IEEE Computational Intelligence Magazine - February 2023 - 38

focuses on the embedding process in the graph without considering
the addition of downstream tasks, such as the addition
of new classes or data instances to tasks, which are
also very important and relevant to the concept of incremental
learning. Second, those models do not consider
performing backward transfers or refining prior embedding
of graph representations when learning new knowledge. In
particular, there is no precise mechanism to address catastrophic
forgetting problems, which is the main challenge
in lifelong learning.
The different characteristics of the graph learning methods
described above are summarized in Table I. The following are
properties that are related to graph lifelong learning:
❏ Graph representation learning. The model aims to learn
the representation of irregular domains, e.g., graphs, and
translate it into feature vectors to solve downstream graphbased
tasks.
❏ Online learning. The model is able to learn in the continuous
data stream.
❏ Knowledge transfer. The model can help future learning
by transferring previous knowledge as initial knowledge
for the new tasks.
❏ Incremental learning. The model should be able to learn
incrementally for new upcoming tasks in terms of new
instances or new classes in the future time points without
training from scratch and relying on previous data as much
as possible.
❏ Knowledge retention. The model should be sturdy from
catastrophic forgetting problems and able to refine previous
experiences when learning new knowledge.
D. Graph Lifelong Learning Scenarios
Maltoni and Lomonaco [24] introduced three scenarios that are
relevant to class-incremental learning: learning new instances,
new classes, and new instances and classes. Here we explain the
content update types in the graph lifelong learning setting:
TABLE I Graph learning concept comparison.
PROPERTIES
CONCEPTS
GRAPH
NEURAL
NETWORK
Graph
Representation
Learning
Online
Learning
Transfer
Knowledge
Incremental
Learning
Knowledge
Retention
Citation
No
No
No
No
[1], [2], [3] [52], [53], [54],
[55]
No
No
[37], [38],
[39], [40],
[41], [42]
Yes
Yes
[9], [56],
[57]
No
No
Yes
No
Yes
Yes
Yes
Yes
Yes
GRAPH SPATIOTEMPORAL
NETWORKS
Yes
DYNAMIC
GRAPH
LEARNING
Yes
GRAPH
LIFELONG
LEARNING
Yes
Definition
1. The objective ofgraph lifelong learning is to learn a
task Tt with graph data Gt that comes sequentially by maximizing
the result of the modelf (parameterized by u) while maintaining
the performance and avoiding the catastrophicforgetting problemfor
tasks T1; T2; ...; Tt1.
F. Taxonomy
This section presents a categorization ofgraph lifelong learning
research. The categorization is based on the one presented for
general lifelong learning, [24], [48], as explained in Section IIA,
which we have found is also relevant to use for graph lifelong
learning. The unique considerations in the case of graph
lifelong learning are how these methods consider graph structure
data in the incremental learning process. The hybrid
approach is also added to categorize the current methods that
combine more than one approach. Thus, the existing graph
38 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2023
❏ Learning new instances (NI). This refers to the case
where new training patterns appear in future time points
based on new conditions, but without the addition ofnew
classes. In graph learning problems, this can be indicated by
the emergence of new nodes and their attributes that are
completely different from the existing nodes. Thus, it can
create new relationships in graph data. It is necessary to
accommodate the new information of newly appeared
nodes and relations to improve the scalability ofmodels.
❏ Learning new classes (NC). This is when new training
patterns that correspond to previously unseen classes
become available. Once new classes appear, the model
should be able to accommodate the new information to
solve the tasks based on the new classes. Moreover, previous
experiences should be maintained.
❏ Learning new instances and classes (NIC). New training
patterns and new labels become available in future
observation. Newly emerged data instances can belong to
both previous classes or new classes that can improve the
prior experience and enrich the model capability based on
new knowledge.
As mentioned by Maltoni and Lomonaco [24], NI and NIC
are often more appropriate than NC in real-world applications.
E. Notation ofDomain
A graph is composed of a set of vertices (or nodes) V containing
attributes with a total number ofvertices denoted as jVj¼
n, and a set of edges E. A vertex or a node can be represented
as vi 2 V, and an edge to define a relation can be represented
as eij ¼ðvi; vjÞ2 E which determines the relationship between
vertices vi to vj. Graph data can be represented as G ¼ðA; XÞ,
where A 2f1; 0gnn is the adjacency matrix and X 2 Rnd
represents features in nodes where n is the number of nodes,
and d is the dimension of a feature vector. In graph lifelong
learning setting, the change of graph data based on time t
can be represented as G ¼ðG1; G2; ...; GtÞ where Gt ¼ Gt1
þDGt. Moreover, the graph lifelong learning problem will
have a collection oftasks T ¼ðT1; T2; ...; TtÞ.
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