The document describes the Ant-Miner algorithm for classification using ant colony optimization. It begins with an introduction to ant colony optimization and how it was inspired by the foraging behavior of real ants. It then provides details on the key steps of the Ant-Miner algorithm, including rule construction, pruning, and pheromone updating. The algorithm uses a heuristic function based on information theory and positive feedback to iteratively construct and refine classification rules from training data.
In computer science and operation research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graph.
This presentation provides an introduction to the Ant Colony Optimization topic, it shows the basic idea of ACO, advantages, limitations and the related applications.
Introduction to Computational Intelligent
Motivation
Main umbrella: Natural Computing
Computational options: Levels of Abstraction
Definition: CI
Basic Properties of CI
CI Main Paradigms
Examples of Natural phenomenas
Computational Intelligence: Modeling Methodology
Applications of CI
Recommended References
In computer science and operation research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graph.
This presentation provides an introduction to the Ant Colony Optimization topic, it shows the basic idea of ACO, advantages, limitations and the related applications.
Introduction to Computational Intelligent
Motivation
Main umbrella: Natural Computing
Computational options: Levels of Abstraction
Definition: CI
Basic Properties of CI
CI Main Paradigms
Examples of Natural phenomenas
Computational Intelligence: Modeling Methodology
Applications of CI
Recommended References
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Swarm intelligence, a branch of artificial intelligence is a part which discusses the collective
behaviour of social animals such as ants, fishes, termites, birds, bacteria. The collective behaviour of
animals to achieve target can be used in practical applications. One of the applications is ant colony
optimization. Ongoing research of ACO, there are diverse applications namely data mining, image
processing, power electronic circuit design etc. One of that is network routing. By using ACO, we can
find the shortest path in network routing
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Successful applications coming from biologically inspired algorithm like Ant Colony Optimization (ACO)
based on artificial swarm intelligence which is inspired by the collective behavior of social insects. ACO
has been inspired from natural ants system, their behavior, team coordination, synchronization for the
searching of optimal solution and also maintains information of each ant. At present, ACO has emerged as
a leading metaheuristic technique for the solution of combinatorial optimization problems which can be
used to find shortest path through construction graph. This paper describe about various behavior of ants,
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Abstract
Image compression is most essential requirement for efficient utilization of storage space and transmission bandwidth. Image compression technique involves reducing the size of the image without degrading the quality of the image. Currently many image compression algorithms are used to deal with increasing amount of data involved but still finding the alternative solution is the area of research. This paper reviews some of the Meta heuristic optimization algorithms used for image compression. These algorithms are based on swarm intelligence. Swarm intelligence is a relatively new area that deals with the study of behavior among many entities or objects interacting within the natural or artificial systems. In past few years Swarm Intelligence based algorithms have been applied to a wide variety of problems in combinatorial and continuous optimization, telecommunications, swarm robotics, networking, image processing etc. This paper provides an insight of many optimization techniques used for image compression like Ant Colony Optimization (ACO) algorithm , Harmony Search Algorithm (HSA) and Artificial Bee Colony algorithm, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). Ant Colony Optimization algorithm is inspired by the behavior among real ant’s while searching for the food source. Harmony Search Algorithm is inspired by the harmony improvisation process followed while playing music. Particle swarm optimization is an optimization technique inspired by social behavior of bird flocking or fish schooling. Artificial Bee Colony algorithm is motivated by the behavior exhibited by honey bees while searching for the food source. Genetic Algorithm is based on processes observed in the natural evolution.
Keywords: Image compression, Ant Colony Optimization (ACO), Harmony Search Algorithm (HAS), Artificial Bee Colony (ABC) algorithm, Particle Swarm Optimization (PSO), Genetic Algorithm (GA).
The assembly process is one of the most time consuming and expensive manufacturing activities.
Determination of a correct and stable assembly sequence is necessary for automated assembly system. The objective of
the present work is to generate feasible, stable and optimal assembly sequence with minimum assembly time.
