Towards Association Rules as a Predictive Tool for Geospatial Areas

Evolution

Asma Gharbi

1,2

, Cyril De Runz

3,4,1

, Sami Faiz

and Herman Akdag

LIASD, University of Paris 8, Saint-Denis, France

LTSIRS, University of La Mannouba, Tunis, Tunisia

CReSTIC University of Champagne-Adrenne, Reims, France

Sorbonne Universit

e, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606, Paris, France

Keywords:

Association Rules, Spatial Dynamics, Prediction, Sequential Association Rules, Class Association Rules.

Abstract:

Although it was basically presented as an exploratory tool rather than a predictive tool, numerous follow up

researches have enhanced association rule mining, which contributes in making it a powerful predictive tool.

In this context, this paper review the main advances in this datamining technique, then attempts to describe

how they can, practically, be harnessed to deal with problems such as the prediction of geographical areas

evolution.

1 INTRODUCTION

Geographical areas, such as cities are large, com-

plex, and dynamic systems evolving and changing

their characteristics under the effect of divers social,

economic, political, and environmental factors. The

need for understanding, projecting, and planning their

evolution, mainly consisting in land use/cover change

(LUCC), has emerged decades ago as an attempt to

accommodate urban dynamics while preserving and

restoring the environment. For instance, in (Gharbi

et al., 2014), urban areas have been perceived as

collections of geographical entities (GEs) temporally

and spatially related to one another and continuously

evolving on two main levels: the spatial level related

to their morphologies and locations, and the func-

tional level regarding their vocations or use. Indeed,

GEs’ evolutions have been represented in form of se-

quences embedding their land use and spatial conﬁg-

uration histories.

In the present paper, we propose a solution based

on a widely adopted prediction hypothesis according

to which, the best predictor of future is the past. In

this context we quote the words of great minds in

different domains such as, Robert Kiyosaki, the fa-

mous American business man, and ﬁnancial literacy

activist and commentator, who pointed out that: ”The

best way to predict the future is to study the past,

or prognosticate.”; Jules Henri Poincar

e, a French

mathematician, theoretical physicist, engineer, and

philosopher of science, who said that ”If we knew

exactly the laws of nature and the situation of the

universe at the initial moment, we could predict ex-

actly the situation of the same universe at a suc-

ceeding moment.”; and last, but not least, we may as

well quote the clinical psychologist Albert Ellis who

asserted that, in the psychology domain, ”The best

predictor of future behavior is past behavior”. The

hypothesis above, which constitutes the core of our

work, corresponds to a popular datamining approach

known as frequent pattern mining (FPM). This ap-

proach consists in identifying items, sequences, and

the frequently co-occurring structures in a given past

database, with the objective of discovering relation-

ships among the different variables describing the

data. Such correlations or associations are generally

represented in form of rules. Since decades, FPM has

known abundant ameliorations and improvements to

adequately respond to tasks such as prediction.

In this context, this paper suggests the use of asso-

ciation rule mining (ARM) to extract evolution rules

for a certain geographical area, based on time series

spatio-temporal data. Therefore, we starts in section 2

by deﬁning the association rule mining problem, pre-

senting the progress it has known over years, how this

progress has contributed in making association rules a

powerful predictive tool which motivates its employ-

ment for spatial dynamic prediction. Thereafter, we

dedicate the third section for describing how we used

adapted association rules for urban dynamic predic-

Gharbi, A., Runz, C., Faiz, S. and Akdag, H.

Towards Association Rules as a Predictive Tool for Geospatial Areas Evolution.

In Proceedings of the 2nd International Conference on Geographical Information Systems Theory, Applications and Management (GISTAM 2016), pages 201-206

ISBN: 978-989-758-188-5

201

tion. Finally, in section 4, we draw a conclusion.

