Mining Substitution Rules: A Knowledge-based Approach using
Dynamic Ontologies
Rupal Sethi and B. Shekar
Decision Sciences and Information Systems Area,
Indian Institute of Management Bangalore,560076, Bangalore, Karnataka, India
Keywords: Substitution Rules, Interestingness, Affordances, Dynamic Ontology, Market Basket.
Abstract: Association Rule Mining has so far focused on generating and pruning positive rules using various
interestingness measures. However, there are very few studies that explore the mining process of
substitution rules. These studies have incorporated a limited definition of substitution, either in statistical
terms or based on manager’s static knowledge. Here we attempt to provide a customer-centric model of
substitution rule mining using the lens of affordance. We adopt a knowledge-based approach involving a
dynamic ontology wherein objects are positioned based on the affordances they are preferred for. This
contrasts with the traditional static ontology approach that highlights manager’s static knowledge base. We
develop an Expected-Actual Substitution Framework to compare relatedness between items in the static and
dynamic ontologies. We present Affordance-Based Substitution (ABS) algorithm to mine substitution rules
based on the proposed approach. We also come up with a novel interestingness measure that enhances the
quality of our substitution rules thus leading to effective knowledge discovery. Empirical analyses are
performed on a real-life supermarket dataset to show the efficacy of ABS algorithm. We compare the
generated rules with those generated by another substitution rule mining algorithm from the literature. Our
results show that substitution rules generated through ABS algorithm capture customer perceptions that are
generally missed by alternate approaches.
The field of Artificial Intelligence (AI) is actively
exploring the use of formal ontologies as a way of
specifying knowledge for solving problems related
to diagnosis, planning and design (Chandrasekaran,
Josephson and Benjamins, 1999; Gruber, 1995).
However the knowledge elicitation process in AI is
restricted to a static representation in Knowledge
Based Systems (Nau and Chang, 1986). Static
knowledge-based systems assume a one-shot
computation, usually triggered by a user query, often
missing to consider dynamic scenarios where there
is a need to react and evolve in the presence of
incoming information (Brewka et al., 2016).
In most knowledge-based systems, problem
solving is done by manipulating rules of the form
“IF conditions THEN actions”, often labelled as
association rules (Galárraga et al., 2013).
Association Rule (AR) Mining is one of the popular
techniques of data mining which discovers
relationships between groups of items. Algorithms
like Apriori (Agrawal and Srikant, 1994) mine rules
on the basis of frequency of occurrence of items in
transaction data. This approach is restricted to
positive association rules only. Positive AR is a
relationship between items or groups of items which
exists in the transaction set. One possible positive
AR may be “IF customers buy bread, THEN butter
is bought along with it”.
Recently there has been a shift of focus from
positive associations to substitution relations (Chen
and Lee, 2015). Substitution relations depict items
that are purchased as replacement to another item
(Teng, Hseih and Chen, 2005). For example, Bread-
Bun, Pepsi-Coke or Chair-Stool. These items may
not be a part of the same transaction (Shekar and
Natarajan, 2006). Thus, traditional AR mining
algorithms (Agrawal and Srikant, 1994) cannot
generate rules comprising substitute items. We
classify research done on substitution rule mining
under two categories: objective approach and
subjective approach, given in Figure 1.
Sethi, R. and Shekar, B.
Mining Substitution Rules: A Knowledge-based Approach using Dynamic Ontologies.
DOI: 10.5220/0006577400730084
In Proceedings of the 10th International Conference on Agents and Artificial Intelligence (ICAART 2018) - Volume 2, pages 73-84
ISBN: 978-989-758-275-2
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
Figure 1: Classification of related work in substitution rule
Objective substitution is divided into two more
categories, namely statistical and transaction-based.
