CMC CMC CMC Computers, Materials & Continua 1546-2226 1546-2218 Tech Science Press USA 13576 10.32604/cmc.2020.013576 Article IWD-Miner: A Novel Metaheuristic Algorithm for Medical Data ClassificationIWD-Miner: A Novel Metaheuristic Algorithm for Medical Data ClassificationIWD-Miner: A Novel Metaheuristic Algorithm for Medical Data Classification AlMuhaideb Sarab salmuhaideb@ksu.edu.sa BinGhannam Reem Alhelal Nourah Alduheshi Shatha Alkhamees Fatimah Alsuhaibani Raghad Department of Computer Science, College of Computer and Information Sciences, King Saud University, Riyadh, 11362, Saudi Arabia *Corresponding Author: Sarab AlMuhaideb. Email: salmuhaideb@ksu.edu.sa 21 11 2020 66 2 1329 1346 11 8 2020 19 9 2020 © 2020 AlMuhaideb et al. 2020 AlMuhaideb et al. This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Medical data classification (MDC) refers to the application of classification methods on medical datasets. This work focuses on applying a classification task to medical datasets related to specific diseases in order to predict the associated diagnosis or prognosis. To gain experts’ trust, the prediction and the reasoning behind it are equally important. Accordingly, we confine our research to learn rule-based models because they are transparent and comprehensible. One approach to MDC involves the use of metaheuristic (MH) algorithms. Here we report on the development and testing of a novel MH algorithm: IWD-Miner. This algorithm can be viewed as a fusion of Intelligent Water Drops (IWDs) and AntMiner+. It was subjected to a four-stage sensitivity analysis to optimize its performance. For this purpose, 21 publicly available medical datasets were used from the Machine Learning Repository at the University of California Irvine. Interestingly, there were only limited differences in performance between IWD-Miner variants which is suggestive of its robustness. Finally, using the same 21 datasets, we compared the performance of the optimized IWD-Miner against two extant algorithms, AntMiner+ and J48. The experiments showed that both rival algorithms are considered comparable in the effectiveness to IWD-Miner, as confirmed by the Wilcoxon nonparametric statistical test. Results suggest that IWD-Miner is more efficient than AntMiner+ as measured by the average number of fitness evaluations to a solution (1,386,621.30 vs. 2,827,283.88 fitness evaluations, respectively). J48 exhibited higher accuracy on average than IWD-Miner (79.58 vs. 73.65, respectively) but produced larger models (32.82 leaves vs. 8.38 terms, respectively).

 Ant colony optimization AntMiner+ IWDs IWD-Miner J48 medical data classification metaheuristic algorithms swarm intelligence Introduction

The medical field is evolving rapidly and it is difficult to overstate its actual and potential importance to human life and societal functioning [1,2]. The focus of this paper is classification problems that can be used to support clinical decisions, such as diagnosis and prognosis. A diagnosis involves providing the cause and nature of a disorder, and a prognosis predicts a disorder’s course [3]. Medical data sets contain collections of patients’ recorded histories vis-à-vis diagnoses and/or prognoses. Predictor features for these diagnoses and/or prognoses are given as a set of independent attributes describing a patient case (e.g., demographic data, pathology tests and lab tests). The instances that correspond to attributes, which tend to be continuous or discrete values of a fixed length, are formally given as as D={(xi,yi),i=1,…,Nex} , where Nex is the number of examples, xi is a vector of the predictor features used to predict yi and yi∈{1,…,Ncl }, Ncl is the number of all possible discrete classes.

The goal of this study is to predict the unknown target class (output) by approximating the relationship between the predictor features (input) and the class.

A central issue in medical data classification is the communication of the acquired knowledge to medical practitioners in a transparent and understandable manner. The model obtained will be used to support a decision made by a human. The acceptance of machine learning models presented for the purpose of medical diagnosis or prognosis is highly dependent on its ability to be interpreted and validated [4]. The use of transparent comprehensible models also allows discovering new interesting relations, and opens new research trends, particularly in the biomedical field [5]. In some cases, obtaining explanations and conclusions that enlighten and convince medical experts is more important than suggesting a particular class. Based on that, Lavrač et al. [6] distinguish between two types of machine learning algorithms according to the interpretability of the acquired knowledge. Symbolic machine learning algorithms, like rule learners and classification trees, can clearly justify or explain their decision through their knowledge representation. On the other hand, subsymbolic machine learning algorithms place more emphasis on other factors, like the predictive accuracy for example. These methods are sometimes called black box methods because they produce their decision with no clear explanation. Examples of this category include artificial neural networks including deep learning methods [7–9], support vector machines [10] and instance-based learners [11]. Statistical learning methods like Bayesian classifiers [12] provide a probability that an instance belongs to some class based on a probability model rather than providing a concrete classification. Learning requires some background knowledge about initial probabilities, and is computationally heavy especially if the network layout is previously unknown.

This work respects the importance associated with generating transparent models that can be easily understood by humans, relating to the syntactic representation of the model as well as the model size. Thus the main requirements of this work are summarized as follows. First, the difficulties associated with medical datasets must be expected, namely the existence of heterogeneous data types, multiple classes, noise, and missing values. Second, model comprehensibility is a central requirement. This includes (a) Knowledge representation of the model must be transparent, and in a form that is easily interpreted by the users, and (b) The size of the obtained knowledge representation must be manageable. Smaller sizes are preferred to larger ones, given a comparable predictive accuracy. Third, the proposed classification model must have a comparable predictive accuracy to current benchmark machine learning classification algorithms, in order to gain acceptance and credibility.