2 ASSOCIATION RULE:

DEFINITION AND EVOLUTION

2.1 Problem Statement

Association rule mining is a fundamental datamin-

ing task which aims at discovering useful regulari-

ties, called associations, in a given database, through

identifying all the frequently co-occurring items. The

formal deﬁnition of association rules can be stated as

follows: Let D be a transaction database and T a set

of transactions (T={t

, t

, ..., t

}) of D, composed

of a set of items I={i

, i

, ..., i

}, such that t

⊆

I. An association rule represents an implication in the

following form:X −→ Y, where X and Y are sets of

items, called itemsets; X, Y ⊂ I; and X ∩ Y =

Since it was ﬁrst introduced in (Agrawal et al.,

1993), association rule mining has been a focused re-

search area in machine learning and knowledge dis-

covery, over decades. Apriori is one of the most popu-

lar ﬁrst presented algorithms. It proceeds in two steps:

1. Generation of all frequent itemsets using a level-

wise complete search algorithm. It generates can-

didate itemsets, based on the downward closure

property. Then it scans the database to determine

their support values and keep only the frequent

ones. An itemset is called frequent if its support

count (the number of transactions containing this

itemset) is equal or greater than a user-speciﬁed

minimum support (minsup).

2. Generation of conﬁdent association rules from the

found frequent itemsets. In other words, a rule

with a conﬁdence value above a user-speciﬁed

minimum conﬁdence (minconf).

2.2 Evolution of the Concept

Association rule mining is a datamining technique

characterized by its understandability, simplicity over

other supervised techniques, intuitiveness and, ease

of implementation. This technique represents a sim-

ple method, free from model-based assumptions, that

is, it eschews linearity assumptions underlying many

classical supervised classiﬁcation, regression, and

ranking methods, and directly models conditional

probabilities (ex: P(y|a)). In fact, association rule

mining proceeds by looking for correlations based on

subsets of frequently co-occurring past events (items)

in order to generate a set of if-then rules. Unlike clas-

siﬁcation rule mining techniques which can predict

only one attribute, association rules involve the pre-

diction of any attribute in the data set. The generated

rules form, then, richer models that are, moreover, in-

terpretable and easy to understand by human users

(i.e., given the rule if X then Y, it is obvious that Y

was recommended because X is satisﬁed).

The key strength of ARM is its completeness and ex-

haustivity in terms of generation of rules. Indeed,

in traditional classiﬁcation techniques (e.g., decision

tree, decision lists, neural networks, etc.) a small sub-

set of rules is produced, based on various heuristics,

however, ARM consists in ﬁnding all the frequently

appearing patterns in the given database. Thus it

doesn’t miss any detailed rule that might be important

in some application cases. Another main advantage of

ARM over some other supervised learning paradigms

is its ability to handle the ”cold start” problem (i.e.,

related to small training datasets). Actually, in these

paradigms, a large sample is necessary for general-

ization, as bounds scale only with the sample size.

However, in association rules, the user-speciﬁed min-

sup threshold guarantees that predictions can be made

only when there are enough data, even if it is a small

amount of it.

Besides to their proper strengths ARM has, over

years, undergone improvements and extensions. Al-

thought its capability to generate rules in linear time

and even scale up to large database, ﬁrst algorithms

(i.e, Apriori) presented three main challenges: the

multiple scans of transaction database, the generation

of a huge number of candidates, and the tedious work-

load of support counting for candidates.Tremendous

number of algorithms attempting to deal with these

challenges and aiming at improving the computa-

tional capacity and the use efﬁciency of the memory

have been reported. Most of them have focused on

three main ideas:

• Reducing passes of transaction database scans

like partitioning-based algorithms, transaction re-

ducing algorithms, and algorithms without candi-

date generation (FP-growth, H-mine), etc.)

• Shrinking the number of candidates: sampling-

based algorithms, hash-based algorithms,

condition-based algorithms, etc.

• Facilitating support counting of candidates like

algorithms using vertical data format (ECLAT),

hash-based algorithms, etc.

More explanation of these latter with references of ex-

amples of their implementations and examples of al-

gorithms corresponding to further methodologies, can

be found in (Aggarwal et al., 2014).

