32

thus attracting intense research
interests from scholars. The
Resource Description Framework
(RDF) describes knowledge in the
form of subject-predicate-object
triples and interpreted as directed
labeled graphs. However, the graph
structure doesn't have flexible
operability and direct computability
in the theoretical framework,
although it can be understood intuitively.
Therefore, we proposed a
tensor-based knowledge analysis
framework in this article, which
suppor ts
the representat ion,
The performance
of all subsequent
knowledge
technology
processes depend
heavily on whether
the knowledge
representation is
expressive and
effective.
fusion, and reasoning of knowledge
graphs. First, we employ
Boolean tensors to represent heterogeneous
knowledge graphs completely. Then, we present
a series of graph tensor operations for the
modification, extraction, and aggregation of high-order
knowledge graphs. Furthermore, we perform tensor
1-mode product operation between the knowledge graph
representation tensor and the entity representation tensor
to obtain the relation path tensor, so as to infer the relationship
between any two entities. Finally, we demonstrate
the practicality and effectiveness of the proposed model by
implementing a case study.
Background
With the popularization of mobile terminals and the
deepening of network applications, especially the development
of technologies such as the Internet, big data,
cloud computing, and the Internet of Things (IoT), people
have become the most sensitive social sensors [1],
[2]. By further incorporating social information, the
cyberphysical-social systems evolve rapidly into more
complex systems that integrate human, machine, and
information, that is, CPSS. In CPSS, the seamless connection
of IoT, the large-scale deployment of heterogeneous
sensors, and the rapid development of existing
computing power, storage space, and network bandwidth
Predicate
(e1, r1, e3)
(e2, r2, e1)
(e3, r3, e2)
e3
r1
e1
r2
r3
e2
r1
r2
r3
(a)
(b)
Subject/Object
e1
e2
e3
have led to the geometric growth
of digital information and further
facilitated CPSS big data formation
[3], [4]. The CPSS big data
exhibits characteristics of being
enormous in quantity, uneven in
quality, updated in real time, and
manifold in data sources; thus, it
is difficult to intuitively manage
and uti l ize these data, which
attracts many scholars to devote
themselves to the effective processing
of data [5], [8]. They commit
to discovering and extracting
semantic information and valuable
knowledge from data of different
sources and di fferent
structures and storing it in the
XG (3, 3, 2) = 1
Figure 1. The examples of the RDF data model and the tensor data
model: (a) RDF and (b) tensor.
32 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE April 2022
knowledge graph. Therefore, more standardized and
high-quality data lives in the knowledge graph, which
builds the bridge from massive data that is generated by
the interaction and communication between various
objects to smart applications and services [9], [10].
The concept of knowledge graph became widely popular
when it was delivered by Google's search engine [6] in 2012.
Over recent years, many large-scale knowledge bases have
emerged, such as YAGO, DBpedia, FreeBase, and so on,
which are built to provide users with intelligent services in
CPSS including semantic search, assisted intelligent question
and answer, explainable artificial intelligence, and so
on [7]. The primary task in the knowledge graph, knowledge
representation, plays an influential role since the performance
of all subsequent knowledge technology processes
depend heavily on whether the knowledge representation is
expressive and effective. Web Ontology Language and RDF
schema are utilized by the World Wide Web Consortium for
representing information on the web. They are the extensions
of the RDF in the data model and logical structure.
RDF describes knowledge in the form of subject-predicateobject
triples, denoted by (s, p, o) for convenience. As
shown in Figure 1(a), the triples are visualized in a directed
labeled graph. It can be concluded that s, p, and o are treated
in a different way, namely, the subject
and object are interpreted as nodes, while
the predicate is interpreted as edges. What's
more, the graph structure doesn't have flexible
operability and direct computability in
the theoretical framework, although it can
be understood intuitively.
In recent years, many scholars have carried
out a lot of theoretical research and
practical exploration in the efficient representation
and calculation of multisource
heterogeneous big data [13]. As an extension
of vector and matrix, tensor, also
known as a multiway array, is a powerful

IEEE Systems, Man and Cybernetics Magazine - April 2022

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