Context Emergence Using Graph Theory
Defining and Modeling Context for Industrial Assets Using Graphs
Bharath Rao and Arila Atanassova-Barnes
GE Software,2623 San Ramon Blvd, San Ramon, CA, USA
rao@ge.com, arila.barnes@ge.com
Keywords: Context, Graph theory, IoT, Industrial Internet, Modeling.
Abstract: Traditionally, context in software is modeled as a global variable, static class, or similar mechanisms that are
initialized when an application is loaded and updated periodically through the lifetime of the application as
the end user interacts with instructions. This approach is limited to customizations, personalization and
initialization based on previously captured, mostly static information. It is a replay of a previous state. In this
paper we propose a new approach to defining and modeling context for software applications using graphs.
Context is fundamentally interaction-based and comes into play when one entity interacts with another to
achieve a goal in a given environment constrained by time and location. By capturing the interactions between
entities in a graph, context becomes emergent rather than declarative and can be learned from user
interactions. The context is discovered by first-degree graph traversal of interacting entities. The discovered
context is used to achieve context sensitive goals in environments with a large number of interconnected
entities such as the Internet of Things (IoT).
1 INTRODUCTION
To support decisions based on goals and actions in
industrial scenarios, it is critical to detect and evolve
context of operational environments in such a way
that the system remains adaptive and dynamic and
can react to changing goals in real time (Loren, 2015).
For the purpose of this paper we start with the
following definition of context: ‘Context is any
information that can be used to characterize the
situation of an entity. An entity is a person, place, or
object that is considered relevant to the interaction
between a user and an application, including the user
and applications themselves.’ (Abowd et al., 1999)
Entities can be modeled as vertices in a graph and
relationships can be modeled as edges. This enables
us to represent any set of relationships as a graph.
Using graph relationships and paths, the use of simple
graph operations enables us to determine context and
leverage it to achieve goals. We present a novel
approach that allows context to emerge organically
based on the entity relationship graph rather than
being explicitly maintained.
2 GRAPH APPROACH TO
CONTEXT
2.1 Information as a Graph
All known information at any given time may be
represented as a graph. The graph itself is made up of
a set of vertices and edges.
=
(
,
)
. (1)
In an open world assumption, all vertices are
presumed to exist and a graph can simply be defined
as a set of edges bounded by two vertices. Such a
graph can be described as a directed, labeled multi-
graph. Such multi-graphs may be modeled as a set of
triples (W3C, 2014), each triple is a 3-tuple
containing the subject , predicate and object
representing an arc in a directed graph. The subject is
the vertex at the origin of the arc, the object is the
destination and the predicate is the label on the arc.
=
(
, ,
)
, (2)
={} . (3)
213
Rao B. and Atanassova-Barnes A.
Context Emergence Using Graph Theory - Defining and Modeling Context for Industrial Assets Using Graphs.
DOI: 10.5220/0005887302130217
In Proceedings of the Fifth International Symposium on Business Modeling and Software Design (BMSD 2015), pages 213-217
ISBN: 978-989-758-111-3
Copyright
c
2015 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
Maintaining the relationship graph then simply
becomes a matter of adding a triple when a new
relationship is formed and removing a triple when a
relationship is dissolved and archived.
2.2 Context as a Function of Graph
For context modeling we present a light asset-centric
ontological approach (RDF) and leverage graph
theory for both the storage of the asset related data
and the inference of new contexts dependent on goals.
As edges are added and removed over time, a
characteristic pattern develops around an entity as an
emergence (Lewes, 1874). This emergent context
may be used to avoid manually maintaining a context.
More context does not necessarily improve the
accuracy of the inference in a considerable manner.
(Guan et al., 2007) Rather than creating an exhaustive
context model, our approach is to let it grow
organically.
Definition 1: The context of any entity is the set of its
first-degree connections.
=
{
| =
⋁
=
}
. (4)
The entity may be connected to other entities or may
simply point to a value. This includes both inbound
and outbound connections in case of directed graphs.
Definition 2: The common context between any two
entities is the intersection of their individual contexts,
i.e., their first-degree connections.
=
⋂
. (5)
Definition 3: Emergent Context of entities is the union
of their contexts that naturally arises as old
connections dissolve and new connections form.
=
⋃
. (6)
Definition 4: Goal based context is a subset of the
emergent context that is relevant for the aforesaid
goal.