Statistics-based approach encompasses algorithms
that generate substitute items through measures like
correlation. On the other hand, transaction-based
research refers to conceptual work where
substitution is defined not from the point-of-view of
statistics but more from the angle of transactional
In order to statistically tap items absent in
transactions, Brin, Motwani and Silverstein (1997)
discuss substitutes in the context of mining negative
association rules. Negative rules depict relationships
between items that conflict each other. These
negative relationships may help in identifying
substitute items. Wu, Zhang and Zhang (2002) use
an objective measure of interestingness to calculate
covariance between items and thus identify negative
relationships. Antonie and Zaiane (2004) extended
the work of Brin et al (1997) by using Pearson’s
correlation coefficient as a measure of negative
association and developed an algorithm to generate
negative rules with a sliding correlation coefficient
threshold. Chen and Lee (2015) furthered this work
to generate non-redundant substitution rules by
combining the concept of frequent closed itemsets
with Pearson correlation coefficient. One of the
pioneering research works to formally define
substitution rules and provide the relevant mining
process was by Teng, Hseih and Chen (2005). They
use chi-square as a measure of interestingness to
access the correlation between items.
Shekar and Natarajan (2006) define
substitutability from a transactional orientation.
They define direct substitutes as items that are
purchased individually in different transactions and
indirect substitutes as items that are purchased along
with a common object. Similar approach has been
adopted by Wang, Liu and Ma (2007) where they
measure intensity of substitutability through rules
containing composite items. Suppose rule X
signifies occurrence of Z in the presence of either X
or Y. Then, X and Y would act as substitutes, since
one of them is required for the occurrence of Z.
Subjective substitution category takes into
account the usage of subjective interestingness
measures. Here, one strand of research pertains to
tapping the manager’s domain knowledge through
static ontology. The research that we present here is
towards understanding customer perceptions of
substitution through dynamic ontology.
Savasere, Omiecinski and Navathe (1998) use a
hierarchical structure to define substitutability based
on the position of an item in the taxonomy. They
restrict their definition to sibling substitutions
wherein items that are siblings in a taxonomy are
expected to exhibit similar behavior and hence are
substitutable. They use unexpectedness as a measure
of interestingness for capturing negative
relationships. A similar approach has been adopted
by Yuan, Buckles, Yuan and Zhang (2002). They
also use the concept of locality of similarity while
defining sibling rules. Sibling rules are a pair of
positive association rules where both siblings are
expected to be related to the same consequent. This
approach is however restricted to a static ontology
that does not accommodate changes in customer
purchase patterns.
Substitution is defined in statistical terms or
defined on the basis of the static knowledge of a
manager. On the contrary we define a substitute as a
product that is similar to another product on the
basis of customer perceptions that are essentially
dynamic. Our definition is adopted from Nicholson
and Snyder (2011) who define a pair of substitutes
as two goods where one good may, as a result of
changed conditions, replace the other in use. The
changed conditions may occur as a result of change
in customer goals while buying a product. This
highlights the fact that research on substitution rule
generation needs to focus on the function that
defines substitution between two products.
In this paper, we define substitution using the
lens of affordance. This lens points to various
features or applications an item may be used. This
may be in contrast to a manager’s typical
expectations. We use a knowledge-based dynamic
ontology towards this purpose. A dynamic ontology
is represented as a hierarchical structure where items
are positioned based on the affordances behind their
purchase. Unlike a static ontology where the
position of items is based on manager’s prior
knowledge, a dynamic ontology is constructed “on
the fly” on the basis of varying customer purchase
patterns. The sets of substitutable items obtained
from the proposed dynamic ontology are then used
ICAART 2018 - 10th International Conference on Agents and Artificial Intelligence
to generate substitution rules. Further we also define
an interestingness measure for the proposed
affordance-based substitution rules and use the same
in evolving a classification framework.