Actually, the numerous efforts made to improve

the performance of existing mining algorithms, has,

considerably, helped with the objective of efﬁciently

GISTAM 2016 - 2nd International Conference on Geographical Information Systems Theory, Applications and Management

202

handling the huge amount of data required for some

prediction applications. Besides to these efforts

mainly related to performance issues, other advances

in association rule mining have been proposed which

enhanced their analytical and most importantly pre-

dictive capabilities and broaden their application

scope (e.g., spatio-temporal dynamics). Among these

one may mention, spatio-temporal association rule

mining to capture time and space dependent patterns,

quantitative and fuzzy association rule mining to bet-

ter handle real life descriptors, mining with multiple

minsups to not skip rarely occurring but important

patterns, and class association rule mining to cover

other tasks such as classiﬁcation and prediction. Class

Association rule (CAR) mining algorithms consist in

discovering rules in the form of a−→b, where the

consequence part (b) have to be an item labelled as

a class. These rules can then be used to predict the

class of unclassiﬁed records. This method enables

users to decrease the number of generated rules by

precising which form of rule they are interested in.

CARs showed, as well, success in different prediction

applications. It was even reported in many experi-

mental studies, as for instance (Thabtah et al., 2004),

that this approach can outperform traditional classiﬁ-

cation methods, such as decision trees, in constructing

a more accurate predictive systems.

2.3 Association Rules in the Prediction

Framework

A predictive association-based model uses the an-

tecedent of a rule to predict the consequent of the rule.

In other words, it indicates what item is likely to occur

given the occurrence of a certain itemset. This type of

models have been employed for many applications in

different domains, one may cite predicting customer’s

likely future purchases, in the context of basket mar-

ket analysis (Chen et al., 2014); in biology, the predic-

tion of proteins functions, based on the proteinprotein

interaction networks (Park et al., 2015); in medicine,

the prediction of the risk level of the patients having

heart disease (Ilayaraja and Meyyappan, 2015); and

last but not least, in the energy management ﬁeld as-

sociation rules have been employed for the prediction

of buildings Occupant Location. In fact, this problem

consists in determining the location of buildings occu-

pants, based on their movement historic, to maximize

heating, ventilation, air conditioning (HCAC) energy

efﬁciency. In other words, operate HCAC systems in

accordance with occupant movements to satisfy their

needs without squandering energy (Ryan and Brown,

2013).

Several other works such as (Lin and Li, 2015)

have demonstrated how association rule mining can

also be employed for extracting spatio-temporal pat-

terns related, for instance, to urban dynamics (e.g.,

urban growth or land use/cover change). This type

of application discovers patterns related to spatio-

temporal relationships which are typically embed-

ded in geospatial data instead of being explicitly en-

coded in the database. Spatial association rules han-

dle pieces of information such as location and topol-

ogy of items to extract frequent patterns mainly show-

ing the interaction of two or more space-depending at-

tributes or spatial objects. While the Temporal rules,

captures timedependent attributes to reveal knowl-

edge about the cyclic, periodic or sequential nature

of some patterns. The real added value of mining as-

sociation rules in a temporal context is to gain more

predictive capabilities. For instance in sequential rule

mining (Rudin et al., 2013), both, the occurrences of

items and the order between these occurrences counts

in producing rules that attempt to determine what

event will next be revealed based on sequences of past

events.

Spatial and temporal relationships could have hi-

erarchical aspects. For instance, in the case of land

cover an industrial zone can be also denoted as a de-

veloped zone in a higher hierarchy level. Hence both

rules involving ”developed zones” and others involv-

ing ”industrial zones” are then generated. In this con-

text, Association rules has been extended to Multi-

level association rules which support the hierarchi-

cal aspect of patterns such as spatio-temporal rela-

tionships. Association rules are conventionally de-

signed for handling only categorical data. However,

spatial relationships include as well, metric relation-

ships such as distance that are described with numer-

ical data. This issue has been addressed by present-

ing quantitative association rule mining which has

been combined afterward with fuzzy sets theories to

address the imperfect aspects of spatial relationships

(e.g., determining degrees of neighborhood through

partial membership to intervals of the distance at-

tribute) (Farzanyar and Kangavari, 2012).

3 OUR PROPOSAL

In this section we propose an apriori based approach

for mining rules predicting the evolution of geograph-

ical areas. Our goal is to demonstrate how the ad-

vances mentioned in section 2 can be harnessed to

make association rule mining suitable for this predic-

tion problem. Based on spatio-temporal data, we aim

at extracting rules which involve particular temporal

and spatial relationships in order to indicate the next

Towards Association Rules as a Predictive Tool for Geospatial Areas Evolution

203

evolution (i.e., next land cover for a certain geograph-

ical zone).