⊆
. (7)
2.3 Graph Path Notation
We introduce the following notation for describing
sets of graph paths from , which may be effectively
used as queries.
A path is a non-empty sub-graph of such that
the edges
connect one vertex to the next and every
vertex
is distinct.
= {(
), (
),...,(
)},
=
⋁
, (8)
Where
and
represent outgoing and
incoming arcs from vertex
respectively.
Let the path expression
be the subset of all
paths in that start with vertex
.
=
{
|
=
}
. (9)
Let the path expression
be the subset of all
paths in that start from any subject having a
predicate (i.e., all paths beginning from any vertices
and an outgoing edge with label ) to any vertices.
=
{
|(
)=(
)
}
. (10)
Let the path expression
be the subset of all
paths in that start from any object having a predicate
(i.e., all paths beginning from any vertices and an
incoming edge with label ) to any vertices.
=
{
|(
)=(
)
}
. (11)
Let the path expression
°
be the subset of all
paths in that have p as its first predicate.
°
=
⋃
. (12)
The path elements in (9) to (12) can be chained to
specify a subset of paths that follow any specific
pattern. For example, the path expression
is the
subset of all paths from (9) that begin with subject
and predicate (i.e., all paths beginning from a vertex
and an outgoing edge with label ) to any vertices.
=
{
|
=⋀
=
}
. (13)
The expression
is the subset of all paths
from (13) that have a successor predicate .
=
{
|
=⋀
=⋀
=
}
.
The expression
represents the set of all
paths beginning with the subject and having an
outgoing predicate and an incoming object .
=
{
|
=⋀
=⋀
=
}
.
Let the path expression
{
,
}
represent a
branched path which splits after
into as many
branches as the number terms within the braces where
represents a chain of path expressions defined in
Fifth International Symposium on Business Modeling and Software Design
214
(9) to (12). This notation may be nested, enabling us
to specify arbitrary branching.
{
,
}
=
{
,
}
=
{
,
}
,
{
,
}
=
⋀
. (14)
For example,
{
,
} =
⋀
.
°
{
, } =
°
⋀
°
.
2.4 Contextual Goals
Defining how the system behaves in a given context
is key to context sensitive computing. This context-
specific behaviour can be modeled as a set of goals.
Goals are composed of constraints and actions. In a
general graph, especially one as large as the IoT, there
could be billions of entities and some of the more
complex entities such as power plants may have
thousands of goals per entity. In an environment
where multiple entities interact, prioritizing goals to
evaluate can be a complex problem. An entity needs
to quickly prioritize goals to evaluate. Mapping the
common context from Definition 2 to a set of goals
would ensure that goals in the common context are
given priority.
In our example below, goals relating to
California Plant 3 and Repair Process
are prioritized and can be obtained by a simple
lookup.
Figure 1: Portion of graph of entities and their known
relationships.
Figure 1 represents a small portion of the graph
that’s relevant to a specific goal, the assignment of a
work-order to a qualified operator. The Assignment
link from WorkOrder to the operator does not yet
exist; adding it is the goal of this exercise.
From our definitions, we have:
Operator’s context, from (4):
Location: California Plant 3
Certification: Repair Process
Employer: GE
Type: Operator
Asset’s context, from (4):
Location: California Plant 3
Certification: Repair Process
applicableTo: WorkOrder
Type: Turbine
Common context for the Operator and Asset
Interaction, from (5):
California Plant 3
Repair Process
2.5 Contextual Constraints
Constraints define when a goal is applicable and are
specified as a set of paths. If all constraint paths
specified by the goal exist, then the goal can be
evaluated.
Let be the path expression that represents a
contextual constraint as in Section 2.3
=
. .
. (15)
is said to exist when it contains at least one path
satisfying . For a branched path as in (14), all
branches should exist.
Example Contextual Constraint 1: Only an
operator present in the same location should service
Asset.
Decomposing the path expression above by its
constituents, the initial term
represent the location of Asset, the succeeding
term
represents all entities that are in the
same location as Asset and the final term
limits the above to our contextual
goal of all operators in the same location as Asset.
Example Contextual Constraint 2: Only an
Operator who is a GE employee and is certified in the
relevant repair process should service Turbines.