2.1 Dynamic Ontology
An ontology is an explicit specification of a
conceptualization (Gruber, 1995). In AI, ontologies
are used to represent knowledge in the form of
objects, concepts and relationships among them
(Genesereth and Nilsson, 1987). Ontologies are
always specific to the domain of discourse as they
form the foundational vocabulary of the area under
study (Chandrasekaran, Josephson and Benjamins,
1999). In this paper, we adopt the ontology-based
approach in the context of a supermarket where
knowledge representation is a scheme of classifica-
tion of products. It is represented as a hierarchical
structure with parents as classes and leaves as
products in that class. This ontology structure
captures the domain knowledge of a manager in
terms of classification of all the products. However,
the definition of categories of products and their
distinctions are not restricted to a manager’s
knowledge (Ratneshwar and Shocker, 1991). A
categorization has different connotations for
customers as well as for a manager. Categorization
is a means to simplifying information, better
decision making and having efficient interpersonal
communication among customers (Shocker, Bayus
and Kim, 2004). This notion is not taken into
account while creating static ontologies in a
supermarket scenario. In such static representations,
products never change their hierarchical positions
once they get classified (Li and Tsai, 2009). Hence it
is difficult for managers to update their knowledge
from trends in purchase patterns.
We suggest dynamic ontology as an add-on to
static knowledge representation. A dynamic
ontology in the context of a market basket scenario,
would overcome the problem of static product
categorization by incorporating customer chara-
cteristics and temporality into the classification.
Customer preferences depend on a number of factors
such as context, age, time, location, trust and new
experiences (Rana and Jain, 2015). Customers might
categorize products based on physical resemblance
(Butter and Margarine), perceived similarity of
producers (Coke and Pepsi) or category label fit
(Facewash and Bathing Bar) (Day, Shocker and
Srivastava, 1979). Two other factors that shape
dynamic categorization of products are word of
mouth among customers (Lee and Lee, 2009) and
seasonality (Rana and Jain, 2015). Thus, product
categorization is contingent on both customer
purchase patterns and manager’s prior knowledge.
We define dynamic ontology through a tree structure
comprising affordances as classes and products as
leaves. Products are linked to an affordance class
through a containment function that defines the
degree to which the particular affordance is
connected to that product.
2.2 Affordance
The concept of affordance originates in ecological
psychology. Affordances are viewed as relational
action possibilities that emerge from interaction
between an object and its user (Gibson, 1977). This
interaction is contingent on the features of an object
and the abilities of a goal-seeking user (Stoffregen,
2003). In the absence of either of these, affordance
may not exist. Product categorization cannot be
considered without taking into account the effects of
purpose (Shocker, Bayus and Kim, 2004). Since one
product can serve multiple purposes, different users
may ‘afford’ it differently based on their goals
(Leonardi, 2013). For instance, someone may use a
remote control to switch on a television device while
another may use it as a paper-weight. Customers’
past experiences and knowledge are also important
factors while defining product categories and hence
substitutability between items. We use affordance as
a lens to define the proposed dynamic ontology that
helps to mine interesting substitution rules. In this
paper, we define affordance as a ranked list of
features of a product which are preferred by
customers while buying the product. Choice and
ranking reflect the intentions (or expectations) of a
customer to accomplish a goal with the help of that
Intuitively, customers tend to substitute products in
the same category because of the similarity of
functions served by the products. However, the role
of substitution can be more abstract based on inter-
category replacement of products. Depending on the
situation or customer’s goals, two products in very
different categories may be substitutes to each other.
Mining Substitution Rules: A Knowledge-based Approach using Dynamic Ontologies
For example, in order to accomplish the goal of
cleaning the toilet, a customer may either buy Coke
or Harpic whichever is available or is less
expensive. Hence substitution here, is based on the
situation or the context rather than brand or physical
resemblance of products. Traditionally in a static
taxonomy, Coke and Harpic would form parts of
different classes like Beverages and Toiletries
respectively. Hence they might be distant from each
other making them a less likely substitutable pair in
the static ontological structure. However, with the
help of a dynamic ontology Coke and Harpic would
be substitutable based on the affordance shared by
them. In this case ‘acidic’ is the common affordance.
3.1 Formal Characterization of
Dynamic Ontology
We represent a dynamic ontology as a n-ary tree
representing multiple classification of products
(items) based on affordances preferred by the
customers while purchasing them. This hierarchical
structure comprises ‘has-a’ relationships instead of
‘is-a’ relationships. We represent dynamic ontology
where V is a set of vertices that comprise
affordances A as classes (non-leaf nodes) and
products P as leaf nodes. E is the set of edges
connecting the nodes and is the containment
function that assigns weight to each edge in E.
