RADAR: Finding Analogies Using Attributes of Structure
ABSTRACT RADAR is a model of analogy retrieval that employs the principle of systematicity as its primary retrieval cue. RADAR was
created to address the current bias toward semantics in analogical retrieval models, to the detriment of structural factors.
RADAR recalls 100% of structurally identical domains. We describe a technique based on “derived attributes” that captures structural descriptions
of the domain’s representation rather than domain contents. We detail their use, recall and performance within RADAR through empirical evidence. We contrast
RADAR with existing models of analogy retrieval. We also demonstrate that RADAR can retrieve both semantically related and
semantically unrelated domains, even without a complete target description, which plagues current models.
- SourceAvailable from: cc.gatech.edu[Show abstract] [Hide abstract]
ABSTRACT: A theory of analogy must describe how the meaning of an analogy is derived from the meanings of its parts. In the structure-mapping theory, the interpretation rules are characterized as implicit rules for mapping knowledge about a base domain into a target domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domains; and (b) the theoretical framework allows analogies to be distinguished cleanly from literal similarity statements, applications of abstractions, and other kinds of comparisons. Two mapping principles are described: (a) Relations between objects, rather than attributes of objects, are mapped from base to target; and (b) The particular relations mapped are determined by systematicity, as defined by the existence of higher-order relations.Cognitive Science A Multidisciplinary Journal 01/1983; · 2.59 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: Case-based reasoning (CBR) focuses on analogy in the context of solving real-world problems. Its research methodology of computational modeling is aimed at deriving hypotheses about cognition. CBR's computational models show the roles of encoding, retrieval, and adaptation in analogical reasoning processes. In addition, its algorithms provide insight into what it might take to enhance human cognition. CBR as a plausible cognitive model can thus advise on educational philosophy, educational practice, and design of educational software.American Psychologist 02/1997; 52(1):57-66. · 6.87 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: We present a model of similarity-based retrieval which attempts to capture three psychological phenomena: (1) people are extremely good at judging similarity and analogy when given items to compare. (2) Superficial remindings are much more frequent than structural remindings. (3) People sometimes experience and use purely structural analogical remindings. Our model, called MAC/FAC (for "many are called but few are chosen") consists of two stages. The first stage (MAC) uses a computationally cheap, non-structural matcher to filter candidates from a pool of memory items. That is, we redundantly encode structured representations as content vectors, whose dot product yields an estimate of how well the corresponding structural representations will match. The second stage (FAC) uses SME to compute a true structural match between the probe and output from the first stage. MAC/FAC has been fully implemented, and we show that it is capable of modeling patterns of access found...12/2000;
LNAI (Lecture Notes in Artificial Intelligence), 2464, pp. 20-27, 2002.
RADAR : Finding analogies using attributes of
Brian P. Crean1 and Diarmuid O’Donoghue2
1Galway-Mayo Institute of Technology, Castlebar Campus
Westport Road, Castlebar, Co.Mayo, Ireland also 2
2Department of Computer Science, NUI Maynooth,
Co. Kildare, Ireland.
Abstract. RADAR is a model of analogy retrieval that employs the principle of
systematicity as its primary retrieval cue. RADAR was created to address the
current bias toward semantics in analogical retrieval models, to the detriment of
structural factors. RADAR recalls 100% of structurally identical domains. We
describe a technique based on “derived attributes” that captures structural
descriptions of the domain’s representation rather than domain contents. We
detail their use, recall and performance within RADAR through empirical
evidence. We contrast RADAR with existing models of analogy retrieval. We
also demonstrate that RADAR can retrieve both semantically related and
semantically unrelated domains, even without a complete target description,
which plagues current models.
An analogy is a structure-based comparison between a problem domain (the target)
and some known domain (the source). Existing similarities form the basis for
transferring additional information from the source to the target domain. “So, IF the
nucleus is like the sun and the planets orbit the sun, THEN the electrons must also
revolve about the nucleus”. Yet much research has focused on interpreting
predetermined analogies rather than discovering new candidate analogies.