In the present work, geographical entities are char-

acterized by their functions (e.g., land use/cover), spa-

tial relationships are represented by their neighbor-

hood interrelations, and temporal relationships are

represented by sequential occurrences (successions)

of GEs (see ﬁgure 1).

Figure 1: The Considered Spatio-temporal Relationships.

As regards identifying the spatial relationships of

neighbourhood among entities, two approaches may

be adopted. The ﬁrst one deﬁnes neighbouring enti-

ties as directly adjacent ones, and the second, consid-

erate that, given two GEs E1 and E2, E2 is a neigh-

bour of E1 if the distance between them is under or

equal to a user-speciﬁed threshold. In the second case,

the continuous numerical attribute of distance will be

discretized into two categorical values: neighbour and

non-neighbour. However, the strict membership or

non-membership to either of these categories can lead

to a problem of misestimating distance values near the

borders. In order to deal with this problem, we pro-

pose to consider the concept of partial membership

using a membership function deﬁned based on fuzzy

sets theories.

It is worth noting that this approach supports

two different applications: addressing entities con-

sisting in geographically delimited zones and address-

ing buildings as the studied entities. In the ﬁrst case,

the functional level of evolution is related to land

use/cover change, and in the second, it regards func-

tions of building (e.g., residential, industrial, admin-

istrative, leisure equipements, etc)

3.1 Dataset

In our context, the Spatio-temporal database describes

all the geographical entities situated in the studied

geographical zones at different consecutive dates.

Corine Land Cover Database is an example, of which

an extract is given in ﬁgure 5. It provides pieces

of information regarding their functional (e.g., land

cover), and spatial characteristics (e.g., locations, sur-

face area, form, etc).

The ﬁrst task in applying association rule min-

ing consists in proposing, from the available spatio-

Figure 2: Spatio-temporal Data.

temporal data, an appropriate format for the learning

dataset. This latter will, afterwards, be used to ex-

tract adequate rules for our prediction problem. The

dataset, in the present approach, is composed of in-

stances that each represents the evolution history of a

geographical entity (see ﬁgure 3.a).

Figure 3: An Example Illustrating the Extraction of Learn-

ing Attributes.

In fact, the evolution trajectory (history) of a certain

geographical entity is encoded in the form of a trans-

action composed by:

• A sequence of its past evolutions (sequence of

past functions). In the example illustrated in ﬁg-

ure 3.b the SPF attribute corresponds to < SPF :

• A set of items representing the functions of the

neighbouring entities of each entity involved in

the evolution sequence . In the example above,

< F : f

;N: f

>, represents the neighbourhood

relationship between the entities E2 and E5, re-

spectively, characterized by the functions f

and

• An item representing the succeeding function ( f

)

Hence, the set of attributes of our dataset is A={sp f

sp f

, sp f

,..., sp f

, N

,..., N

, s

,..., s

}. n de-

notes both the number of transactions which is equal

to the number of sequences of past evolutions, and the

number of successors. x denotes the number of neigh-

bours, n<F={ f

, f

, ..., f

} with F is the set of all

possible functions of entities. In the context of the

GISTAM 2016 - 2nd International Conference on Geographical Information Systems Theory, Applications and Management

204

Figure 4: Structure of the Learning Database.

example above, 4 depicts the structure of the learning

database. Rows correspond to the different evolution

trajectories and columns to the attributes (SPF, N, S).

Using this dataset format, our objective is to ﬁnd

rules that predict the attribute S based on the other at-

tributes N and SPF. A predictive evolution rule should

be in this form:

< SPF =< f

> ∧ < F = f

;N = f

>−→< S = f

3.2 Preliminary Results

Figure 5: An extract of First Generated Rules.

In order to test our proposed dataset format (ﬁgure

4) mainly in terms of relevance of generated rules,

we run Apriori. The preliminary results showed that

only rules involving the neighbourhood attribute have

been generated. Besides their form does not match

the speciﬁed interesting form which requires solu-

tions related to: considering rare but important items

(SPF, S), and guaranteeing the generation of interest-

ing rules only (i.e., SPF ∧ N −→ S).