Automated assembly has the advantage of greater process capability and scalability. It is faster, more efficient and
precise than any conventional process. Ant Colony Optimization (ACO) method is used for generation of stable
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A Multi-Objective Ant Colony System Algorithm for Virtual Machine PlacementIJERA Editor
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A new move towards updating pheromone trail in order to gain increased predic...ijsrd.com
Ant miner algorithm is used to find the classification rule which helps to do classification of the data. Ant miner uses the Ant Colony Optimization (ACO) which deals with artificial systems that is inspired from the foraging behavior of real ants. Here the task is to improve the pheromone update method in the current system. Pheromone updating is dependent mainly on the initial pheromone of the term, and term Q (quality of term) which is added to current accumulated pheromone. In this methods a try is made to lay pheromone on trail such that selection of terms is not biased and unified behavior for the system as a whole, produce a robust system capable of finding high-quality solutions for problems. Here in this approach amount of pheromone added with the used term is not directly dependent on accumulated pheromone but also on the Q (quality of rule). So here in Q is modified and multiplied in ways that help to get better solution. For this use of rule length is done and manipulated in ways that support approach to achieve goal. Thus, aim is to improve the accuracy and sustaining rule list simplicity using Ant Colony Optimization in data mining.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Ant Colony System with Saving Heuristic for Capacitated Vehicle Routing Problemijtsrd
The ACO heuristics is a distributed and cooperative search method that imitates the behavior of real ants in its the search for food. The Capacitated Vehicle Routing Problem CVRP is a well known combinatorial optimization problem, which is concerned with the distribution of goods between the depot and customers. This paper will apply the Ant Colony System ACS with Savings heuristic algorithm to solve Capacitated Vehicle Routing Problem. This problem will be solve to determine an optimal distribution plan that meets all the demands at minimum total cost by applying the ACS algorithm. In this paper, we consider that there is a single depot or distribution center that caters to the customer demands at a set of sales points or demand centers using vehicles with known limited capacities. The demand at each of these demand centers is assumed to be constant and known. Due to its limited capacity, the vehicles may need to make several trips from the depot for replenishment. This system will implement the transportation cost of CVRP and can find the minimum cost routes between the depot and the customers by using the Benchmarks datasets. Aye Aye Chaw "Ant Colony System with Saving Heuristic for Capacitated Vehicle Routing Problem" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27884.pdfPaper URL: https://www.ijtsrd.com/computer-science/artificial-intelligence/27884/ant-colony-system-with-saving-heuristic-for-capacitated-vehicle-routing-problem/aye-aye-chaw
Swarm intelligence systems often comprise a population of essential agents interacting locally with one another and their surroundings. Again, nature, particularly biological systems, is a frequent source of inspiration. Although no centralized control structure dictates how individual agents should behave, local and, to some extent, random interactions between such agents create "intelligent" global behaviour unknown to the respective agents.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
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Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
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http://sandymillin.wordpress.com/iateflwebinar2024
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Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2. Outline
Introduction
Problem Statement
Behavior of Real Ants
Ant Colony Optimization
(ACO)
Applications of ACO
Importance of ACO in
classification
Ant-Miner
Example
Results
Conclusions
References
3. Introduction
The goal of data mining -
Extract (comprehensible) knowledge from data
Comprehensibility is important when knowledge will be used
for supporting a decision making process.
The classification task in data mining and decision making consists in
associating an object/case to a class (among a predefined set of
classes) based on the object/case’s attributes.
Discovering classification rules is an important data mining task,
which generates a set of rules that describe each class or category in
a natural way.
4. Introduction
Ant Colony Optimization (ACO) was First introduced by Marco
Dorigo in 1992.
Parpinelli, Lopes and Freitas [Parpinelli et al. (2001)] proposed
the algorithm Ant-Miner (Ant Colony-based Data Miner).
Based on the behavior of real ant colonies and on data
mining concepts.
Discover classification rules in data sets.
5. Problem Statement
Discovering rules for classification using ACO
Given- training set
Goal- (simple) rules to classify data
Output- ordered decision list
6. Behaviour of real ants
Ants go towards the food while laying down pheromone trails
Shortest path is discovered via pheromone trails
Each ant moves at random
Pheromone is deposited on path
Shorter path, more pheromone rails (positive feedback system)
Ants follow the intense pheromone trails
8. Ants are almost blind.
Incapable of achieving
complex tasks alone.
Rely on the phenomena of
swarm intelligence for
survival.
Behaviour of real ants
Capable of establishing shortest-route paths from their colony
to feeding sources and back.
Use stigmergic communication via pheromone trails.
9. Ants follow existing pheromone trails with high probability.
What emerges is a form of autocatalytic behavior: the more
ants follow a trail, the more attractive that trail becomes for
being followed.
The process is thus characterized by a positive feedback loop,
where the probability of a discrete path choice increases with
the number of times the same path was chosen before.
ACO algorithms are called autocatalytic positive
feedback algorithms
Behaviour of real ants
10. Ant colony optimization technique is based on the technique
known as Swarm Intelligence [Bonabeau et al. (1999)],
which is a part of Artificial Intelligence.