Weight represents the degree of match of an
affordance ai for a product pj. This is given by the
frequency of transactions that contain ai and pj
together. also gives importance to the order of the
ranking of ai for pj. For a particular transaction tk
that contains product pj and affordance ai with a
, containment function is given by (2):
The rationale for formalizing as the inverse of
rank r is as follows. Lower the value of r (i.e. feature
being ranked higher in the ranklist), higher the
degree of match of that affordance for the product.
As r increases, the value of decreases. This is
because of the decrease in importance for affordance
ai given by the customer.
is updated dynamically with the recurrence of
ai and pj in a transaction. At any point in time,
resultant is the cumulative mean that includes the
current occurrence along with prior occurrences.
Our affordance-based approach to constructing a
dynamic ontology adheres to the fact that each
object may have multiple affordances, based on
users’ varying goals (Leonardi, 2013). Since the
dynamic ontology is constructed from individual
transactions and without resorting to a manager’s
knowledge base, it reveals differing sets of
affordances for a product-purchase.
A static knowledge representation is based on
the objective reality (Hirschheim and Klein, 1989)
and this is given by a manager’s domain knowledge
and past experiences. Generally static hierarchical
structures are not updated with changes in customer
preferences. The proposed notion of dynamic
ontology is based on the subjective reality that
reflects changing customer perceptions exhibited
through their purchase behavior. Subjectivity in the
ontology is captured through affordances specified
by customers in the appended transactions. This
necessitates evaluation of ontological stances
pertaining to the dynamic structure and differen-
tiating them from those in a static structure.
3.1.1 Concepts
A concept C is defined as an affordance class which
specifies the feature of a particular object because of
which it is purchased by the user. The difference
between a concept and an affordance is that concept
is a single entry in the affordance ranklist specified
in the transaction. For example, a customer might
buy Coke with affordance (Taste=Sweet,
Ingredient=Cola, Nature=Fizzy). Here, Taste,
Ingredient and Nature are three different concepts.
3.1.2 Meta-concepts
A meta-concept M
is defined as an additional
attribute of abstract concept C which enhances the
information about user purchase decision. For
example, consider a concept Taste. Meta-concepts
associated with Taste could be sweet, bitter, salty
and the like.
3.1.3 Instances
An instance I is an actualization of concepts and
meta-concepts in a real-world object. A product p is
an instance of concept C if it contains C in the
ICAART 2018 - 10th International Conference on Agents and Artificial Intelligence
affordance ranklist. In the dynamic ontology, an
instance I can be a direct descendant of a concept C
or can be a descendant of the meta-concepts of C.
For example, biscuit is an instance that belong to
concept taste and meta-concept salty.
3.1.4 Relationship between Concepts
Two concepts C
and C
are related to each other iff
there is at least one product p that is simultaneously
classified under C
(or under one of the descendants
of C
) and under C
(or one of the descendants of
We introduce a measure Concept Relatedness
(CR) that captures the degree of similarity between
two concepts. Two concepts would be highly similar
if a lot of products share the two concepts in their
affordance ranklist specifications. For example,
concepts taste and ingredient would be related to
each other since many edibles possess both concepts
as affordances.
 
In a static representation, concepts are related
only through their positions in the tree. However, in
dynamic ontologies, concepts are related through a
transaction-based factor p. This transaction-based
factor highlights customer preferences for relating
two affordances or features together. This approach
contrasts with the manager-centric approach that is
limited to his prior knowledge from the static tree
3.1.5 Relationship between Meta-Concepts
Meta-concepts are related through their position in
the tree. M
and M
are siblings since they belong
to the same concept C. Sibling meta-concepts can
either be mutually exclusive or mutually-inclusive
based on the instances they share. For example,
Coke is sweet but a biscuit may be both sweet and
salty. Thus, in this case, the meta-concepts sweet
and salty corresponding to concept Taste are
In case of mutually-exclusive meta-concepts,
there is only one path from a product to the related
abstract concept. However, for mutually-inclusive
meta-concepts, there may exist multiple paths from a
product to the abstract concept. Thus, for mutually-
inclusive meta-concepts, the containment function is
defined in (5).