The aim is to achieve this goal by restricting our attention to rule-based models because they are transparent and comprehensible from the perspective of users. More specifically, we confine our attention to metaheuristic methods because they offer three key advantages: fast problem solving, amenability to relatively large problem contexts and the generation of algorithms which are multi-dimensionally robust [13–15]. There are two kinds of metaheuristic algorithms: single-solution based and population-based. The former chooses one solution to improve and mutate during the search lifetime e.g., simulated annealing [16,17] and variable neighborhood search [18,19]. By contrast, population-based algorithms improve the entire population. Evolutionary algorithms [20] and swarm intelligence [21,22] are examples in this respect.

We focus on developing and testing a novel algorithm based on swarm intelligence which fuses aspects of two extant algorithms. Accordingly, the remainder of the paper is structured as follows. In Section 2 we summaries related work in this domain of research. Next, methodological details pertaining to the development of IWD-Miner are presented in Section 3. In Section 4, the algorithm is subjected to a four-stage sensitivity analysis for the purpose of performance optimization. In Section 5, we compare the performance of the optimized IWD-Miner against AntMiner+ and J48. Finally, brief conclusions including limitations and suggestions for future research are provided in Section 6.

 Related Work Swarm Intelligence Algorithms

Swarm intelligence (SI) methods are inspired by the collective behavior of agents within a swarm. SI behaviors have two properties: Self-organization and division of labor. Thus, they focus on the relationships between individuals’ cooperative behaviors and their prevailing environment [23–25]. Self-organization can produce structures and behaviors for the purpose of task execution [26,27]. Since there are different tasks carried out by specialized individuals concurrently inside the swarm, a division of labor must be applied, where the cooperating individuals are executing concurrent tasks in a more efficient way than if unspecialized individuals executed sequential tasks [28,29]. The occurrence of indirect actions, such as cooperative behavior and communication between individuals inside a limited environment, is called stigmergy [30,31].

Relying on the behaviors of social animals and insects like ants, birds and bees, SI algorithms aim to design systems of multiple intelligent agents [32]. Examples of imitated social behaviors are a flock of birds looking to discover a place that has enough food and ants finding an appropriate food source within the shortest distance.

 Intelligent Water Drops

Many SI algorithms have been developed, one example being Intelligent Water Drops (IWDs) which was first put forward by Shah-Hosseini [33] and then elaborated on by that author in subsequent publications [34–36]. As its name suggest, this algorithm mimics what happens to water drops in a river [37]. The river is characterized by its water flow velocity and its soil bed, both of which affect the IWDs [35]. Initially, an IWD’s velocity will equal a default value and the soil will be initiated as zero before subsequently changing while navigating the environment. There is an inverse relationship between velocity and soil. Thus, a path with less soil produces more velocity for an IWD [37]. The time taken is directly proportional to the velocity and inversely proportional to the distance between two locations [35].

An ( N,E ) graph represents the environment of IWD algorithms, where E denotes the set of edges associated with the amount of soil and N reflects the set of nodes. Each IWD will travel between N through E and thus gradually construct its solution. The total-best solution TTB depends on the amount of soil included within the edges of that solution. The algorithm terminates once the expected solution is found or once the maximum number of iterations itermax is reached.

 Ant Colony Optimization

Other examples of SI algorithms are framed in terms of ant colony optimization (ACO). Individual ants have limited capabilities, such as restricted visual and auditory communication. However, a group of ants, together in a colony, has impressive capabilities, such as foraging for food. That type of natural optimization behavior achieves a balance between food intake and energy expenditure. When ants find a food source, each ant has the ability to produce chemicals (called pheromones) to communicate with the rest of the ants. Ants search for their own path that will lead from the source (nest) to the destination (food source). The path will be labelled with pheromones and is thus followed by other ants.

The first person to leverage the cooperative behavior of ants for producing an algorithm was Marco Dorigo in his doctoral research [38]. His work has since been developed and extended by many scholars e.g., [39–42].

Drawing on earlier work by Dorigo and others, Parpinelli et al. [43] proposed the Ant-Miner algorithm for classification problems wherein the classification rules are represented as IF ( term1∧term2∧…∧termn ), THEN class , where n is the number of possible terms chosen. Only categorical attributes are operationalised in this version of Ant-Miner and the algorithm is divided into three phases: rule construction, rule pruning and pheromone updating. First, in the iterations of the rule construction phase, the ant will start to search for terms for constructing the rule. Each term will be added to the partial rule based on the probability Pi,j of choosing termi,j , the heuristic value ηi,j of termi,j, which, according to information theory, is measured by entropy, and the pheromone trail value τi,j. In this step, if the constructed rule has irrelevant terms, it will immediately be excluded, which is important for enhancing the quality of the rule. Assigning a pheromone value occurs in the pheromone updating phase; that is, in the first iteration, each trial of termi,j will be given the same pheromone value, which is small when the number of attribute values is high, and vice versa. Then, deposited pheromone values will be increased if termi,j is added to the rule, and decreased for pheromone evaporation.

Since the original publication of Ant-Miner, scholars have developed and explored variants. For example, Martens et al. [44] proposed a technique using a modified version of Ant-Miner classification methods based on the MAX-MIN Ant System algorithm [41]. This new version is called AntMiner+. In this variant, a directed acyclic graph is used in the rule construction phase and only the best ant performs the pheromone updating and rule pruning phases. Reference [45] proposed another variant which they called mAnt-Miner+ wherein multi-populations of ants are considered i.e. an ant colony divided into several populations. The populations run separately with the same number of ants. After all ants have constructed rules, the best ant is selected to update pheromones, thus minimising the cost of computation compared to the case where all ants can update pheromones.

 Methodology IWD-Miner

In what follows we detail the development of a novel algorithm which can be viewed as a fusion of IWDs and AntMiner+. More specifically, the skeleton of the algorithm is as per the latter, but with ants replaced by IWDs and pheromones replaced by soil.

