Background

Classification is the process of dividing data samples into different groups using the machine learning (ML) approaches [1]. This technique has been extended to a wide range of computational and biological applications such as identifying potential gene/miRNA/protein biomarkers [2], repurposing drugs against different diseases [3], suggesting novel therapeutic modalities for curing illnesses [4], diagnosing heart and diabetes sicknesses [5], and better perceiving biological phenomena [6]. In this line, several ML strategies have been developed, resulting in the generation of computer-aided health decision support systems [7]. These strategies aimed to improve the ML and feature selection (FS) algorithms mainly because of their effects on the performance of a classification model [8]. For instance, to diagnose diabetes disease in its early stages, Patil et al. utilized C4.5 and k-means clustering ML algorithms and achieved ~ 92.38% value of tenfold cross-validation accuracy on the Pima Indian Diabetes (PID) dataset [9]. To this end, the researchers removed serum insulin and triceps skinfold features and reduced the total number of samples from 768 to 625. The researchers then determined the data patterns using the k-means algorithm and eliminated 192 other instances. Based on the obtained patterns, a decision tree was formed, and the produced model was evaluated. Although these researchers generated a proper prediction model with a high value of accuracy on the PID dataset, their methods suffered from overfitting because of removing a remarkable number of the data instances. To tackle such a limitation, Aslam et al. examined a three-step ML method [10]. In the first phase, based on different statistical methods (e.g., Kolmogorov–Smirnov test and t-test), the existing diabetes features were ranked, and some subsets of diabetes features were produced using a progressive FS manner. In the second phase, for every generated subset of features, a genetic programming technique was employed. In the third phase, the usefulness of the produced features was measured using the k-nearest neighbor (KNN) and support vector machine (SVM) classifiers. The results demonstrated that the Gaussian process-SVM (GP-SVM) technique resulted in about 87% of accuracy. In addition to the PID dataset, several studies targeted other biological/clinical datasets and suggested some real-world consistent prediction models [11,12,13]. For this purpose, the prior studies combined various computational techniques such as the teaching learning-based optimization algorithm (OA) with the fuzzy wavelet neural network [14], the rough set theory with the backpropagation neural network [15], and the fuzzy concept with the min–max neural networks [16]. The mentioned computational strategies have been applied to the Cleveland heart disease (CHD) [17], Statlog heart disease (SHD) [18], Wisconsin diagnostic breast cancer (WDBC) disease and mammogram datasets [19, 20], respectively. Some researchers also designed other types of hybrid ML techniques and applied them to different biological/clinical datasets [21,22,23,24]. The mentioned studies encounter several limitations, including low prediction power, inability in grouping multiclass data (more than two classes), overfitting, and filtering the samples with missing values. Therefore, Arabi et al. suggested a ML approach that creates a specific model for every class of existing data [25, 26]. For this purpose, the researchers acquired several regression and classification datasets from the ML repository of the University of California, Irvine (UCI). Then, after normalizing the obtained data, a distinct model was generated for every class of data. For example, if the data of interest included three classes, three individual machines were designed for each of them. In the next phase, a cascade-like artificial neural network was designed and trained using the world competitive contests (WCC) optimization algorithm [27]. The performance of the methods was investigated on the different partitioned train and test datasets (e.g., 70%-30% or 60%-40%), indicating that their methods outperformed other ML approaches in terms of classification criteria. Although the described technique by Arabi and coworkers yielded a model with a higher prediction ability, their ML method was not suitable for large-size datasets.

To address the above-mentioned constraints, in the present study, we extended the Trader optimization algorithm for selecting a near-optimal subset of features and generating an efficient prediction model in terms of classification criteria [28]. Additionally, to get better prediction results, a voting-based ML framework was proposed, labeling data samples based on the consensus of predictions obtained from different artificial machines. To evaluate the proposed machine learning approaches, in all the computational experiments, the fivefold cross-validation technique was used.

