Diagnosis of vertebral column pathologies using concatenated resampling with machine learning algorithms

Disease prediction using ML classifiers

Rajpurkar et al. (2017) developed an algorithm to detect pneumonia patients using the chest X-rays. The proposed algorithm called CheXNet is a neural network and consists of 121 layers including input/output and convolutional layers. The chest x-ray dataset which is used for training and testing the neural network contains 100,000 x-ray-images with fourteen different diseases. The study shows promising results in the diagnosis of the different thoracic pathologies including pneumonia. Similarly, the performance of various machine learning classification algorithms has been analyzed in Wroge et al. (2018) for their capability to predict Parkinson’s Disease. The work is based on the model construction and validation using a voice dataset collected from both normal persons as well as persons with Parkinson’s disease. Thus the study presented the effectiveness of the applicability of supervised classification models in the diagnosis of Parkinson’s disease with an accuracy of 85%. Despite the dataset used in the study is high dimensional and contained noise, the prediction accuracy is good.

The efficacy of various statistical and machine learning models is investigated in Huang et al. (2017) for diagnosing breast cancer. In particular, support vector machines (SVM) have been explored and their high performance is reported against other machine learning classifiers. Similarly, Samb et al. (2012) performed experiments on various medical datasets and proposed a modified RFE-SVM model. The ionosphere, the SpamBase, and the SPECTF Heart datasets from the UCI repository have been used in the study. To improve the performance of the final classifier, the RFE-SVM algorithm has been combined with local operators which showed significant classification enhancement.

An ensemble machine learning model is proposed in Mandal (2015) to increase the accuracy of traditional machine learning classifiers. The ensemble aims at enhancing the classification accuracy for spine diagnosis. The Bayesian network is used along with the Tabu search algorithm as a classifier. Haar wavelets are used as the projection filter for attribute ranking and relevant feature selection. Results have been compared with SINPATCO platform methods (MLP, GRNN, SVN). The comparative analysis reveals that the ensemble model beats the traditional machine learning models in classification.

Besides the disease prediction from various features extracted from numeric and image data, several researchers focus on using the ML classifiers for biological studies. For example, the authors identify the antioxidant candidates which are influential to maintain health (Ho Thanh Lam et al., 2020). A machine learning-based model is proposed to predict the antioxidant candidates using a benchmark set of sequencing data. Results using 10-fold cross-validation show that RF can identify antioxidant proteins with the highest accuracy of 84.6%. Similarly, Le et al. (2020a) devised an eXtreme Gradient Boosting (XGBoost) model to identify Methylguanine-DNA methyltransferase (MGMT) status in patients with IDH1 glioblastomas. The study uses 53 patients with proven GBM to obtain biomedical features using multimodality MRI for improving the model’s performance, and F-score analysis is performed to identify important features. A total of nine radionics features are identified which fall under the curve of 0.896. Using these identified features, the XGBoost achieves the highest predictive performance and stability with an accuracy of 0.887 and an AUC of 0.896.

Use of ML classifiers for pathology disease

Besides the above-mentioned studies, several researchers focus on methods that are related to pathology diagnosis. For example, Seera & Lim (2014) developed an intelligent system for classification for the diagnosis of diabetes, liver disorders, and breast cancer. Dennis & Muthukrishnan (2014) proposed an efficient prediction system based on the Adaptive Fuzzy System. It is based on the combination of a genetic algorithm and the fuzzy set. The achieved accuracy on several datasets is approximately 77.0% compared to 79.39% of the existing systems for disease classification. Similarly, a strategy based intelligent medical decision system in proposed in Gorunescu & Belciug (2014). The proposed system is composed of several classifiers including Naive Bayes, self-organizing maps, k-nearest neighbor, multilayer perceptron, SVM, genetic algorithm, probabilistic neural network, radial basis function, and neural networks. The system performs classification for breast cancer and liver fibrosis.

K-nearest neighbor and genetic algorithm have been used in Jabbar, Deekshatulu & Chandra (2013) to develop a hybrid system for the classification of heart disease. In this study, three ensemble approaches based on a tree with linear non-ensemble machine learning models are used for the automatic diagnosis of inter-vertebral pathologies. The performance of the model is evaluated using unbalanced datasets. The experiments have been conducted to make comparisons among different classification models. Results indicate that the proposed approach outperforms other machine learning algorithms regarding the accuracy, precision, recall, and F₁ score.