 
 
  
We take weighted average of all possible
containment functions from the mutually-inclusive
meta-concepts to the concept. This is done to include
all customer choices related to that concept
mentioned in the affordance ranklist. The rankings
for the same are also taken care of. For example,
is calculated as weighted average of
. The
weights are assigned based on the frequency of
customers preferring sweet versus salt tastes for
3.1.6 Relationship between Instances
Instances are related to each other through a
containment function . A containment function
defines the degree of match between instances I
under concept C, represented through respective
edge weights.
Figure 2: Sample dynamic ontology representation.
Figure 2 shows a sample dynamic ontology
representation comprising concepts, meta-concepts
and instances along with relationships. Solid lines
represent complete containment and broken lines
represent partial containment. Complete containment
refers to the fact that a child only belongs to one
parent. For instance, Sweet is completely contained
by Taste i.e. it will not belong to any other concept
such as Size or Ingredient. On the other hand, partial
containment refers to the concept of multiple
inheritance (Solé-Ribalta, Sánchez, Batet and
Serratosa, 2014) in ontologies. Like, Beer inherits
from two different concepts Taste and Ingredient.
Mining Substitution Rules: A Knowledge-based Approach using Dynamic Ontologies
Broken lines connect products in the form of
instances to meta-concepts through containment
function . Thus, two instances will be siblings only
with respect to a concept-meta-concept pair. The
degree of this sibling relationship between two
instances with respect to a given concept is given by
their respective containment functions. For example,
in Figure 2, Coke and Harpic are siblings with
respect to the concept (Content=Acidic) with
varying degrees of match.
3.1.7 Affordance-based Substitute Sets
We define concept-level substitute sets, S(c) that are
created from the dynamic ontology as follows:
These substitute sets comprise all instances in
the form of leaf nodes in the dynamic ontology
which share common affordances. Consider the
dynamic ontology representation given in Figure 2.
For Taste as a concept, the members of its substitute
set are:
from two paths Taste-Sweet-Coke (k=1) and
Taste-Bitter-Beer (k=2).
4.1 Expected Relatedness
Static ontology is represented as a n-ary tree which
defines “is-a” relationships between products and
their categories. It is based on manager’s domain
knowledge and is often not updated with changing
trends in customer purchase patterns. A static
ontology depicts manager’s expectedness of
products as substitutes based on their positions in the
tree. We define a measure called Expected
Relatedness to quantify manager’s expectations of
two products being related and hence substitutable.
Expected Relatedness is defined in terms of
hierarchical relationship with respect to a common
ancestor item. Shaw, Xu and Geva (2009) have
defined Diversity. We make use of this in defining
Expected Relatedness as the complement of
Diversity. Thus, we have the following for products
and p
  
 
  
 
Diversity is the ratio of the average of number of
levels for p
and that for p
(with respect to their
common ancestor), to the height of the tree (Shaw et
al, 2009). We define Expected Relatedness (ER)
between two products as the complement of this
4.2 Affordance Relatedness
We need to operationalize the distance between two
products in a dynamic ontology. This is done by
introducing a measure called Affordance
Relatedness. It captures customer perceptions of
substituting products based on common features or
Affordance Relatedness (AfR) is based on
distances in a dynamic ontology. Distance between
two products in a dynamic ontology cannot be
calculated through their structural positions. This is
because it is not constructed as levels of
classification of products but as features shared
among products. Thus we calculate relatedness
between two products p
and p
sharing common
concept (affordance) c as the difference in their
containment functions for c. We consider
normalized instead of absolute . This is to ensure
that there is no over-estimation of AfR for the two
products. Computed values of are obtained only
from transactions containing the particular concept
for a product. This value is not normalized for
transactions that contain different concepts for the
same product. Thus, it is necessary to normalize
with the sum of containment functions related to all
concepts shared by p. The difference after
normalization thus presents the true picture of
affordance relatedness for that product.