Analogy retrieval is an essential yet complex process, where numerous similarity
constraints (semantic, structural and pragmatic) can be considered in judging the
usefulness of a source/target pairing . The retrieval process is further complicated
when one considers that cross-domain analogies need not share superficial semantic
features between the participating domains. Structural similarity has received a great
deal of acceptance in analogical mapping, yet has had startlingly little impact on
analogy retrieval models. We believe that it is not unreasonable to include structural
considerations within the retrieval process itself. Systematicity  would allow a
deliberate broadening of knowledge to reach retrieval and subsequent stages, and
thereby form new analogies
Frequently, domains lacking obvious semantic resemblance can be used to form
useful analogies , for example “Nuclear war is like a game of tic-tac-toe” (adopted
from the motion picture “War Games”). Taking a recognised domain like tic-tac-toe
that frequently ends in a draw (no winner) can lead to recognising the futility of
nuclear war i.e. no winner. In order to interpret a possible candidate analogy we first
must discover it. Yet in current models, retrieval is governed by the semantic content
(meaning) of entities common to both analogs. Such systems can only retrieve
domains that are represented similarly - and the retrieval of structurally similar
domains is purely accidental. It is merely a happy coincidence that any semantically
similar domains ever have the same structure as each other. A crucial consequence of
these inflexible retrieval models, is their inability to explain the role of analogy in
creativity, inspiration and insight as identified by Boden .
Initially, we want to retrieve a structurally identical source domains, given some
target domain problems. However, analogies are typically formed between a smaller
target domain and a larger source - since the source must supply additional
information to the target domain. Therefore, not only are we looking for isomorphic
source domains, but we also wish to identify homomorphic sources.
These factors will undoubtedly increase the possibility of retrieving inappropriate
source domains. Current retrieval models reject many inappropriate sources by their
inability to form a large mapping. However, our technique could use the analogical
validation phase to reject inappropriate comparisons. A model of structural retrieval
would also have to operate in a computationally tractable manner. In this paper we
introduce the RADAR (Retrieving Analogies utilising Derived AttRibutes) model and
its method of encoding structural traits of domains through derived attributes. We
detail its operation, and how it improves over current analogy retrieval models.
2. Existing Analogy Retrieval Models
Before we discuss models of analogy retrieval we briefly describe our objectives from
an information retrieval perspective. As we shall see, existing models have very poor
recall, because they either ignore or severely dis-favour semantically distant domains.
Thus, they are impotent from the perspective of generating creative analogies.
Furthermore, the precision of some models is very poor because semantic similarity is
independent of the structural similarity required to form an analogy. We wish to
explain how structurally similar domains, even ones that are semantically un-related
to the target, might be retrieved. Such comparisons underlie many breakthroughs in
science - “the heart is a pump, the brain is a telephone networks, light is a wave vs.
light is a particle”. Crucially, no current model of analogical retrieval can explain
how a target domain can cause the retrieval of a semantically unrelated source.
Consider the following target sentence (taken from ), where Felix is a cat and Mort
is a mouse.
T1 : “Felix bit Mort causing Mort to flee from Felix”
We wish to find domains that are structurally similar to T1, so that we can later
identify any cross-domain analogies. So, for the given source we might wish to
identify a candidate source domain such as S2, where Mary is a woman and Frank is a
S2 : “Mary seduced Frank causing Frank to kiss Mary”
Of course, most cross-domain analogies will be invalid but we must at least have
the potential to retrieve them. Identifying the useful analogies from these cross-
domain comparisons is the task for the later mapping and validation phases.
2.1 Analogy Retrieval Models
With domains described by content vectors, MAC/FAC  creates a skeletal
description by counting the number of times distinct predicates and objects occur in a
representation. Estimating the structural overlap between source and target is
presented by a dot product computation on the respective content vectors. The highest
dot product and all those within a 10 % range are deemed structurally similar.