Predicting vertebral column pathology using ML classifiers

The assistance of machine learning algorithms and models to diagnose the vertebral column pathologies is gaining wide attraction. da Rocha Neto et al. (2011) used biomechanical features dataset containing six features and three types of target data such as disk hernia, spondylolisthesis, and healthy for classification. It aggregated the disc hernia and spondylolisthesis pathologies classes into one pathology class and the health class remained unchanged. The research used an SVM classifier with linear kernel and KMOD (kernel with moderate decreasing). The model is trained using 80% and 40% training data and SVM achieved the highest results with KMOD (Ayat et al., 2001). SVM achieved an accuracy score of 0.859 using KMOD kernel accuracy when trained on 80% training data. Similarly, the authors developed an LMT (logistic model tree) for automatic prediction of vertebral column pathologies in Karabulut & Ibrikci (2014). The proposed model is the combination of the logistic regression and decision tree. The proposed approach is comprised of preprocessing and classification where preprocessing is the oversampling of data using the SMOTE technique. Later, the classification model LMT is trained using the preprocessed data to achieve higher accuracy of 89.73%.

Along the same direction, Akben (2016) used machine learning algorithms such as KNN, SVM, DT (decision trees), NB (Naïve Bayes), and MLP for vertebral diagnosis. The same six biomechanical features are used and the highest achieved accuracy is 83.22% using the MLP algorithm. Unal & Kocer (2013) also used the MLP and SVM to diagnose the vertebral column pathology and achieved 85.48% accuracy with the MLP model. Alafeef et al. (2019) used the X-ray images to collect five biomechanical features and diagnose the vertebral column pathologies. These features are extracted from the x-ray images of 422 subjects. Subjects are divided into three classes including disc hernia, spondylolisthesis, and normal. To enhance the effectiveness of the classifiers, the data is preprocessed to weight every vertebral feature using a set of weights computed based on Shannon entropy and the fuzzy C-means clustering algorithm. These weighted features are used to train the neural networks model.

The authors proposed using sequential feature selection to select the best features in Prasetio & Riana (2015). Later, hyperparameter tuning is carried out to select the best hyperparameter setting for machine learning models. Among LR, RF, KNN, and XGBoost, KNN achieved the highest accuracy of 93.54%. The ensemble approach tends to increase the classification accuracy, so, an ensemble approach is proposed in Jiménez & Quintero-Ospina (2019). The research uses radial basis, functions neural networks (RBF), SVM, and PNN (probabilistic neural networks). The output of the models is combined using the weighted criteria and the achieved accuracy is 90.2%.

Despite the higher classification accuracy reported in the above-mentioned research works, they are limited by several factors. Predominantly, the dataset contains three target classes where the ratio of data for target classes is not equal. So, the imbalanced dataset affects the accuracy of the classifiers. Similarly, the number of features used in the dataset is small, i.e., only six features. The size of the dataset is also small, comprising only 310 records in total which can affect the classification accuracy. Furthermore, a large number of previous studies use linear and neural networks-based models for vertebral column problem. Such models perform better on binary and large datasets and their performance is compromised when used for multi-class classification on small datasets. To overcome such limitations, the current study considers linear, as well as, tree-based ensemble models on the re-sampled dataset to enhance the classification accuracy. For a summary of the discussed research works, Table 1 is provided.

Disc herniation

Intervertebral discs are a fibro-cartilage cushion between two vertebrae in the vertebral column. These discs are made up of the annulus fibrosus, a dense collagenous ring, and nucleus pulposus, a jelly-like material forming the inner core of the vertebrae (Baldit, 2018). Disk herniation is the condition when this jelly-like material (nucleus pulposus) protrudes through the outer ring (annulus fibrosus) of the disc towards spinal nerves as shown in Fig. 1. This process can cause the symptoms of low to severe back pain as well as numbness, or pain in other body parts like legs. These symptoms are caused by the pressure put on the spinal nerves by the protruded nucleus pulposus (Vialle et al., 2010).

Spondylolisthesis

Spondylolisthesis condition occurs due to the slippage of one vertebral body compared to the other adjacent vertebral body as presented in Fig. 2. This displacement causes symptoms of back pain and can also cause pain in one or both the legs. The grading of illness is based on the degree of slippage of one vertebral body concerning the adjacent vertebral body (Tenny & Gillis, 2019).