Initialization

A directed acyclic construction graph is configured following Martens et al. [44]. This is based on the predictor features in the input datafile. Initial parameter values are as per Tab. 1. The graph is initialized with an equal amount of soil on all edges (1000). There are 1000 IWDs and each begins its trip with zero soil (soilIWD) . The velocity of each IWD is 4 based on [34]. Optimal velocity is then determined experimentally. While travelling, each IWD constructs its solution, gathers soil and gains velocity.

Initial parameter values
Parameters Values
InitSoil(IS) 1000
VelIWD 4
nbIWD 1000
ρIWD , ρn −0.9, 0.9
Move Operator

IWDs move through the construction graph commencing from the Start vertex towards the End vertex forming a rule as follows. From the current value (node) in the current vertex group (attribute), the IWD probabilistically chooses a value (node) from the next vertex group (attribute) according to the heuristic used, the velocity of the IWD and the soil available on graph edges (Eq. (1), which is also a function of Eq. (2), where vc(IWD) is the list of nodes visited by this IWD, εs=0.001andg(soil(i,j)) is used to shift soil(i,j) on the path joining nodes i and j ).

pIWD(j)=f(soil(i,j))α×HUDβ∑k∉vc(IWD)⁡f(soil(i,k))α×HUDβ

f(soil(i,j))=1εs+g(soil(i,j))

A heuristic then measures the undesirability of a move by an IWD from i to j (Eq. (3)). Next, the IWD’s velocity (Eq. (4)) and soil (Eq. (5), which is also a function of Eq. (6)) are updated. The path with less soil will have a higher chance of being selected and the solution is constructed in a sequential coverage manner, where the data points covered by the rule are removed from the dataset as per the AntMiner+ approach [44].

HUD=|Tij∉ClassIWD||Tij|

where Tij reflects the set of remaining training instances that contain termij , ClassIWD represents the class that the IWD contributes to for rule extraction, av=1,cv=1 and bv=0.01 .

VelIWD(t+1)=Vel(t)+avbv+cv⋅soil2(i,j)

soilIWD=soilIWD+Δsoil(i,j)

Δsoil(i,j)=1ε+HUD(j)VelIWD(t+1)

Objective Function

To evaluate the complete rule (solution) represented by an IWD, we follow the AntMiner+ approach [44] and use both rule confidence and rule coverage as fitness as in Eq. (7). Rule confidence is a measure of how many instances containing this specific condition belong to this class at the same time. It measures the reliability of a rule. On the other hand, rule coverage concerns how many instances in this class contain this specific condition over the total instances.

Q=freq(ruleIWD,classrule)freq(ruleIWD)+freq(ruleIWD,classrule)TD

where the numerators of confidence and coverage reflect the number of rules correctly classified by this IWD; the denominator of confidence is the total number of instances covered by this IWD’s rule ( freq(ruleIWD) ); and the denominator of coverage is the total instances in the dataset ( TD ).

 Convergence

The convergence process for solving classification problems is inspired by IWDs and AntMiner+. It aims to limit the evaluated IWDs to reach the targeted rules to complete the search faster. This is achieved when all soil in the global best path is arcmin shown in Eq. (8) and all soil on the remaining paths is arcmax (Eq.(9))

arcmin=iterations((ρIWD−ρnnbIWD)(1ε))

arcmax=(ρ0ρs)iterationsIS

where nbIWD is the number of IWDs, ρn is the local soil updating parameter, ρIWD is the global soil updating parameter, ρ0 is the complement of ρn , ρs is the complement of ρIWD and IS represents the initialization of the soil.

 Termination

Termination depends on many factors, including reaching the minimum convergence threshold, which represents the allowable number of convergence rules (equals 10). Termination also occurs if no water drops find a rule to cover any data instance.

 Pseudocode

As shown in Algorithm 1, the graph is constructed in Line 1. Then, there are two main cycles: outer and inner. The initialization of the soil and the heuristic occurs on the remaining datapoints in the training set in each outer cycle in Lines 3 and 4.

Pseudocode for IWD-Miner
1. ConstructGraph();
2. while NotTerminationCondition() do
3.       InitilizeSoil();
4.      InitializeHeuristic();
5.       while NotConverged() do
6.           IWDs = CreateNewWaterDrops();
7.           i= Start point
8.          ConstructSolution( IWDs );
9.           TTB= FindBestIWD( TIWD)
10.           PruneRule( TTB )
11.         UpdatePathSoil( TTB );
12.      end
13. rule= extractRule();
14.  RemoveFromTrainingset(CoveredByRule);
15.  end

In the inner cycle, the IWDs are created in Line 6. They begin their trip at a Start point and construct a solution (Line 8 of Algorithm 1 and elaborated on in Algorithm 2). This involves choosing a value from the next variable starting with α , β , Class and then the other variables following Eqs. (1)–(3) (Line 4 in Algorithm 2). Next, each IWD updates its velocity (Line 5 in Algorithm 2 using Eq. (4)) and soil (Line 6 in Algorithm 2 using Eq. (5) and Eq. (6)). When all IWDs are complete, the best solution is selected based on its fitness in Line 9 according to Eq. (7).