Methods

The UCI repository has collected various datasets from different scopes and provided a suitable resource for machine learning applications. From this repository, a total of 13 clinical/biological datasets, utilized in various research work as gold-standard input files, were obtained (Table 1). These datasets included different numbers of samples and features/genes, so they seemed to be qualified for evaluating the proposed method in different conditions. The proposed framework, shown in Fig. 1, was applied to these data, and the results were compared from a wide range of classification measurements.

Table 1 The properties of the datasets obtained from the UCI repository
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Fig. 1
figure 1

The framework of the proposed voting-based machine learning method for classifying biological/clinical datasets. The final prediction is determined by aggregating the outputs of different models. \({\mathrm{F}}_{{\mathrm{p}}_{\mathrm{i}}}\) shows the total number of models that predicted a given sample belongs to the ith group

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The acquired data were preprocessed in two phases that completed missing values and normalized the data, sequentially. To complete the missing values of a given sample, firstly, ten other samples (not including the missing values and sharing a high value of Pearson correlation coefficient (> 0.5) with the sample of interest) were chosen if plausible. Secondly, the missing value of the sample of interest was determined based on calculating the interpolation of the related values. Finally, for normalizing the data, Eq. 1 was used, which converts the data of a feature to range [0, 1].

$$x_{{i.j_{new} }} = \frac{{x_{{i.j_{current} - min_{j} }} }}{{max_{j} - min_{j} }}$$
(1)

where xi,j, minj, and maxj represent the value of the ith row and jth column of a given data, and the minimum and maximum values of the jth column, respectively.

Our previously suggested Trader optimization algorithm (OA) was modified and developed to select an optimal/near-optimal subset of features/genes [29, 30]. In this line, as shown in Fig. 2, the algorithm generated some potential candidate solutions (CS) randomly, each of which included a set of selected features/genes and was displayed using an array (Eq. 2).

$${\text{CS}} = \left[ {{\text{V}}_{{1}} ,{\text{V}}_{{2}} ,{\text{V}}_{{3}} , \ldots ,{\text{V}}_{{\text{n}}} } \right]$$
(2)

where CS and Vi stand for a candidate solution and its ith variable, respectively.

Fig. 2
figure 2

The flowchart of the suggested Trader optimization algorithm for selecting a near-optimal subset of features/genes. The algorithm generates some random candidate solutions (CS) and evaluates them using the value of accuracy obtained from the support vector machine (SVM) classifier. Next, the algorithm divides the CSs into several groups and modifies them with three operators. At the final step, the best acquired CS is introduced as a near-optimal subset of features/genes, which can enhance the prediction ability of the SVM classifier

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The CSs were then divided into several groups in a random manner. Every group and the sum of its CSs’ scores represented a trader and its finances/benefits, respectively.

In the next step, the produced CSs were evaluated using the SVM classification technique (i.e., the accuracy obtained from SVM, was considered as the worthiness/fitness/score of a given subset of features). Since some of the datasets consisted of more than two classes, to calculate the value of accuracy, a mean-based method (Eq. 3) was used.

$$Accuracy = \frac{{\mathop \sum \nolimits_{i = 1}^{C} TP_{i} }}{N}$$
(3)

where TPi, C, and N show the total number of true positives of the ith class, the total number of data classes, and the total number of data samples, respectively.

Based on the calculated fitness values, the CSs of every group were separated into master and slave CSs (MCS and SCS, respectively), consequentially showing the best CS and the remaining CSs of a group. Next, the CSs went through a series of changes using the three operators of the Trader algorithm, and new CSs were produced. The first operator of Trader (the retailing operator (Eq. 4)) created minor modifications in the SCS. This operator usually plays an essential role in improving the CSs in the last steps of the algorithm.

$$\forall_{j \in S} \left( {SCS_{i,j} = SCS_{i,j} + k \times random\left( {0 , SCS_{i,j} } \right)} \right)$$
(4)

where SCSi,j and k indicate the jth variable of the ith slave CS and a random value (i.e., either -1 or 1), respectively. Additionally, S displays a set of randomly selected variables of the ith slave CS.