Swarm intelligence is an approach to problem solving that
takes stimulus from the social behaviours of insects and of
other animals.
Swarm Intelligence
11. Swarm Intelligence
A swarm is a large number of homogenous,
simple agents interacting locally among
themselves, and their environment.
Achieving a collective performance which
could not normally be achieved by an
individual acting alone.
Constitutes a natural model particularly suited
to distributed problem solving.
Swarm-based algorithms have recently
emerged as a family of nature-inspired,
population-based algorithms that are capable
of producing low cost, fast, and robust
solutions to several complex problems.
12. Stigmergy
Form of indirect communication in a group of similar
organisms is known as stigmergy.
Two individuals interact indirectly when one of them modifies
the environment and the other responds to the new
environment at a later time. This is stigmergy.
Real ants use stigmergy using – PHEROMONES.
Pheromone is a secreted or excreted chemical factor that
triggers a social response in members of the same species.
Stigmergy provides the ant colony shortest-path finding
capabilities
13. How stigmergy works in ACO?
Ants secret pheromone while traveling from the nest to food,
and vice versa in order to communicate with one another to
find the shortest path.
Ants are forced to decide whether they should go left or right,
and the choice that is made is a random decision.
Pheromone accumulation is faster on the shorter path. The
difference in pheromone content between the two paths over
time makes the ants choose the shorter path.
The more ants follow a trail, the more attractive that trail
becomes for being followed.
14. Ant Colony Optimization (ACO)
“Ant Colony Optimization (ACO) studies artificial
systems that take inspiration from the behavior of
real ant colonies and which are used to solve
discrete optimization problems.”
-Source: ACO website, http://iridia.ulb.ac.be/~mdorigo/ACO/about.html
15. Design of ACO Algorithm
The design of the algorithm can be summarized as specification
of the following aspects [Parpinelli et al. (2001)]:
An environment that represents its problem domain in such a way
that it helps in incrementally building a solution to the problem.
A problem dependent heuristic evaluation function (η) that
provides quality measurement for the different solution
components.
A pheromone updating rule, which considers pheromone
evaporation and reinforcement of pheromone trails.
A probabilistic transition rule based on heuristic function (η) and
strength of the pheromone trail (τ) that determines path taken by
ants.
A clear specification of when the algorithm converges for
solution.
17. Algorithm Description
After initializing the parameters and pheromone trail, the ant
construct the solution by managing the colony of ants, which
concurrently and asynchronously visits the adjacent states to
solve the problem of constructing solution.
The ants search the solution by making use of pheromone trails
and the heuristic information. By this way, the ants build the
solution.
Once the solution is build or being built, the ants evaluate the
partial solution which will be used to update the pheromone
trail, to find the deposition of pheromone.
18. Update pheromone trail where the modification are done by the
way of updating. There is chance of increase or decrease in the
deposition of the trail, due to the pheromone evaporation content.
The less the evaporation of the pheromone, the more the
probability of the connection used by ants and good solution is
produced, which will again used by the following ants.
Some problem specific actions are often called daemon actions,
and can be used to implement problem specific and/or centralized
actions, which cannot be performed by single ants. The most used
daemon action consists in the application of local search to the
constructed solutions: the locally optimized solutions are then
used to decide which pheromone values to update.
Algorithm Description
19. Several special cases of the ACO algorithm have been proposed in
literatures. Here we briefly overview, in the historical order in
which they were introduced, the three most successful ones:
Ant system [Dorigo and Colorni (1996)]
Ant colony system (ACS) [Dorigo and Gambardella (1997)]
MAX-MIN ant system (MMAS) [Stutzle and Hoos (2000)]
Some Variants of ACO Algorithm
20. Ant System
Ant system (AS) was the first ACO algorithm proposed in the
literature [Dorigo et al. (1996)].
The main characteristic of this algorithm was that the
pheromone value is updated at each iteration itself by all the
ants involved.
Many algorithms has been developed having this as the basic
structure.
21. In Ant Colony System, a local pheromone update was
introduced where the updation is done at the end, also called
offline updation.
Each ant performs the local pheromone update after each
construction step.
The ants perform different action during one iteration
depending upon the pheromone [Dorigo and Gambardella
(1997)].
Only one ant update the solution at the end whether it is
iteration best or best-so-far.
Ant colony system (ACS)
22. The performance of traditional ACO algorithms, is seen to be
rather poor on large instance problems [Stutzle and Hoos
(1996)].