ConstructSolution(IWDs)
1. while NotMaxNumberOfIWDs() do
2.  InitializeVelocity();
3.  while IWDsNotConstructSolutions () do
4.      j = ChooseNextNode(IWDs);
5.     UpdateVelocity(IWDs);
6.      SoilIWD=SoilIWD+ ComputeSoil( i,j );
7.      i = j ;
8.     UpdateSoil( i,j );
9.  end
10.  SaveRule();
11. end
Data and Pre-Processing

For the purposes of optimizing IWD-Miner and comparing its performance with two rival algorithms, 21 medical datasets are used (Tab. 2). These are all publicly available from the Machine Learning Repository at the Department of Information and Computer Science University of California, Irvine (UCI). Inst. is the number of instances, Attr. is the number of attributes, Num. are numeric attributes, Nom. are nominal attributes, and Class refers to the number of classes. The percentage of overall missing values ( %MV ) was computed as #missingvalues(Inst.×Attr.)×100 , the percentage of instances with missing values ( %Inst.MV ) was computed as Inst.withmissingvaluesInst.×100 . Finally, IR is the class imbalance ratio which can be applied if the dataset contains a binary class imbalance or multi-class imbalance; there is no universally agreed threshold for the class imbalance ratio but sometimes 1.5$]]>IR>1.5 is used [46].

Overview of the UCI datasets
No. Dataset Inst . Attr . Num . Nom . Class %MV %Inst.MV IR
1 Echo 132 12 9 3 2 8.33 100 2.08
2 Wdbc 569 31 30 1 2 0 0 1.68
3 Haber 306 3 3 0 2 0 0 2.77
4 Puba 345 6 6 0 2 0 0 1.37
5 Dia 768 8 8 0 2 0 0 1.86
6 Breast-cancer 286 9 3 6 2 0.34 3.14 2.36
7 Breast-w 699 9 9 0 2 0.25 2.28 1.9
8 Diabetes 768 8 8 0 2 0 0 1.86
9 Heart-c 303 13 6 7 5 0.18 2.31 1.19
10 Heart-statlog 270 13 6 7 2 0 0 1.25
11 Hepatitis 155 19 6 13 2 5.71 48.9 3.84
12 Mammographic_masses 961 5 1 4 2 3.37 16.85 1.15
13 ThoracicSurgery 470 19 3 13 2 0 0 5.71
14 Caesarean 80 5 2 3 2 0 0 1.35
15 Pima_diabetes 768 8 8 0 2 0 0 1.86
16 Liver-disorders 345 6 6 0 2 0 0 1.37
17 Spectfheart 267 44 44 0 2 0 0 3.85
18 Thyroid 7200 21 21 0 3 0 0 40.15
19 Cleveland 303 13 13 0 5 0.18 2.31 12.61
20 Saheart 415 9 8 1 2 0 0 1.88
21 Haberman 306 3 3 0 2 0 0 2.77

Next, we used the Fayyad and Irani Discretizer as per the approach employed in AntMiner+. Finally, we used correlation-based feature subset selection which resulted in 10 features being selected.

 Evaluation

We use standard 10-time, 10-fold cross-validation to evaluate algorithm performance with respect to each of the datasets. Five different performance criteria are used to gauge the relative efficacy of different variants of IWD Miner (Section 4) as well as the relative efficacy of the optimized IWD-Miner compared to two extant, rival algorithms (Section 5).

The first criterion is sensitivity as in Eq. (10), where TP represents the number of positive records that have been correctly predicted as positive and pos refers to the number of positive records.

Sn=TPpos

The second criterion is specificity as in Eq. (11), where TN represents the number of positive records that have been correctly predicted as negative and neg refers to the number of negative records.

Sp=TNneg

The third criterion is accuracy as in Eq. (12), where FP represents the number of negative records that have been incorrectly predicted as positive and FN represents the number of positive records that have been incorrectly predicted as negative:

Acc=TP+TN(TP+TN+FP+FN)

The fourth criterion is model size (Eq. (13a) for decision lists and Eq. (13b) for decision trees), where Rules denotes the average number of rules per individual, T/R is the average number of terms per rule, and TL is the total number of leaves in a tree. Note that the measuring unit for Size is terms, while that for SizeJ48 is leaves.

Size=Rules×T/R

SizeJ48=TL

The fifth and final criterion is efficiency ( AES ) which is measured by the average number of evaluations needed to find a solution in successful runs, undefined when a solution is not found. The measuring unit for AES is fitness evaluations.

 Sequential Optimization

In what follows IWD-Miner is subjected to a four-stage sensitivity analysis. The best performing model from each stage is taken forward to the next stage in a process of sequential optimization.

Stage One: Path Update Procedure

First, we compared two models: IWD−MinerBest and IWD−MinerEach (Tab. 3). The former only updates the soil path of the best IWD (Algorithm 1, Line 11) and as such does not consider the soil update between adjacent vertexes (Algorithm 2, Line 8). The latter updates the soil paths of all IWDs and chooses the best performing model. As such, the path’s soil is updated twice: first when each IWD’s selected vertex updates the path between the previous vertex and the next vertex (Algorithm 2, Line 8) and second when the path’s soil of the best IWD is updated (Algorithm 1, Line 11). In terms of the differential performance of these two models across the 21 datasets, Wilcoxon signed-rank tests did not detect a statistically significant difference between the two models in terms of Sp (p = 0.986), Sn (p = 0.765), Acc (p = 0.768) or Size (p = 0.375). However, there was a significant difference between the two models as measured by AES (p = 0.001), where IWD−MinerEach had the performance advantage. Accordingly, IWD−MinerEach is taken through to the next stage.