Crucially, MAC/FAC cannot retrieve semantically distant domains due to weak
predicate and object similarity in the content vectors. Its frailty is also evident when
presented with a partial source and target description. Consider S3 (additional
information to S2)
S3 : “Frank and Susanne are married. Mary seduced Frank causing
Frank to kiss Mary, so Susanne divorced Frank”.
The respective T1/S3 content vector is weakened due to again the non-identicality
of the domains on which MAC/FAC is dependant, signifying it is vulnerable when
dealing with partial descriptions.
ARCS  uses tokenised semantic similarity between representations as pre-
selection criteria in the creation of a parallel constraint satisfaction network.
Structural correspondence is determined on the basis of isomorphic similarity
between source(s) and target predicate arguments. ARCS uses a standard parallel
connectionist relaxation algorithm to allow the network to settle. After the network
settles sources are deemed suitable based on their activation strength. ARCS
perseverance with semantic similarity as a filtering process means it casts
semantically disparate domains aside from the outset, i.e. Felix the cat is not similar to
Frank the man. In relation to the original T1 and S2, ARCS immediately rejects any
possible retrieval due to weak semantic correspondence, the only recognised
similarity is the higher-order predicate, cause. This indicates that ARCS is unable to
retrieve semantically distant domains.
HRR’s  combine semantic and structural similarity with an inclusive vector
representation. Semantic identity is encoded into each entity in a representation. The
structural traits of the representation are brought to the surface as role filler
assignments (e.g. agent, patient) and are encoded along with each entity or predicate.
HRR’s structural retrieval is diminished by its tendency to favour more semantically
similar source(s). Consider T1 and S2, the absence of semantic similarity between
objects and predicates in both source and target, severely limits the possibility of
semantically distant domains being retrieved (also borne out by Plates original results
). The resultant “convolution” product (used by HRR’s to estimate similarity) is
considerably weak. HRR’s suffer from a similar affliction as MAC/FAC in its
inability to tolerate the loss of significant information. If presented with T1 and S3, the
absence of identical structures between representations will weaken the measures of
similarity even further. Though HRR’s attempt to combine semantics and structure in
retrieval, problems with non-identical structure and semantics are very problematic to
Though CBR (Case-Based Reasoning) is similar to analogy retrieval in many
respects, we exclude CBR from discussion in this paper as CBR is primarily
concerned with intra-domain retrieval and is not concerned with retrieving
semantically distinct domains.
3. Derived attributes
One method to effect structural-based retrieval is to re-describe the domain
description via micro-features. We use derived attributes to determine the structural
characteristics of a domain representation. Derived attributes describe features of the
representation itself, rather than qualities related to the real world. These structural
attributes are not tailored to suit individual domains but are used to describe any
conceivable domain. Each derived attribute describes a particular construct of the
domain through a calculated value. A number of simple derived attribute types (Fig 1)
can be used to capture the structural characteristics of the domain’s representation.
Derived attributes such as the number of predicates and objects in a domain can
convey simple structural detail. The identification of cyclic paths (loops) in the
representation is also beneficial i.e. in fig 1, the path containing the entities cause,
seduce, frank and kiss is an instance of a loop as it cycles back to the starting point.
These derived attributes can distinguish between identically structured domains and
similarity-structured domains - an important distinction as already highlighted in the
operation of current models. For illustrative purposes the predicate representation of,
S2, cause (seduce, kiss), seduce(mary, frank), kiss (frank, mary) can be described by
the derived attributes in fig 1.
Fig. 1. Derived attribute description of S2
Number of Loops : 3
Loop size : 4
Connectivity : 3
Number of predicates : 3
Number of atoms : 5
The derived attributes depicted in fig 1 are just a subset of the structural
composition of domains, other derived attribute types such as number of roots,
longest path etc. can also be incorporated. These structural attributes are independent
of any semantic primitive descriptions housed in these domains and hence cannot be
influenced by semantic considerations.