°
°
{
,
}
This path expression uses the direction agnostic
operator from (12) and branching from (14)
Context Emergence Using Graph Theory: Defining and Modeling Context for Industrial Assets Using Graphs
215
2.6 Contextual Actions
Actions are simply graph changes such as new arcs
added to the graph. These added arcs grow the context
and are the elemental constituents of the emerging
context.
A contextual action Γ specifies the exact paths to
subject and object and supplies the predicate used to
insert or remove an arc into the context graph.
Let ∏ represent the union of all contextual
constraints
to
∏
=
⋃
⋃…⋃
. (16)
Let Γ
∏
be the contextual action where p
represents the predicate to be added and
and
represent the path to the subject and object within
∏
Γ
∏
= (
,p
,
) . (17)
Example Contextual Action: Assign WorkOrder
to Operator.
Γ
∏
= (
,
) . (18)
In the above:
Subject path:
Predicate:
Object path:
From figure 1, its clear that both constraint paths
exist in and therefore the action can be performed.
The new arc can be inserted at the location specified
in (18). If multiple matches are found, then the system
may simply pick one. If none are found, the operation
may not be performed or be deferred to a human.
3 APPLICATIONS
We believe that the technique above is generally
applicable to any software-defined context.
We have shown an example of operator
assignment based on discovered context. This can be
extended to the context discovery of any interacting
entities whose relationships and attributes are
modeled as a graph.
Context discovery and modeling in large graphs
such as the Internet of things (IoT) poses special
challenges (Pereira et al., 2013). The IoT is a very
large graph, possibly in the tens or hundreds of
billions of entities and quickly finding the context of
any entity or between any two entities is critical to
scalability.
In addition, many IoT entities are likely to lose
connectivity to the Internet but need to interact with
other entities that they are connected to on a local or
ad-hoc network.
Our approach enables us to emerge context in a
decentralized manner by focusing on the context of
any interacting entities and deal with the challenge of
huge graphs by reducing the context to a small
subgraph as described in section 2.
Entities can maintain a graph model of their
attributes and relationships and let the context emerge
naturally over their lifetime. This enables them to act
independently without the need for a central
repository that aggregates and serves as the authority
for context of billions of entities.
4 RELATED WORK
Goals in the IoT and the Industrial Internet space are
related to events. Detecting events in real time is
another major challenge for context-aware
frameworks in the IoT paradigm (Pereira et. al, 2013).
The graph of entities and their relations is
continuously and dynamically updated as the users of
the system interact with the graph triggered by sensor
events or time-based events.
Nguyen et. al. address this challenge using a
context-aware framework that uses a form of context
graph. They introduce the notion of a graph made of
context nodes and action nodes: ‘the basic idea of
contextual graph relies on the fact that past contexts
can be remembered and adapted to solve the current
context. The context is managed to organize in the
graph type. In the contextual graph, rather than
creating a solution from scratch, the contexts similar
to the current context are retrieved from memory. The
best match is selected and adapted to fit the current
context based on the differences and similarities
between the two contexts.’ (Nguyen et. al., 2008.)
Their approach is also focused on the paths going
through a node to discover context. We improve
upon Nguyen et al. by further constraining the model
by introducing the definitions of context goal,
constraints, and common context.
Fifth International Symposium on Business Modeling and Software Design
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5 CONCLUSIONS AND FUTURE
WORK
No single system yet exists that could fully satisfy the
criteria and challenges for the context-aware
requirements for any large system of interconnected
entities, especially one on the scale of IoT. The
inherent complexity requires more dynamic approach
that emerges from the system interactions as the
system evolves rather than being pre-calculated. We
believe that our graph approach to emergent context
gets us closer to the larger goal of a complete
contextual system for the Internet of Things.
Our approach can be generalized by extending
Definition 1 to context from one to the nth degree,
enabling a much larger graph and more indirect
constraints and goals.
We could also extend the approach to interaction
of multiple entities by extending Definition 2 from
two to n entities.
Although Definition 3 implies an archived
historical record of every link ever formed and
dissolved, we only use the current state of the graph
in this paper. The ability to use historical arcs could
open new possibilities such as affinity discovery.
GE Software is currently investigating methods
connected to this paper’s contributions on a broad
class of complex industrial and IoT applications such
as analytics on large asset graphs.
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https://www.gesoftware.com/blog/big-data-meets-big-
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