Optimisation: path update procedure
IWD−MinerEach IWD−MinerBest
Acc Avg 73.11 ± 0.162 73.22 ± 0.159
Min 43.01 ± 0.022 43.16 ± 0.035
Max 95.70 ± 0.006 95.91 ± 0.006
Sp Avg 60.21 ± 0.315 60.06 ± 0.314
Min 2.71 ± 0.026 1.43 ± 0.010
Max 96.13 ± 0.009 96.48 ± 0.064
Sn Avg 75.25 ± 0.237 74.92 ± 0.236
Min 20.56 ± 0.008 20.63 ± 0.008
Max 98.48 ± 0.008 98.48 ± 0.008
Size Avg 8.51 8.66
Min 0.09 0.16
Max 37.99 40.94
AES Avg 5,628,922.60 11,958,791.01
Min 34,600.10 1,832.90
Max 85,157,856.00 89,350,560.00

The superior performance of IWD−MinerEach with respect to AES can be understood in the following terms. As IWDs are affected by each other, updating the soil path of each IWD increases the probability of choosing the same path by the next IWD, which means producing a large number of duplicate rules. Hence, a small number of unique rules will be evaluated after the filtering step. Considering performance with respect to the properties of the datasets, IWD−MinerEach had a better AES in most datasets featuring high imbalance ratios ( IR ) such as wdbc, haberman and saheart. Moreover, the best Max AES value was associated with the thyroid dataset, which has the largest number of instances and the highest IR. Furthermore, for most datasets with missing values (%MV) and instances with missing values (%Inst.M,) IWD−MinerEach had better AES. Examples include the breast-cancer dataset, mammographic-masses dataset and heart-c dataset. In sum, as %MV , %Inst.MV , the number of instances and IR increase so does the relative performance of IWD−MinerEach compared to IWD−MinerBest in terms of the AES criterion.

 Stage Two: Global Soil Updating Parameter

Next, we experimented with three different values of the global soil updating parameter ρIWD : −0.5, −0.7 and −0.9 (Tab. 4). Similar to what was observed above in stage one, these three models performed similarly well across the 21 datasets. Friedman tests did not detect statistically significant differences in performance in terms of Sp ( p = 0.172), Sn (p = 0.538), Acc (p = 0.495) or Size (p = 0.827). However, there was a significant difference between the three models as measured by AES (p = 0.000) with ρIWD = −0.5 having the performance advantage. Accordingly, IWD−MinerEach (stage one) with ρIWD = −0.5 (stage two) is taken forward to stage three.

Optimization of global soil updating parameter
ρIWD=−0.5 ρIWD=−0.7 ρIWD=−0.9
Acc Avg 73.53 ± 0.151 73.24 ± 0.156 73.11 ± 0.162
Min 42.99 ± 0.029 42.49 ± 0.006 43.01 ± 0.022
Max 95.98 ± 0.007 96.08 ± 0.008 95.70 ± 0.00
Sp Avg 59.77 ± 0.308 60.18 ± 0.322 60.21 ± 0.315
Min 1.57 ± 0.018 1.98 ± 0.027 2.71 ± 0.026
Max 96.11 ± 0.008 96.25 ± 0.010 96.13 ± 0.009
Sn Avg 76.18 ± 0.219 74.83 ± 0.242 75.25 ± 0.237
Min 21.24 ± 0.010 18.23 ± 0.113 20.56 ± 0.008
Max 98.95 ± 0.005 98.58 ± 0.007 98.48 ± 0.008
Size Avg 8.82 8.90 8.51
Min 0.15 0.07 0.09
Max 39.32 41.55 37.99
AES Avg 5,026,373.13 8,441,961.26 5,628,922.60
Min 5,762.50 10,039.30 34,600.10
Max 76,647,384.00 146,220,480.00 85,157,856.00
Stage Three: Number of IWDs (<inline-formula id="ieqn-163"> <alternatives><inline-graphic xlink:href="ieqn-163.png"/><tex-math id="tex-ieqn-163"><![CDATA[$\bi{nbIWD}$]]></tex-math><mml:math id="mml-ieqn-163"><mml:mrow><mml:mi mathvariant="bold">n</mml:mi><mml:mi mathvariant="bold">b</mml:mi><mml:mi mathvariant="bold">I</mml:mi><mml:mi mathvariant="bold">W</mml:mi><mml:mi mathvariant="bold">D</mml:mi></mml:mrow></mml:math> </alternatives></inline-formula>)

Here our purpose is to explore the impact of the number of IWDs ( nbIWD ) on model performance. We compared the performance of four model variants across the 21 medical datasets. Specifically, we explored the ramifications of 500, 750, 1000, 1250 and 2000 IWDs (Tab. 5). Interestingly, no significant differences in performance were revealed across the five models with respect to any of the performance criteria according to Friedman tests: Acc (p = 0.785), Sp (p = 0.394), Sn (p = 0.938), Size (p =0.450) and AES (p = 0.349). Accordingly, we retain the default value of 1000 IWDs.

Optimisation: number of IWDs
nbIWD=500 nbIWD=750 nbIWD=1000 nbIWD=1250 nbIWD=2000
Acc Avg 74.98 ± 0.027 74.70 ± 0.035 74.57 ± 0.033 74.50 ± 0.051 74.44 ± 0.034
Min 58.99 ± 0.097 57.97 ± 0.167 62.09 ± 0.150 60.13 ± 0.161 56.57 ± 0.140
Max 93.61 ± 0.035 92.13 ± 0.038 87.70 ± 0.035 87.21 ± 0.181 92.46 ± 0.036
Sp Avg 59.93 ± 0.075 68.23 ± 0.089 60.32 ± 0.090 64.43 ± 0.096 59.59 ± 0.094
Min 17.80 ± 0.051 14.68 ± 0.052 21.62 ± 0.039 20.91 ± 0.048 35.99 ± 0.090
Max 94.51 ± 0.067 95.83 ± 0.288 91.07 ± 0.078 96.10 ± 0.281 91.07 ± 0.071
Sn Avg 80.61 ± 0.052 80.61 ± 0.056 79.66 ± 0.059 79.64 ± 0.083 80.41 ± 0.064
Min 51.51 ± 0.105 51.83 ± 0.087 53.71 ± 0.087 52.65 ± 0.071 49.83 ± 0.095
Max 95.36 ± 0.018 95.82 ± 0.019 94.68 ± 0.013 95.01 ± 0.016 94.44 ± 0.023
Size Avg 7.57 7.85 7.94 7.56 7.80
Min 0.90 0.75 0.84 0.79 0.71
Max 16.58 18.25 15.22 15.74 15.06
AES Avg 885,857.32 862,568.74 1,013,528.48 957,618.48 948,579.48
Min 3,629.90 3,666.50 5,762.50 2,410.10 3,441.80
Max 1,465,441.20 1,762,808.20 1,876,326.10 1,542,044.50 1,698,935.80

The revealed insensitivity of the algorithm in this respect can be understood in the following terms. IWD-Miner filters duplicate rules so that only unique rules are left; varying the number of IWDs impacts on the number of rules but not the number of unique rules.