We now describe RADAR (Retrieving Analogies using Derived AttRibutes), which
bases analogy retrieval in the ‘search space’ of structural attributes. The premise of
RADAR’s retrieval algorithm is that domains with the same derived attributes must
also have identical structure. Each domain in long-term memory is examined for its
structural description, which generates various derived attributes types and their
values. These values are stored in derived attributes stores and linked to the source in
When presented with a target analog, the target is also rendered into its own
structural attributes, and the target’s derived attributes activate the corresponding
stores. All concepts in memory that have the same attribute value for a particular type
will be identified through spreading activation. This indicates they are structurally
identical for each structural feature. Activation values discriminate the strongest
source(s) from dissimilarly structured analogs through a threshold level that rejects
any concept below a certain similarity measure. The stronger the activation value, the
more structurally identical a candidate source is to a target.
4.1 Identical Structure Retrieval
Presenting S2 (source) and T1 (target) from above, we demonstrate how RADAR
retrieves identical structures. Retrieval is driven by the derived attributes of T1, so any
source that shares a corresponding derived attribute value will receive activation.
RADAR successfully retrieves S2 with and overall similarity metric of 100%. This
100 % signifies that both source and target share all derived attribute values and
hence are structurally identical. This was as expected because the source
representation is isomorphic with the target. Current models rely heavily on semantic
similarity to guide retrieval but this demonstrates retrieval where semantic similarity
is negilable, consequently are constrained by the targets semantic influence and
unable to retrieve this valid analogy.
It also demonstrates RADAR’s ability to retrieve creative analogies such as the
“Nuclear war is like a game of tic-tac-toe”, which again current models cannot
retrieve. Identical results were obtained when presented other structurally identical
domains that do share some semantic similarity, again Plate’s “Spot bit Jane causing
Jane to flee from Spot”, Gick and Holyoak’s  surgeon/general analogy, etc. These
domains contain identical structural and RADAR, as expected, retrieves the identical
sources based on identical structural attribute values.
4.2 Partial Structural Retrieval
This demonstration examines RADAR’s ability to retrieve useful sources from
memory, where the structural overlap between source and target is incomplete.
(missing predicates and objects). This is vital as analogies are frequently used for
learning, requiring that the source have more structure than the target - and
consequently a different structure to it. Each source is broken down into its derived
attribute pairings (fig 2) and stored in structure memory. RADAR again creates a
basis for retrieval by analyzing the target, T1 for its derived attribute values. Again,
RADAR successfully retrieved the appropriate source, S3, though with a smaller
similarity scoring. As we can see from fig 2 the structure of the analogues do not
match exactly, and this is reflected in the derived attribute values (again fig 2). But a
subsection of the representations do share identical structure - the loops structure.
Both share three loops of size four. The loop structures identify a structural similarity
and brings it to the surface.
Figure 2: Structural representation of the S3’s Love Triangle Story
We readily accept the argument that if more information were missing then
retrieval accuracy would decay. This is of course a fact of retrieval, poor
representations lead to miss-guided retrieval (if any). Remove the predicate Divorce
(Susanne, Frank) from the representation, and the resultant derived attribute values
would reflect this change. But we would argue that there does come a point in
reminding, in the human cognitive process and cognitive modeling, when significant
information is missing, retrieval will tend to be poor or not take place at all. This is
perfectly analogous to the existing situation where semantically based retrieval
performs poorly with missing information - but cannot retrieve outside its own
domain. Likewise if more predicates or objects were added to the target, i.e. the
proposition move-in-with (Frank, Mary) then the structure changes, but again there is
a common substructure (loop structure). This experiment confirmed that RADAR
operates successfully when presented with partial domains, on the provision that there
exists some coherent structure between the representations. RADAR is the only
model that considers partial source/target parings in retrieval.
Number of Loops : 4
Loop size : 4
Connectivity : 4
Number of predicates : 5
Number of atoms : 8
5. Performance and Future Work
RADAR’s overall performance was examined with a long-term memory containing
frequently cited domains, chosen randomly from the analogy literature. In all seventy
domains were stored. Domains were of varying complexity with an average of 8
predicates (ranging from a minimum of 1 to a maximum of 25 predicates) and 14
entities (also ranging from a minimum of 3 to a minimum of 39 entities) per domain.