Cumulative Affordance Relatedness (CAfR) is
the relationship between two products based on all
concepts shared by them. We compute this by taking
ICAART 2018 - 10th International Conference on Agents and Artificial Intelligence
the complement of maximum of all AfRs relevant to
and p
  
4.3 The E-A Substitution Framework
It is essential to assess the quality and
interestingness of substitutable sets (or pairs) of
products generated from the proposed dynamic
ontology-based approach. This is done by comparing
the item relatedness of substitute pairs through their
positions in the static and dynamic ontologies.
Substitution in the static ontology is based on
manager’s expectations resulting from prior domain
knowledge. On the other hand, substitution in the
dynamic ontology comes from actual customer
purchase patterns. Thus, we propose an Expected-
Actual (E-A) Substitution Framework to compare the
quality of substitute sets obtained from our dynamic
ontology with the static managerial knowledge.
Horizontal direction of the E-A framework in Figure
3 represents the degree of relatedness between
products in the dynamic ontology. This is based on
the affordances they share. Vertical direction
represents the degree of relatedness between
products in the static ontology. This is based on the
manager’s expectations of their categorization. The
comparison yields us four different possible
Figure 3: Expected-Actual Substitution Framework.
Conforming Substitutes
Here Cumulative Affordance Relatedness is high and
Expected Relatedness is also high. This results in the
substitutable pair of products being conforming.
This is because manager expects products to be
substitutable (i.e. they belong to the same parent in
the static ontology). In addition, they also share
common concepts in their affordance ranklist (in the
dynamic ontology) as highlighted by the purchase
transactions. Hence, conforming substitutable pairs
do not present any interesting knowledge to the
Obsolete Substitutes
Cumulative Affordance Relatedness being low and
Expected Relatedness being high, result in the
substitutable pair of products becoming obsolete.
This is because these products are expected to be
substitutable by the manager but in actuality
customers never substitute them on the basis of any
common concept. Hence the manager needs to
modify his existing knowledge about this pair of
obsolete products through some actionable event.
Unrelated Substitutes
If Cumulative Affordance Relatedness and Expected
Relatedness are both low, then the substitutable pair
of products is unrelated. This is because these
products are neither expected to be substitutable by
the manager nor do they share any common
affordance. Such unrelated pairs of substitutable
products will not result in interesting negative rules
getting generated.
Unexpected Substitutes
Here Cumulative Affordance Relatedness is high and
Expected Relatedness is low. This is unexpected
because the manager never expected these products
to be substitutable. However in actuality customers
often substitute them based on common concepts.
Hence, these unexpected pairs of substitutable
products yield most interesting insights for the
4.4 Substitute Interestingness Measure
We define a composite measure of interestingness
that encompasses all the four quadrants of the E-A
framework. This measure is the arithmetic difference
between positions of two products in the dynamic
ontology (CAfR) and the same being represented in
the static ontology (ER).
This measure of Substitute Interestingness (SI)
represents the additional knowledge made available
to the manager vis-à-vis his expected beliefs. The
rationale behind subtraction is removal of the
already known previous beliefs of the manager
regarding substitution of products.
Consider the four scenarios of the E-A
framework for the calculation of SI. Products falling
in the bottom-left quadrant and those falling in the
Mining Substitution Rules: A Knowledge-based Approach using Dynamic Ontologies
top-right quadrant will have low values for SI. This
essentially says that conforming and unrelated
substitutes do not provide rich insights for the
manager. However, the bottom-right and the top-left
quadrants will have high values for SI, thus telling
the manager to investigate these unexpected and
obsolete substitutes for possible useful
interestingness insights.
We mine substitution rules with the help of substitu-
tion sets obtained from the dynamic ontology. We
generate rules comprising products with high affor-
dance relatedness and high interestingness values.
Two products X and Y form a substitution rule
Y, if the following hold:
1) 
2) 
and 
are thresholds for dynamic ontology
relatedness and interestingness, respectively.
The Affordance-based Substitution (ABS)
algorithm for generating substitution rules is given
To study the effectiveness of our model, we ran ABS
algorithm on a real-world supermarket dataset.