The second operator of Trader (the distributing operator (Eq. 5)) aimed to improve the SCSs by transferring data from their related MCSs. For this purpose, for a given SCS, some variables were randomly chosen from an MCS, and then, their values were transferred to that SCS.

$$\forall_{j \in S} \left( {SCS_{i,j} = MCS_{i,j} } \right)$$
(5)

where SCSi,j, MCSi,j, and S are the jth variable of the ith SCS, the jth variable of the ith group’s MCS, and a set of randomly chosen variables of the ith CS, respectively.

The third operator of Trader, the importing-exporting (IE) operator (Eq. 6), aimed to correct the MCSs and change CSs globally. For this purpose, an MCS was considered the importer while the others as exporters. Like two previous operators, the IE operator acted randomly and changed a given MCS in a similar method described for the second operator.

$$\forall_{j \in S, k \in M} \left( {MCS_{i,j} = MCS_{k,j} } \right)$$
(6)

where MCSi,j, MCSM,j, S, and M display the jth variable of the ith importer MCS, the jth variable of the Mth exporter MCS, a set of randomly chosen variables of the ith importer MCS, and a set of randomly chosen variables of the Mth exporter MCS, respectively.

The proposed OA was compared with other popular OAs in the same conditions. For instance, all the algorithms had a time order of O(n3) and called an identical number of the objective function (SVM) during a distinct run.

Results

The proposed method was implemented in the MATLAB programming language, and the outputs were examined in terms of various criteria associated with evaluating the modified optimization algorithm (Trader) and proposed voting-based classification system. To evaluate the usefulness of Trader in selecting informative features/genes, it was applied to the downloaded datasets (Table 1), and the outcomes were compared with four other public/effective optimization algorithms. These algorithms (i.e., WCC [27], LCA [31], PSO [32], and ICA [33]) were chosen because of their diversities and proper functionalities reported in the prior studies. Because the values of OAs’ parameters strongly affected their efficiencies, a trial–error method was employed to regulate them [34]. The initial population size of the algorithms was set to 100, and, their steps iteration parameter was regulated to 50. Besides, in every iteration, each of the algorithms changed 30% of candidate solutions. The results of this section were organized into three sections described as follows.

The first part of the results compared the performance of the mentioned OAs in terms of improving the prediction power of a learner. To this end, the data of features/genes, chosen by the algorithms, were passed to SVM [35], and the learner then created a model for classifying them. As mentioned in the materials and methods section, OAs generated some random potential answers and modified/improved them using their operators. Hence, it was usually expected to get better results in the jth iteration than in the ith iteration (j > i) (the convergence behavior of OAs) [36]. For the datasets consisting of > 10 features/genes, the convergence behavior of the algorithm was followed, and the mean outcomes of 50 individual executions, were depicted (Fig. 3). Since the performance of the algorithms on the SHD and CHD datasets were similar, only the convergence diagram of the algorithms on the SHD was displayed. Based on the acquired results, Trader was able to select more distinctive features and get higher values of accuracy than the other algorithms. Therefore, it can be articulated that the proposed OA had a better convergence behavior than other compared OAs.

Fig. 3
figure 3

The convergence behavior of the OAs on the a SHD, b HEP, c PAR, d WDBC, e LUNG, f ARRYTM, g PARKINSON, h ARCENE, and i GENEEXPR datasets

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In every individual run, due to generating and changing CSs based on stochastic operators, the OAs selected a diverse subset of features and produced different values of accuracy. However, the final accuracy values must be similar to each other (the stability behavior of OAs) [37,38,39,40]. To examine this property of the OAs in detail, they were executed 50 times, and the distribution of their outputs was illustrated using boxplots (Fig. 4). The obtained outcomes indicated that Trader generally boosted the performance of SVM (via selecting the most informative features) and showed a more stable behavior than the other OAs.