 Stage Four: Initial IWD Velocity (<inline-formula id="ieqn-175"> <alternatives><inline-graphic xlink:href="ieqn-175.png"/><tex-math id="tex-ieqn-175"><![CDATA[$\bi{Ve}{\bi{l}^{\bi{IWD}}}$]]></tex-math><mml:math id="mml-ieqn-175"><mml:mrow><mml:mi mathvariant="bold">V</mml:mi><mml:mi mathvariant="bold">e</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="bold">l</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="bold">I</mml:mi><mml:mi mathvariant="bold">W</mml:mi><mml:mi mathvariant="bold">D</mml:mi></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math> </alternatives></inline-formula>)

Finally, we explore the impact of alternative initial IWD velocity ( VelIWD ) values. Again, leveraging the 21 medical datasets, we compared the model where VelIWD = 4 with three models where VelIWD = 0, 8 and 10 (Tab. 6). Friedman tests did not detect statistically significant differences between the four models in terms of Sp (p = 0.440) and Size (p = 0.113). However, significant differences were revealed with respect to the remaining three criteria: Sn (p = 0.043), Acc (p = 0.035) and AES (p= 0.000). The model where VelIWD = 10 proved to be superior in terms of AES , but in terms of Sn and Acc, the model where VelIWD = 8 performed best. We therefore opted for VelIWD = 8 in the final version of IWD-Miner.

Initial IWD velocity
VelIWD=0 VelIWD=4 VelIWD=8 VelIWD=10
Acc Avg 72.50 ± 0.030 73.53 ± 0.032 73.65 ± 0.028 71.95 ± 0.038
Min 44.06 ± 0.036 42.99 ± 0.029 42.90 ± 0.022 44.26 ± 0.036
Max 95.71 ± 0.006 95.98 ± 0.007 95.96 ± 0.009 95.80 ± 0.012
Sp Avg 75.36 ± 0.074 76.18 ± 0.075 76.46 ± 0.064 74.14 ± 0.081
Min 21.12 ± 0.013 21.24 ± 0.010 19.36 ± 0.085 20.80 ± 0.008
Max 98.60 ± 0.007 98.95 ± 0.005 98.33 ± 0.010 97.48 ± 0.034
Sn Avg 60.43 ± 0.070 59.77 ± 0.073 70.40 ± 0.068 59.81 ± 0.079
Min 1.140 ± 0.009 1.570 ± 0.018 3.140 ± 0.023 3.860 ± 0.036
Max 97.54 ± 0.024 96.11 ± 0.008 95.96 ± 0.005 95.75 ± 0.009
Size Avg 8.82 8.82 8.38 7.75
Min 0.17 0.15 0.09 0.22
Max 36.72 39.32 40.94 36.74
AES Avg 5,607,029.83 5,026,373.13 4,314,405.43 2,195,514.68
Min 5,634.10 5,762.5 3,972.70 1,315.00
Max 82,980,864.00 76,647,384.00 72,491,256.00 34,774,200.00

IWD velocity controls the amount of soil that will be gathered by each IWD as it moves; greater velocity leads the IWD to accumulate more soil by removing it from the path [47]. The amount of soil removed from the riverbed by an IWD during movement will affect the probability of the next IWD choosing the same path, which generates similar rules. Thus, the number of rules will decrease after applying a filtering step to retain only unique rules. This explains why a velocity of 10 proved superior in terms of efficiency but the lower value of 8 had the advantage in terms of other performance criteria.

 Algorithm Inter-Comparison

We explored the relative performance of the optimized IWD-Miner against AntMiner+ and J48. Default settings were used for both rival algorithms, with an equal number of agents between AntMiner+ and IWD-Miner.

AntMiner+ is closely related to our algorithm and thus it seems prudent to evaluate whether and the extent to which the former can be modified in ways which have performance advantages. J48 was chosen as a comparator because it is a well-known and widely used classification algorithm which produces transparent models. IWDs is not amenable to classification problems in its original form hence its omission from this exercise.

We compared the optimized IWD-Miner with the rival AntMiner+ algorithm in terms of accuracy, efficiency, sensitivity, size of model and specificity. With the exception of efficiency, these same metrics were then used to compare IWD-Miner and J48. Efficiency is not calculable with respect to J48, hence its omission. The detailed results are shown in Tab. 7 and Tab. 8. Wilcoxon signed-rank tests did not detect a statistically significant difference between IWD-Miner and AntMiner+ in terms of Acc (p = 0.414), Sp (p = 0.244), Sn (p = 0.876) or Size (p = 0.322). However, a significant difference between the two algorithms was revealed with respect to AES (p = 0.010) with IWD-Miner exhibiting superior performance. The same non-parametric test was then used to compare the performance of IWD-Miner and J48. No significant differences were revealed between the two models in terms of Sn (p = 0.986) or Sp (p = 0.821). J48 exhibited superior performance in terms of Acc (p = 0.04) but our proposed algorithm was revealed to have a statistically significant advantage in terms of Size (p = 0.000). Taking the breast-w dataset as an example, both IWD-Miner and J48 were comparable in terms of accuracy but the size of the former model was much smaller than the latter: 8 vs. 27.