Transaction data D was obtained for a period of 13
months from November 2015 to December 2016.
The transactions covered 113 items, that were then
classified into 11 product categories. A random
sample of 110 customers of the supermarket was
drawn to collect the affordance data through a
survey instrument. The descriptive statistics of the
sample is given in Table 1. The survey pertained to
ranking various features of the 11 selected product
categories based on customer preferences while
purchasing items from that category. We obtained a
total of 4120 transactions. They were then appended
with product and affordance ranking data. We
obtained the static ontology pertaining to the 11
product categories from the manager of the
supermarket. The static ontology consisted of 5
levels with categories such as personal care, edibles
and the like.
Table 1: Descriptive Statistics of 110 customers surveyed.
7.1 Dynamic Ontology
We ran the ABS algorithm on the supermarket
dataset to generate affordance-based substitution
rules. Feature rankings recorded from the survey
Table 2: Matrix representation of dynamic ontology from
supermarket dataset.
ICAART 2018 - 10th International Conference on Agents and Artificial Intelligence
Figure 4: E-A framework for the substitute pairs.
were categorized into 8 affordance classes (A
). The
resultant dynamic ontology included edge weights
(containment functions)
for each product-
affordance pair. The matrix representation of the
dynamic ontology is given in Table 2.
7.2 Relatedness Measures and E-a
We computed the two relatedness measures, CAfR
and ER, for the substitute sets obtained from the
dynamic ontology constructed from the supermarket
dataset. The E-A framework based on the
distribution of the resulting 55 substitute pairs is
presented in Figure 4.
Substitute pairs are distributed across all four
quadrants of the E-A framework. Analysis of the
four quadrants in Figure 4 is as follows:
Conforming Substitutes
This quadrant provides the least interesting
knowledge for a manager. Product pairs here are
expected to be substitutable with respect to the
manager’s static ontology as well as through
customer oriented dynamic ontology. For instance,
P007-P011 (Facewash-Soap) are conforming
substitutes. Both are siblings in the static ontology
(ER=0.75) and have a high affordance relatedness in
dynamic ontology (CAfR=0.70).
Obsolete Substitutes
This quadrant provides interesting information with
which a manager may modify prior knowledge about
obsolete substitutes pairs. For example, consider
P003-P009 (Hair Oil-Shampoo). Although both are
siblings in the static ontology (ER=0.5), they do not
substitute each other in the dynamic ontology
(CAfR=0.4). Thus, it is evident that static ontology
will not suffice for the analysis of such substitution
Unrelated Substitutes
Unrelated substitutable products will not result in the
generation of interesting substitution rules because
of low relatedness values in both static and dynamic
ontologies. Consider P001-P008 (Room Freshener-
Toothbrush) neither lie close to each other in the
static ontology (ER=0.25) nor do they have any
common affordances in the dynamic ontology
Unexpected Substitutes
Major concentration of pairs occurs in this quadrant
leading to interesting insights for the manager. The
large concentration also highlights the necessity for
dynamic ontology approach. This may help in
updating the static ontology-based manager’s
knowledge. Consider P001-P004 (Room Freshener-
Deodorant). Both products lie in altogether different
classes in the static ontology, personal care and
household respectively (ER=0.375). However, they
share many concepts, like fragrance, alcohol content,
packaging and size (CAfR=0.56). Thus the proposed
approach will result in their being classified as
7.3 Substitution Rule Generation
Computation of interestingness measure SI was done
for the generated substitution rules. We looked at its
effectiveness in pruning the substitution rules.
Variation in the fraction of rules generated with
Mining Substitution Rules: A Knowledge-based Approach using Dynamic Ontologies
respect to changing SI values is given in Figure 5.
The plot is for three threshold values of CAfR,
namely 0.5, 0.7 and 1. This is because CAfR being
greater than the threshold is one of the necessary
conditions for generating substitution rules. We note
that generated rules increases by 30% when CAfR
threshold is increased from 0.5 to 0.7, and by 17%
when increased from 0.7 to 1. This shows that our
substitution rules comprise items with high
affordance relatedness and low expected relatedness.