3.3 Generation of Candidates

As mentioned above, apriori-based algorithms pro-

ceeds on two steps: the ﬁrst one consists in generat-

ing candidate itemsets then keeping only the frequent

ones, and the second step consists in generating rules

from the found frequent itemsets. For each frequent

itemset f apriori ﬁnds all their nonempty subsets α

then generate conﬁdent rules (i.e., whose conﬁdence

is above minconf threshold) of the form:

( f − α) −→ α

For instance, given the frequent itemset f={A,B,C},

α={A, B, C, AB, AC, BC . An example of generated

rules is B ∧C −→ A. Due to this, a great importance

is granted to the candidate generation step, in order

to prevent generating useless candidates and conse-

quently useless rules. Actually, in our approach we

propose to predict the successor attribute (S) based

on the other attributes (i.e., SPF and N). Hence, any

itemset which misses any of these attributes (S, SPF,

N) cannot produce rules in the required format spec-

iﬁed above. Therefore we propose in our frequent

pattern generation function (FP-Gen( )) to add a con-

straint in order to only keep candidates which include

at least one item for each attribute (see the example in

ﬁgure 6).

Figure 6: Validation of candidat itemsets.

As regards to the SPF attribute, our FP-Gen func-

tion has, also, to handle its sequential nature when

generating candidates as in this attribute, not only the

occurrence of entities matter, but also their order. The

key element in this ﬁrst step of apriori (the frequent

itemsets generation) is the minsup threshold (minsup)

as it is used to assess the frequency of candidate item-

sets. However, using a single minsup assumes that all

items have similar frequencies in the dataset, which

is not the case for different real-life application and

indeed for our prediction problem. Actually, in our

dataset, neighbourhood items are a way more frequent

than other items and setting the minsup too low to cap-

ture rare items can lead to combinatorial explosion.

Therefore we propose, as a solution, to specify multi-

ple minsups, in other words, set a different minsup for

each attribute i.e., minsup(N) 6= minsup(SPF) 6= min-

sup(S). The key element in this ﬁrst step of apriori (the

frequent itemsets generation) is the minsup threshold

(minsup) as it is used to assess the frequency of can-

didate itemsets. However, using a single minsup as-

sumes that all items have similar frequencies in the

dataset, which is not the case for different real-life ap-

plication and indeed for our prediction problem. Ac-

tually, in our dataset, neighbourhood items are a way

more frequent than other items and setting the minsup

too low to capture rare items can lead to combinato-

rial explosion. Therefore we propose, as a solution, to

specify multiple minsups, in other words, set a differ-

ent minsup for each attribute i.e., minsup(N) 6= min-

sup(SPF) 6= minsup(S).

3.4 Generation of Predictive Rules

With regards to rule generation, we aim at generating

only rules where S attributes are in the consequent

part of the rule and the other attributes are in the an-

Towards Association Rules as a Predictive Tool for Geospatial Areas Evolution

205

tecedent part. In this regards, we suggest the use of

class association rule mining wherein each transac-

tion is labelled with a class s. Let S be the set of

all class items corresponding to the attribute S, I be

the set of all items in database corresponding to the

attributes SPF and N, and S ∩ I=

0. A class associa-

tion rule is an implication in the form: a−→b, where

a ⊆ I and b ⊆ S. In CARs candidats are denoted as

ruleitems and are in the following form: (Condset,s).

condset represents a set of items (condset ⊆ I) and

s a class (s ⊆ S). Each ruleitem represents the rule

condset −→ s. The support count of a condset (SCC)

represents the number of transactions in the database

which contain the condset. The support count of the

generated rules (SCR) is the number of transactions of

the database containing the condset and having s as

a class. Like in the traditional association rule min-

ing, apriori in CARM generates all frequent ruleitems

whose support is above a minsup threshold, then, use

them to generate class association rules with a con-

ﬁdence value (SCR / SCC) above the user-speciﬁed

minconf threshold. The distinct particularity in CAR

candidate generation function is that, the joining step

is done by joining condsets of ruleitems having the

same class.