Fig. 4
figure 4

The stability behavior of the OAs on the a SHD, b HEP, c PAR, d WDBC, e LUNG, f ARRYTM, g PARKINSON, h ARCENE, and i GENEEXPR datasets on 50 individual executions

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Further, to investigate whether the performance of Trader and the other OAs was the same or not, the Wilcoxon rank-sum test was utilized. For this purpose, the results of Trader were considered as a test base and compared with the others’ outcomes (Table 2). It was observed that, for most cases, the p-value was less than 0.01 and about close to zero, resulting in rejecting the null hypothesis and validating that Trader outperformed the others in terms of enhancing the prediction power of SVM.

Table 2 The Wilcoxon rank-sum test of the OAs with Trader’s results as the test base
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In the second part of the computational experiments, the proposed algorithm was embedded into a voting-based prediction system. To evaluate this system, different criteria were considered, such as accuracy (ACC), precision (PRE), sensitivity (SEN), specificity (SPC), and F-score (F). The outputs were then organized into several tables as well as receiver operating characteristic (ROC) and precision-recall (PR) curves. The compared machine learning approaches indicated different efficiencies on diverse datasets. Based on the outcomes, the proposed voting-based system generally outperformed the others in terms of the mentioned parameters (Table 3).

Table 3 Comparing the utilized methods based on the fivefold cross-validation technique
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The classification power of the generated models, separating positive or negative data samples into their related classes, was examined using the ROC and PR curves shown in Figs. 5 and 6, respectively. Although most of previously performed studies utilized the ROC and PR diagrams for evaluating the performance of binary classifiers, the presented study extended this concept to multi-class classifiers. To this end, Eq. 3 was used for calculating the values of SEN, SPC, and PRE. The acquired diagrams expressed that the proposed voting-based approach was closer to a perfect classifier than the others were. To display the area under curve (AUC) of the classifiers, for every dataset, two bar diagrams were provided, showing the AUC of the ROC (Fig. 7) and PR (Fig. 8) curves, respectively.

Fig. 5
figure 5

The ROC curve of the algorithms on the a SHD, b HEP, c PAR, d WDBC, e LUNG, f ARRYTM, g PARKINSON, h ARCENE, and i GENEEXPR datasets

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Fig. 6
figure 6

The PR curve of the algorithms on the a SHD, b HEP, c PAR, d WDBC, e LUNG, f ARRYTM, g PARKINSON, h ARCENE, and i GENEEXPR datasets

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Fig. 7
figure 7

The AUC bar diagram for ROC curves on the a SHD, b HEP, c PAR, d WDBC, e LUNG, f ARRYTM, g PARKINSON, h ARCENE, and i GENEEXPR datasets

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Fig. 8
figure 8

The AUC bar diagram for PR curves on the a SHD, b HEP, c PAR, d WDBC, e LUNG, f ARRYTM, g PARKINSON, h ARCENE, and i GENEEXPR datasets

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In the last part of the computational experiments, a comprehensive comparison between the proposed ML method and those suggested in the previous studies was performed. Up to the time of designing the present study, much attention has already been paid to introducing novel ML techniques and generating powerful biological data classifiers. Among these studies, the artificial neural network-based ML approach, introduced by Arabi et al., outperformed the other previously introduced ML methods in terms of the classification benchmarks. Here, the outputs of these studies were collected and then extended with the results obtained from the current study (Table 4). The outcomes indicated that the accuracy of the proposed voting-based ML approach was higher than the accuracy of the previously introduced ML methods. All in all, the suggested voting-based system improved all the criteria by ~ 10%.

