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.

1 INTRODUCTION AND

RELATED WORK

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

Figure 1: Classification of related work in substitution rule

mining.

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

nuances.

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 PRELIMINARIES

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

product.

3 SUBSTITUTION USING

DYNAMIC ONTOLOGY

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





as:







(1)

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

rank 









, containment function  is given by (2):





























(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.











  



















 

(3)





















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.



















(4)

























 























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

structure.

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

mutually-inclusive.

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).













 

(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





and 



. The

weights are assigned based on the frequency of

customers preferring sweet versus salt tastes for

biscuits.

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

and

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:





























(6)







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 ITEM RELATEDNESS AND

THE SUBSTITUTION

FRAMEWORK

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





























 











  

(7)















 













 











  

(8)















 













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

ratio.

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

applications.











































































(9)

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















  



























(10)















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

substitutions.

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

manager.

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

manager.

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).





























 













(11)

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.

5 AFFORDANCE-BASED

SUBSTITUTION RULES

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

below.

6 DATA DESCRIPTION

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.

Mean

Minimum

Maximum

Age

Work

Experience

(months)

22.46

Gender

Male=78%

Female=22%

7 RESULTS AND ANALYSIS

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.

Del

P001

0.97

0.49

0.40

P002

0.66

0.43

0.65

0.44

P003

0.42

0.65

0.81

P004

0.90

0.29

0.38

0.43

0.36

P005

0.60

0.36

0.73

0.44

0.26

P006

0.48

0.46

0.93

P007

0.52

0.70

0.48

P008

0.65

0.82

0.39

P009

0.70

0.41

0.75

P010

0.41

0.32

0.70

P011

0.73

0.38

0.64

0.38

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

Framework

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

rules.

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

(CAfR=0).

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

substitutes.

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

CAfR=0.5

CAfR=0.7

CAfR=1

591

189

0 200 400 600 800

0,1

0,2

0,3

0,4

0,5

Support

# of Substitute Rules

Expon. (# of Substitute Rules)

-0,8

-0,6

-0,4

-0,2

0,2

0,4

0,6

0,8

P001-P002

P001-P003

P001-P004

P001-P005

P001-P006

P001-P007

P001-P008

P001-P009

P001-P010

P001-P011

P002-P003

P002-P004

P002-P005

P002-P006

P002-P007

P002-P008

P002-P009

P002-P010

P002-P011

P003-P004

P003-P005

P003-P006

P003-P007

P003-P008

P003-P009

P003-P010

P003-P011

P004-P005

P004-P006

P004-P007

P004-P008

P004-P009

P004-P010

P004-P011

P005-P006

P005-P007

P005-P008

P005-P009

P005-P010

P005-P011

P006-P007

P006-P008

P006-P009

P006-P010

P006-P011

P007-P008

P007-P009

P007-P010

P007-P011

P008-P009

P008-P010

P008-P011

P009-P010

P009-P011

P010-P011

SI Support

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

8 CONCLUSIONS

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

hitherto not present in the data mining literature.

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