Figure 5: Fraction of rules generated through ABS
algorithm for varying SI and CAFR.
7.4 Comparison between ABS and
SRM Algorithm
We compare our algorithm with Substitute Rule
Mining (SRM) algorithm developed by Teng et al
(2005). We show that substitution rules generated by
ABS are better in terms of efficiency and quality
than those generated by SRM.
The supermarket dataset was appended with
complement items as highlighted by Teng et al (2005,
p.162). The SRM algorithm was then used to generate
substitution rules. We present the changes in the
cardinality of substitution rules with varying support
thresholds in Figure 6. The variation follows a non-
linear curve as the support threshold decreases.
The 189 substitution rules generated by SRM
algorithm with a support threshold of 0.2 are then
compared with the 55 substitution rules generated by
ABS algorithm. The comparison of SRM and ABS
algorithms is presented in terms of support and SI
interest measures in Figure 7.
Out of the 189 rules generated, SRM misses out
27 substitution rules generated by ABS algorithm.
Since substitution rules generated by ABS are
indicative of customer perceptions while substituting
two products, missing these rules is indicative of
exclusion of changing purchase patterns. Thus we
find that ABS algorithm has more potential to
capture customer-perceptions. For instance, the
substitution rule P001
P002 generated by ABS
having interest SI 0.57 is not generated by SRM.
This loss in information is critical because P001 and
P002 are substitutable through an affordance
relatedness (CAfR) of 0.82. A high CAfR highlights
P001 and P002 sharing a lot of concepts in common
making them highly substitutable by customers.
Comparison of the two algorithms also reveals cases
where substitution rules having a low negative value
of SI (from ABS) have a very high support from
SRM. Rule P004
P008 (SI = -0.06, Support =
0.67) is one such case. This is essentially
misspecification pointing to over estimation of
substitution rules.
Figure 6: Number of substitution rules generated by SRM.
Figure 7: Comparison between ABS and SRM algorithm using support and SI values.
-1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1
Fraction of rules generated
Interest Measure, SI
0 200 400 600 800
# of Substitute Rules
Expon. (# of Substitute Rules)
SI Support
ICAART 2018 - 10th International Conference on Agents and Artificial Intelligence
AR Mining literature has focused a lot on generating
positive rules. Researchers have now started
proposing efficient algorithms for mining
substitution rules (Chen and Lee, 2015). However
these algorithms have restricted their definition of
substitution to either statistics or a manager’s static
knowledge. We extend the work on substitution rule
mining by introducing a customer-centric view on
substitution using the lens of affordance.
In a static ontology positioning of items is based
on manager’s previous knowledge. We propose the
concept of a dynamic ontology that is constructed
“on the fly" based on varying customer purchase
patterns. This variation in purchase patterns is
tapped using affordance specified as a ranked list
together with products specified in each purchase
transaction. We propose a containment function that
assigns a value for each product-affordance pair.
These values are then used to form substitute sets
leading to generation of substitution rules. We
provide an Expected-Actual (EA) Substitution
framework that helps classify pairs of substitute
products into four categories: conforming, obsolete,
unrelated and unexpected substitutes. We also use
this framework to come up with a novel
interestingness measure that compares item
relatedness between static and dynamic ontologies
and prunes redundant substitution rules.
Our substitution rule mining process is operatio-
nalized through an Affordance Based Substitution
(ABS) algorithm. A real-life super-market dataset is
used to test the efficacy and effectiveness of the
ABS algorithm. Our results show that substitution
rules generated through ABS algorithm have better
quality in terms of interestingness for a manager. We
compare our approach with the approach given by
Teng et al (2005). The comparison shows that
several high-quality rules generated by ABS get
missed by SBM algorithm (Teng et al, 2005). This
highlights the fact that changing customer-
perceptions are not reflected in current substitution
rule mining algorithms. We also attempt to place the
generated pairs of substitute products in our E-A
Substitution framework. This placement and
distribution provides useful managerial insights
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