Stutzle and Hoos [Stutzle and Hoos (2000)] advocate that
improved performance can be obtained by a stronger
exploitation of the best solutions, combined with an effective
mechanism for avoiding early search stagnation (the situation
where all ants take the same path and thus generate the same
solution).
The authors propose a MAX-MIN ant system that differs from
the traditionally proposed Ant System in three aspects.
MAX-MIN Ant System (MMAS)
23. After each iteration only the best ant is allowed to add
pheromone to its trail. This allows for a better exploitation of
the best solution found.
The range of possible pheromone trails is limited to an interval
[τmax , τmin] so as to avoid early stagnation of the search.
The initial pheromone value of each trail is set at τmax .This
determines a higher exploration at the beginning of the
algorithm.
MAX-MIN Ant System (MMAS)
24. Traveling Salesman Problem [Dorigo and Gambardella (1997)]
Job shop scheduling problem [Ventresca and Ombuki (2004)]
Exam timetabling problem [Eley (2007)]
Routing in communication networks [Zhao et al. (2010)]
Image edge detection [Baterina and Oppus (2010)]
Data mining domain
Clustering [Jafar and Sivakumar (2010)]
Web usage mining [Reena and Arora (2014)]
Classification
And so on…
Applications of ACO
25. ACO algorithm for the classification task
Assign each case to one class, out of a set of predefined
classes.
Discovered knowledge is expressed in the form of IF-
THEN rules:
IF <conditions> THEN <class>
The rule antecedent (IF) contains a set of conditions,
connected by AND operator (term1 AND term2 AND…).
The rule consequent (THEN) specifies the class predicted
for cases whose predictor attributes satisfy all the terms
specified in IF part.
Application of ACO in Classification
26. Why ACO algorithms are important for Data Mining?
ACS use simple agents (artificial ants) that, when working
together, cooperate with each other.
System finds a high-quality solution for problems with a large
search space.
Rule discovery:
Performs a flexible search over all possible logic
combinations of the predicting attributes.
Importance of ACO
27. Algorithm consists of several steps -
Rule construction
Rule pruning
Pheromone updating
Ant-Miner follows a sequential covering approach to
discover a list of classification rules covering all, or almost
all the training cases.
Ant-Miner: An ACO Algorithm for Classification
28. Ant starts with empty rule.
Ant adds one term at a time to rule.
Choice of the terms depend on two factors -
Heuristic function (problem dependent) (η)
Pheromone value associated with each term (τ)
Rule Construction
29. Let, = Heuristic function, = Pheromone amount,
The probability that termij is chosen to be added to the current
partial rule is given by Equation:
is the total number of attributes.
xi is set to 1 if the attribute Ai was not yet used by the current
ant, or to 0 otherwise.
bi is the number of values in the domain of the i-th attribute.
Choice of Terms
ij ij t
ia
30. Based on information theory
In information theory, entropy is a measure of the
uncertainty associated with a random variable –
“amount of information”.
Entropy for each termij is calculated as:
The final normalized heuristic function is defined as:
Heuristic Function
31. Entropy for each termij is given by-
Where,
W is the class attribute (i.e. the attribute whose domain consists
of the classes to be predicted).
k is the number of classes.
is the empirical probability of observing class w
conditional on having observed .
Heuristic Function
| i ijP W A V
i ijA V
32. An ant keeps adding terms one-at-a-time to its current partial rule
until the ant is unable to continue constructing its rule.
Num. of rules >= Num. of ants
Convergence is met
Last k ants found exactly the same rule,
k = No_rules_converg
List of discovered rules is updated
Pheromones reset for all trails
Stopping Criteria
33. Remove irrelevant, unduly included terms in rule
Imperfect heuristic function
Ignoring attribute interactions
Rule pruning-
Iteratively remove one-term-at-a-time
Test new rule against a rule-quality function.
Repeat the process until further removal results no more
quality improvement of the rule.
Rule Pruning
34. Rule-quality function:
TP (true positives) is the number of cases covered by the rule and having
the similar class that is expected by the rule.
FP (False positives) is the number of cases covered by the rule and having
a class that was not expected by the rule.
FN (False negatives) is the number of cases that are not covered by the
rule, whilst having the class that is expected by the rule.
TN (True negatives) is the number of cases that are not covered and
which have a different class from the class that is expected by the rule.
Q´s value is within the range and, the larger the value of Q, the higher
the quality of the rule.
Rule Pruning
35. The initial amount of pheromone dropped at each path is
inversely proportional to the number of values of all attributes,
and is defined by-
is the total number of attributes.
bi is the number of values in the area of attribute i .