Performance evaluation: IWD-Miner <italic>vs</italic>. AntMiner+
IWD-MinerAntMiner+
No. dataset Acc Sn Sp Size AES Acc Sn Sp Size AES
1. Echo 93.44 ± 0.042 93.56 ± 0.038 93.36 ± 0.110 1.59 3,476.32 97.05 ± 0.013 98.16 ± 0.018 94.02 ± 0.013 1.32 7,375.47
2. Haber 82.88 ± 0.095 55.00 ± 0.148 88.83 ± 0.071 3.70 12,782.70 83.63 ± 0.159 67.80 ± 0.290 90.83 ± 0.213 4.32 464.44
3. Pima_diabetes 82.90 ± 0.017 77.48 ± 0.026 88.03 ± 0.067 6.17 657,728.76 83.13 ± 0.143 76.05 ± 0.155 89.83 ± 0.247 5.81 425.22
4. Heart-statlog 72.37 ± 0.021 45.59 ± 0.030 86.72 ± 0.068 8.56 406,286.23 73.24 ± 0.025 47.92 ± 0.022 86.79 ± 0.065 12.11 289,787.52
5. Breast-cancer 95.49 ± 0.023 95.90 ± 0.016 94.74 ± 0.081 8.07 69,463.31 95.07 ± 0.011 95.65 ± 0.012 93.96 ± 0.038 6.69 471,026.34
6. Puba 58.25 ± 0.028 78.33 ± 0.081 43.00 ± 0.107 3.19 16,997.05 56.50 ± 0.037 57.33 ± 0.091 56.25 ± 0.128 3.59 371.97
7. Diabetes 76.05 ± 0.019 89.21 ± 0.033 60.55 ± 0.102 13.35 352,380.86 76.55 ± 0.019 89.64 ± 0.033 61.18 ± 0.090 16.22 1,228,244.77
8. Hepatitis 84.15 ± 0.059 98.33 ± 0.131 3.14 ± 0.71 6.52 14,576.17 84.36 ± 0.044 98.80 ± 0.123 1.86 ± 0.045 5.08 51,631.75
9. Mammographic_mass 77.94 ± 0.006 19.36 ± 0.047 93.11 ± 0.42 9.40 379,055.94 77.87 ± 0.007 17.03 ± 0.028 93.64 ± 0.017 8.48 2,074,373.09
10. Dia 93.59 ± 0.021 89.58 ± 0.101 95.96 ± 0.42 11.01 330,767.61 93.92 ± 0.016 90.14 ± 0.083 96.16 ± 0.024 9.89 2,997,439.44
11. Breast-w 95.96 ± 0.005 84.15 ± 0.147 84.15 ± 0.009 40.94 776,982.53 96.20 ± 0.003 74.28 ± 0.006 85.23 ± 0.009 46.58 913,736.94
12. Caesarean 67.61 ± 0.042 83.92 ± 0.051 36.79 ± 0.103 4.39 15,268.43 67.49 ± 0.058 84.76 ± 0.191 34.93 ± 0.167 5.16 45,977.42
13. Heart-c 43.30 ± 0.018 95.78 ± 0.010 5.24 ± 0.049 0.17 255,311.26 44.26 ± 0.015 91.99 ± 0.032 9.65 ± 0.043 0.19 725,816.85
14. ThoracicSurger 73.58 ± 0.008 88.00 ± 0.171 46.69 ± 0.023 9.35 70,491.62 73.40 ± 0.006 88.05 ± 0.007 46.04 ± 0.014 9.54 618,208.01
15. Liver-disorders 42.90 ± 0.022 96.47 ± 0.006 4.04 ± 0.085 0.09 13,894.39 43.42 ± 0.034 95.04 ± 0.110 6.00 ± 0.139 0.15 383.79
16. Spectfheart 78.89 ± 0.014 89.67 ± 0.085 65.42 ± 0.027 13.64 407,312.67 76.59 ± 0.009 90.40 ± 0.135 59.33 ± 0.032 14.23 538,110.99
17. Thyroid 63.89 ± 0.009 53.10 ± 0.096 67.68 ± 0.052 0.89 23,938,706.00 56.93 ± 0.005 61.16 ± 0.055 55.44 ± 0.027 0.71 47,459,802.69
18. Cleveland 64.41 ± 0.011 66.83 ± 0.016 57.97 ± 0.008 0.93 475,528.89 56.14 ± 0.009 55.25 ± 0.015 58.45 ± 0.007 0.69 753,816.09
19. Saheart 73.13 ± 0.018 88.40 ± 0.073 44.62 ± 0.113 9.17 120,840.07 73.95 ± 0.019 88.47 ± 0.062 46.82 ± -.111 8.82 153,030.40
20. Haberman 53.10 ± 0.113 21.58 ± 0.125 81.17 ± 0.196 15.24 15,701.24 53.23 ± 0.143 20.89 ± 0.155 80.78 ± 0.274 18.98 425.22
21. Wdbc 72.74 ± 0.008 95.37 ± 0.018 18.07 ± 0.005 8.94 785,495.34 74.12 ± 0.008 95.93 ± 0.017 21.28 ± 0.009 11.82 1,042,513.00
Avg 73.65 ± 0.028 76.46 ± 0.064 59.97 ± 0.068 8.35 1,386,621.30 73.19 ± 0.037 75.46 ± 0.078 60.40 ± 0.018 9.07 2,827,283.88
Min 42.90 ± 0.022 19.36 ± 0.047 3.14 ± 0.071 0.09 3,476.32 43.42 ± 0.034 17.03 ± 0.028 1.86 ± 0.045 0.15 371.97
Max 95.96 ± 0.005 98.33 ± 0.131 95.96 ± 0.042 40.94 23,938,706.00 97.05 ± 0.013 98.80 ± 0.123 96.16 ± 0.024 46.58 47,459,802.69
Performance evaluation: IWD-Miner <italic>vs</italic>. J48
IWD-MinerJ48
No. Dataset Acc Sn Sp Size Acc Sn Sp Size
1. Echo 93.44 ± 0.042 93.56 ± 0.038 93.36 ± 0.110 1.59 97.30 97.30 94.40 3
2. Haber 82.88 ± 0.095 55.00 ± 0.148 88.83 ± 0.071 0.93 71.90 71.90 44.80 5
3. Pima_diabetes 82.90 ± 0.017 77.48 ± 0.026 88.03 ± 0.067 9.35 73.44 73.40 67.80 45
4. Heart-statlog 72.37 ± 0.021 45.59 ± 0.030 86.72 ± 0.068 14.35 77.04 77.00 76.10 39
5. Breast-cancer 95.49 ± 0.023 95.90 ± 0.016 94.74 ± 0.081 8.94 75.52 75.50 47.60 8
6. Puba 58.25 ± 0.028 78.33 ± 0.081 43.00 ± 0.107 0.17 66.96 67.00 63.50 51
7. Diabetes 76.05 ± 0.019 89.21 ± 0.33 60.55 ± 0.102 9.17 73.44 73.40 67.80 45
8. Hepatitis 84.15 ± 0.059 98.33 ± 0.131 3.14 ± 0.071 3.70 83.87 83.90 54.20 27
9. Mammographic_mass 77.94 ± 0.006 19.36 ± 0.047 93.11 ± 0.042 6.17 85.18 82.50 82.10 11
10. Dia 93.59 ± 0.021 89.58 ± 0.101 95.96 ± 0.042 8.56 73.44 73.40 67.80 45
11. Breast-w 95.96 ± 0.005 84.15 ± 0.006 84.15 ± 0.009 8.07 94.13 94.10 92.80 27
12. Caesarean 67.61 ± 0.042 83.92 ± 0.147 36.79 ± 0.103 3.19 65.00 65.00 63.40 16
13. Heart-c 43.30 ± 0.018 95.78 ± 0.051 5.24 ± 0.049 13.35 77.56 77.60 23.50 59
14. ThoracicSurger 73.5 ± 0.008 88.00 ± 0.101 46.69 ± 0.023 6.52 84.47 84.50 16.00 1
15. Liver-disorders 42.90 ± 0.022 96.47 ± 0.071 4.04 ± 0.085 0.09 66.96 67.00 63.50 51
16. Spectfheart 78.89 ± 0.014 89.67 ± 0.085 65.42 ± 0.027 9.40 73.41 73.40 43.30 43
17. Thyroid 63.89 ± 0.009 53.10 ± 0.096 67.68 ± 0.052 40.94 99.68 99.70 99.00 33
18. Cleveland 64.41 ± 0.011 66.83 ± 0.016 57.97 ± 0.008 15.24 99.68 53.10 23.60 67
19. Saheart 73.13 ± 0.018 88.40 ± 0.073 44.62 ± 0.113 4.39 67.23 67.20 55.20 34
20. Haberman 53.10 ± 0.113 21.58 ± 0.125 81.17 ± 0.196 0.89 71.57 71.60 44.70 5
21. Wdbc 72.74 ± 0.008 95.37 ± 0.018 18.07 ± 0.005 11.01 97.30 93.50 93.10 25
Avg 73.65 ± 0.028 76.46 ± 0.064 59.97 ± 0.068 0.93 79.58 77.24 61.15 5
Min 42.90 ± 0.022 19.36 ± 0.047 3.14 ± 0.071 9.35 65.00 53.10 16.00 45
Max 95.96 ± 0.005 98.33 ± 0.131 95.96 ± 0.042 14.35 99.68 99.70 99.00 39