In the investigation, the largest loop construct considered was six. Selection is based
on the highest scoring source domain, or group of sources joint highest retrieval score.
Retrieval was classified as successful if the target caused the corresponding source
identified in the literature to be retrieved.
RADAR retrieved the common matches on each occasion and significantly out
performed other models in its ability to retrieve appropriate candidate source
domains. RADAR retrieved an average of 4 sources (6%) when presented with a
target. In each case the correct source was amongst the joint highest active sources.
Significantly, RADAR can retrieve similar structured source when presented with
identical and partial representations even when they share no semantic overlap
between objects or predicates, where other models are deficient.
MAC/FAC ARCS HRR RADAR
Yes Yes* Yes + Yes
No Yes * No Yes
Identical Semantic distant
No No No Yes
Partial Semantic distant
No No No Yes
Table 1. Comparison of RADAR against common retrieval models
* on the provision that pre-selection will have semantic information
+ retrieval accuracy will vary considerably from target
Derived attributes can be manipulated in order to re-describe the structural
description of a representation and increase performance of the retrieval process.
Similar to weighted features , where feature descriptors are weight based on their
importance or usefulness, certain derived attributes can be marked as more relevant
than others. Alternatively a nearest neighbour algorithm can be used to locate similar
sources [O’Donoghue, Crean, in press]. Another technique is to simply increase the
number of derived attributes used to describe a domain.
Domain retrieval using derived attributes is only as efficient as the derived
attributes that supplement the raw domain information. Taking just five attribute types
each with just 10 values, and making the best case assumption that our data is
distributed evenly along each value, then each location in derived attribute space
would represent just 10 domains, for a base of 1,000,000 domains. This indicates the
potential retrieval power of derived attributes. Of course, efficiency is increased with
additional attribute types and values describing new structural qualities with particular
utility to analogy retrieval.
We lay no claim that this is how structural retrieval is performed in human cognition.
The focus of this work was on creating a computational model that is capable of
structural domain retrieval in a computationally tractable manner - which overcomes
the semantic restriction suffered by other models. We have demonstrated the ability of
derived attributes in describing the structural make-up of domains. We then
demonstrated their ability to retrieve semantically related and un-related domains,
whether presented with a partial or complete target domain. We detailed these
findings through the recall and precision performance of RADAR, using commonly
cited domains from the analogy literature. RADAR successfully overcomes the
limitations suffered by current retrieval models.
1. Eskeridge, T.C. “A Hybrid model of continuous analogical reasoning”, In Branden
(ed.), Advances in Connectionist and Neural Computation Theory, Norwood, NJ:
2. Gentner D “Structure-mapping: A theoretical framework for analogy”, Cognitive
Science, volume 7, pp 155 –170, 1983.
3. Kolodner, J. L. “Educational Implications of Analogy a view from Case-based
Reasoning”, American Psychologist, pp 57 - 66 Volume 52, 1997.
4. Boden, M. A. “The Creative Mind”, Abacus, 1994.
5. Plate Tony A., “Distributed Representations and Nested Compositional Structure”,
Graduate Department of Computer Science University of Toronto, 1994 Ph.D.
6. Gentner D, Forbus D., “ MAC/FAC : A model of Similarity-based Retrieval”, pp
504 - 509, Proceedings of the 13th Conference Cognitive Science Society, 1991.
7. Thagard P., Holyoak K. J., Nelson G, Gochfield D., “Analog Retrieval by
Constraint Satisfaction”, pp 259 - 310, Artificial Intelligence Volume 46, 1990.
8. Gick M. L. and Holyoak K. J., “Analogical Problem Solving”, Cognitive
Psychology, volume 12, pp 306 – 355, 1980
9. Blum A. L., Langley. P. “Selection of relevant features and examples in machine
learning”. Artificial Intelligence volume 97, pp 245--271, 1997.