Pheromone Initialization
a
36. Initialize pheromone value
Increase pheromone in trail followed by current ant
According to quality of found rule
Decrease pheromone in other trails not used by ant
Simulate pheromone evaporation
New ant starts with rule construction
Uses new pheromone data!
Process is repeated for a predefined number of ants. This number
is specified as a parameter in the system, called No_of_ants.
Pheromone Updating
37. Increase probability termij will be chosen by other ants in
future
In proportion to rule quality Q (0 <= Q <= 1)
Pheromone updating rule is given by-
Pheromone evaporation-
Amount of pheromone related with each termij which
does not take place in the assembled rule must be
reduced.
Divide the value of each current by the summation of
all
Pheromone Updating
ij
ij
38. The best rule among the rules constructed by all ants is considered a
discovered rule. The other rules are discarded. This completes one
iteration of the system.
When the number of cases left in the training set is less than
Max_uncovered_cases the search for rules stops.
The discovered rules are stored in an ordered rule list (in order of
discovery), which will be used to classify new cases, unseen during
training.
The system also adds a default rule to the last position of the rule list.
The default rule has an empty antecedent (i.e. no condition) and has a
consequent predicting the majority class in the set of training cases that
are not covered by any rule. This default rule is automatically applied if
none of the previous rules in the list cover a new case to be classified.
Rule Discovery
39. Once the rule list is complete, the system is finally ready to
classify a new test case unseen during training.
The system tries to apply the discovered rules, in order.
The first rule that covers the new case is applied – i.e. the
case is assigned the class predicted by that rule’s consequent.
Classification using Discovered Rules
49. For total rule:
TP=1, FN=8, TN=5, FP=0
Q=0.111
Without ‘outlook=overcast’
Q=0.111 (No improvement)
Without ‘temp=81 and humid=75’
TP=2, FN=7, TN=5, FP=0
Q=0.222 – better!
For – ‘Windy= False’
TP=6, FN=3,TN=3, FP=2
Q=0.4 – even better!
For the rule – ‘outlook=overcast’
TP=4, FN=5, TN=5, FP=0
Q=0.444 – BEST !
Ant-Miner Example
52. Well known data sets used for experiment [Lichman (2013)]:
Results
Data set #Cases #Categorica
l attributes
#Continuous
attributes
#Classes
Ljubljana
cancer
282 9 - 2
Wisconsin
cancer
683 - 9 2
Dermatology 358 33 1 6
Hepatitis 155 13 6 2
53. Data set No. of Rules No. of
terms/No. of
Rules
Predictive
Accuracy
of Ant-Miner(%)
Ljubljana cancer 7.10 ± 0.31 1.28 75.28 ± 2.24
Wisconsin cancer 6.20 ± 0.25 1.97 96.04 ± 0.93
Hepatitis 3.40 ± 0.16 2.41 94.29 ± 1.20
Dermatology 7.30 ± 0.15 3.16 90.00 ± 3.11
Results
Table 1 summarizes the results obtained by the proposed AntMiner algorithm
in the four datasets. The table shows the accuracy rate, the number of rules
found and the number of terms (the shown values are the average values of the
cross-validation procedure followed by the corresponding standard deviation).
54. Ant-Miner is better, because:
Uses feedback (pheromone
mechanism).
Stochastic search, instead of
deterministic.
Uses probabilty.
End effect:
Good predictive accuracy.
Reduced number of simple and
short rules.
Drawback: Computational cost,
especially when the search space
(number of predicting attributes) is
too large.
Conclusions
55. Conclusions
Two important directions for future work are as follows.
It would be interesting to investigate a variant of Ant-Miner that
can cope with continuous attributes, rather than requiring that
this kind of attribute be discretized in a preprocessing step.
To investigate the performance of other kinds of heuristic
function and pheromone updating strategy so that the
computation time is reduced.
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Editor's Notes
When one of these two stopping criteria is satisfied the ant has built a rule (i.e. it has completed its path), and, in principle, we could use the discovered rule for
classification.
This second stopping criterion detects that the ants have already converged to the same constructed rule, which is equivalent to converging to the same path in real Ant
Colony Systems.
When an ant completes its rule and the amount of pheromone in each trail is updated, another ants start to construct its rule, using the new amounts of pheromone to guide its search. This process is repeated for at most a predefined number of ants.
Table 1 summarizes the results obtained by the proposed AntMiner algorithm in the four datasets. The table shows the accuracy rate, the number of rules found and the number of terms (the shown values are the average values of the cross-validation procedure followed by the corresponding standard deviation).