The relative accuracy of J48 could be a function of data attributes. For example, using the liver-disorders dataset, which contains 7 attributes, J48 achieved 67% accuracy compared to 43% achieved by IWD-Miner. On the other hand, using the spectfheart dataset, which contains 45 attributes, J48 and IWD-Miner achieved 73% and 93% accuracy, respectively. However, one of the strengths of J48 is the execution time it takes to build the model, which is very small compared to IWD-Miner. Another strength is its ability to handle missing values rather than eliminating records containing missing data, leading to loss of training data.

 Conclusion

The results of the algorithm inter-comparison exercise testify to the competitiveness of IWD-Miner in comparison to two extant alternatives. IWD-Miner was shown to be as good as AntMiner+ in terms of four out of five performance criteria and better than AntMiner+ with respect to the remaining criterion, efficiency. The performance of our algorithm was comparable to that of J48 in terms of two out of four criteria; the latter was advantageous in terms of accuracy but IWD-Miner was superior in terms of resulting model sizes. As such, assuming these results generalize to other contexts (i.e., other datasets), it appears that IWD-Miner could be successfully used for the purpose of medical data classification tasks. Nevertheless, there is ample scope for future research to extend the current study in terms of algorithm development and testing. IWD-Miner takes a relatively long time to run in its current form. To mitigate this issue, we recommend exploring if and the extent to which the convergence process of the algorithm can be improved. Further, although the sensitivity analysis conducted herein suggested limited differences between IWD-Miner variants, there is scope for exploring alternative methods of discretization and feature subset selection and, finally, it may be prudent to implement a delayed procedure for handling missing values after attribute selection.

The authors would like to thank the anonymous reviewers for their constructive comments.

Funding Statement: This research project was supported by a grant from the “Research Center of the Female Scientific and Medical Colleges”, the Deanship of Scientific Research, King Saud University.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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