As mentioned above this approach (CARM) aims

at only producing rules in a speciﬁc form which is

assumed to be adequate for our prediction task. Al-

though it may seem logical to proceed, simply, to a

post-selection of interesting rules, this solution is, in

practice, very difﬁcult and sometimes impossible due

to the combinatorial explosion, in other words, the

huge number of rules that could be generated.

4 CONCLUSION

Association rule mining is a fundamental datamin-

ing task which has been basically presented as an ex-

ploratory tool rather than a predictive tool. In this

research we attempted at reviewing the most impor-

tant advances, in this datamining tool, ranging from

proposing scalable algorithms and efﬁcient method-

ologies for mining frequent itemsets to handling a

diversity of data types and structures and extended

mining tasks. Our overall goal is to show how all

this progress has contributed in making AR a pow-

erful prediction tool. Indeed, we proposed an associ-

ation rule-based approach for predicting the evolution

of geographical areas as an attempt to show how the

progress, done so far, can, practically, be harnessed

for this example of prediction problem.

Our proposal consists in an apriori-based ap-

proach for mining rules predicting the evolevolution

of geographical areas. This approach proposes to ad-

dress issues related to handling spatial and temporal

relationships in the learning dataset, producing rules

involving rare patterns, and making sure to only gen-

erate rules in an adequate form for our prediction

problem.

REFERENCES

Aggarwal, C. C., Bhuiyan, M. A., and Hasan, M. A. (2014).

Frequent pattern mining algorithms: A survey. In Ag-

garwal, C. C. and Han, J., editors, Frequent Pattern

Mining, pages 19–64. Springer International Publish-

ing.

Agrawal, R., Imieli

nski, T., and Swami, A. (1993). Min-

ing association rules between sets of items in large

databases. In ACM SIGMOD Record, volume 22,

pages 207–216. ACM.

Chen, J., Miller, C., and Dagher, G. (2014). Product rec-

ommendation system for small online retailers using

association rules mining. In Innovative Design and

Manufacturing (ICIDM), Proceedings of the 2014 In-

ternational Conference on, pages 71–77.

Farzanyar, Z. and Kangavari, M. R. (2012). Efﬁcient min-

ing of fuzzy association rules from the pre-processed

dataset. Computing and Informatics, 31(2):331–347.

Gharbi, A., de Runz, C., Faiz, S., and Akdag, H. (2014). An

association rules based approach to predict semantic

land use evolution in the french city of saint-denis. In-

ternational Journal of Data Warehousing and Mining,

10:1–17.

Ilayaraja, M. and Meyyappan, T. (2015). Efﬁcient data

mining method to predict the risk of heart diseases

through frequent itemsets. Procedia Computer Sci-

ence, 70:586 – 592. Proceedings of the 4th Inter-

national Conference on Eco-friendly Computing and

Communication Systems.

Lin, J. and Li, X. (2015). Knowledge transfer for large-

scale urban growth modeling based on formal concept

analysis. Transactions in GIS, pages n/a–n/a.

Park, H. A., Kim, T., Li, M., Shon, H. S., Park, J. S., and

Ryu, K. H. (2015). Application of gap-constraints

given sequential frequent pattern mining for protein

function prediction. Osong Public Health and Re-

search Perspectives, 6(2):112 – 120.

Rudin, C., Letham, B., and Madigan, D. (2013). Learn-

ing theory analysis for association rules and sequen-

tial event prediction. Journal of Machine Learning

Research, 14:3441–3492.

Ryan, C. and Brown, K. (2013). Predicting occupant lo-

cations using association rule mining. In Bramer, M.

and Petridis, M., editors, Research and Development

in Intelligent Systems XXX, pages 63–77. Springer In-

ternational Publishing.

Thabtah, F., Cowling, P., and Peng, Y. (2004). Mmac: a

new multi-class, multi-label associative classiﬁcation

approach. In Data Mining, 2004. ICDM ’04. Fourth

IEEE International Conference on, pages 217–224.

GISTAM 2016 - 2nd International Conference on Geographical Information Systems Theory, Applications and Management

206