Table 4 A comprehensive comparison between the proposed voting-based method and the other previously introduced approaches
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Discussion

To classify various types of clinical/biological datasets, the present study introduced a novel wrapper ML method that combined the Trader algorithm for selecting a near-optimal subset of features/genes and the SVM classifier for scoring them. Although the previous studies had suggested several ML methods and algorithms to stratify clinical/biological datasets [53,54,55], they encountered two critical limitations described as follows.

First, some literary works ignored the FS concepts in the data preprocessing step or utilized some heuristic filter-based FS techniques. For instance, several studies ranked and reduced the total number of the existing features/genes in a specific application such as introducing a limited number of genes as potential biomarkers for certain cancer [56]. To this end, some statistical-based FS algorithms have been utilized, such as the data Entropy-based FS method. As demonstrated in many recent bioinformatics-related pieces of research, wrapper-based FS approaches outperformed the filter and embedded-based FS techniques [57, 58], and two-step FS methods usually showed better functionality than single-step procedures [59,60,61]. Besides, in some cases, previous studies presented that filter-based FS techniques may reduce the prediction power of a learner [8, 62]. Hence, given the capabilities of the Trader algorithm in Np-hard problems, this study developed the algorithm for selecting the features and applied it not only to large-size datasets but also to small-size ones. The related outcomes (obtained from both the small and large-size datasets) indicated that the FS concept was a critical preprocessing step for biological applications, and the performance of the algorithms differed from each other on various datasets. In addition to gaining a suitable prediction model, the outputs of the FS phase may be essential for designing diagnosis/treatment plans, such as introducing the selected features/genes/proteins/miRNA as potential biomarkers for a wide range of diseases. The discovered biomarkers might be further investigated to determine their druggability properties and find candidate medicines to inhibit them.

Second, some previously carried out studies tested the usefulness of their methods on small-size datasets [63, 64]. Therefore, their proposed approaches could not be embedded into software packages due to their lower performances on large-size data. To address the mentioned restriction, a voting-based ML framework was introduced and applied to the different datasets having various properties. It was shown that the suggested framework could boost the prediction power of classification systems on both the small and large-size datasets whereas the previously introduced ML techniques lost their performances on large-size datasets. For example, Arabi et al. introduced and developed a perceptron-based artificial neural network for classifying 13 clinical/biological datasets and showed that their designed artificial neural network had a higher prediction ability than the other performed methods [25]. Arabi’s proposed method generated a distinct model for every class of a given data and categorized a data sample into a group whose related model represented the highest value of score. However, the outcomes of the present study exhibited that the mentioned ML method (introduce by Arabi et al.) suffered from overfitting on the small-size datasets. In other words, the proposed voting-based ML system yielded a more powerful prediction model on large-size datasets than the previously performed approaches. On the small-size datasets, the efficiency of the proposed ML framework was slightly lower than that of Arabi’s method in terms of the classification criteria. This issue was probably because of overfitting Arabi’s approach on the small-size datasets.

Like all the other previously carried out studies, the present work also might suffer from some limitations. Especially, the current study was organized based on the five OAs producing non-deterministic but acceptable outcomes. Hence, in designing a healthcare system, the deterministic rate may decrease. To deal with such a limitation, a possible solution can be identifying a proper configuration of algorithms that can correctly display a synergic effect. However, obtaining such a configuration seems to be a challenging task. Collectively, a combination of algorithms, such as various types of operators for changing CSs, might be an advantageous approach.

Conclusion

This study extended our previously introduced optimization algorithm, Trader, to select a near-optimal subset of features/genes and proposed a voting-based machine learning technique to classify large-size biological/clinical datasets. According to the acquired results, it was indicated that the suggested voting-based classification framework yielded better predictions than the other previously performed studies. As a result, this technique can be considered an effective diagnosis/treatment approach such as discovering potential biomarkers and drugs to combat different diseases. In addition, the outcomes indicated that the feature selection concept is an essential preprocessing phase not only for large-size biological/clinical datasets but also for small-size ones, whereas most of the prior studies neglected the effect of the feature selection concept in their computational methods.