Dataset and tools

The classification efficacy of the proposed approach is investigated using the vertebral column pathology dataset available on the UCI machine learning repository. The dataset is designed by Dr. Henrique da Mota in the Group of Applied Research in Orthopaedics (GARO) of the Centre MAcdico-Chirurgical de RAcadaptation des Massues, Lyon, France (UCI Machine Learning Repository, 2011). Each record in the dataset contains six shapes and orientations of the pelvis and lumbar spine based diagnostic attributes including pelvic incidence, pelvic tilt, sacral slope, lumbar lordosis angle, pelvic radius, and grade of spondylolisthesis. The dataset contains a total of 310 records of individual persons as shown in Table 2, from which 150 are spondylolisthesis patients records and 60 are disc herniation patients. The dataset also contains 100 records of healthy persons without any of the given pathologies. As shown in Table 3, the dataset is not balanced, i.e., the ratio of the number of different class instances is not equal.

Data re-sampling methods

It is already stated that the dataset that is used in the current study is not balanced concerning records for each class. It contains 310 records, out of which 150 correspond to spondylolisthesis patients (majority class) while only 60 and 150 records correspond to disc herniation patients (minority class) and healthy persons, respectively. The class imbalance in the dataset can result in a significant bias towards the classification of the majority class. It can affect the classification performance adversely while increasing false negatives in the result. To overcome this issue, two types of data re-sampling techniques have been used, i.e., under-sampling, and over-sampling. Further, the cluster centroid technique is considered from the under-sampling category while two techniques synthetic minority and adaptive synthetic are considered from the over-sampling category. Such techniques have been taken regarding their superior performance.

Concatenated re-sampling

Together with the above-described re-sampling approaches, experiments have been conducted for the usability of another approach named concatenated re-sampling (CR). In this approach, the results of ADASYN, SMOTE, and CC have been concatenated to improve the results of learning models. The technique results have been concatenated along axis ‘0’ as shown in Fig. 4. CR can thus be defined as:

(1) $$C{R}_{(m\times n)}=[ADASY{N}_{(i\times j)},SMOT{E}_{(u\times v)},C{C}_{(p\times q)}]$$where ADASYN_{(i × j)} represents the results of the ADASYN technique, i and j represents the number of attributes/features and records, respectively. Similarly, SMOTE_{(u × v)} and CC_{(p × q)} are the results of SMOTE and CC techniques, where u, p and v, q representing the number of attributes and number of records, respectively. While CR_{(m × n)} is the concatenation results of these three re-sampling techniques where m = i = u = p is the number of attributes and n = j + v + q is the number of records.

Machine learning models

The current study considers four machine learning algorithms including AB, RF, ETC, and LR as the classification algorithms for disc pathologies. Their hyperparameters are tuned to enhance their classification accuracy. The list of parameters used in the experiments and their associated values are given in Table 3.

Proposed methodology

In this study different machine learning techniques have been used to solve the pathologies classification problem. Specifically, four supervised machine learning models have been used such as AB, RF, ETC, and LR with and without re-sampling techniques. The workflow of the model construction is shown in Fig. 5. In the first phase, the dataset has been re-sampled by using re-sampling techniques to balance the given dataset. The record count for each class after applying CC, SMOTE, ADASYN, and CR are shown in Table 5. All re-sampling techniques have been used with their default parameter settings that is the reason ADASYN generates 147 records for normal patients class.

After balancing the dataset by re-sampling, all the records have been shuffled, and the dataset has been split into training and testing subsets. The split ratio of training and testing subsets has been set as 75:25 respectively. All experiments have been conducted using Core i7 7th generation machine on the Microsoft Windows 10 platform in the Python language using Anacondas 3 with a Jupyter notebook.

Performance evaluation metrics

Several evaluation metrics are used to analyze the performance of the selected classifiers and data re-sampling methods. These metrics are discussed briefly in the following sections.

A confusion matrix is a table layout used to visualize the performance of a classification model using a test data set for which the actual values are known (Wisdom, 2018; Data School, 2015; Rustam et al., 2020). The typical layout of a confusion matrix is given in Fig. 6. Considering three classes spondylolisthesis, normal, and hernia represented by class 0, 1, and 2 respectively, each cell of the confusion matrix can be described as follows

• P00: The cell value shows the number of predictions where class 0 was correctly classified (as class 0). The value represents the true positive (TP) for class 0.

• P01: The cell shows the number of predictions where class 1 was incorrectly classified as class 0.

• P02: This cell shows the number of predictions where class 2 was incorrectly classified as class 0.

• P10: The cell shows the number of predictions where class 0 was incorrectly classified class 1.

• P11: The cell shows the number of predictions where class 1 was correctly classified (as class 1). This cell represents TP for class 1.

• P12: The cell shows the number of predictions where class 2 was incorrectly classified as class 1.

• P20: The cell shows the number of predictions where class 0 was incorrectly classified as class 2.

• P21: The cell shows the number of predictions where class 1 was incorrectly classified as class 2.

• P22: The cell shows the number of predictions where class 2 were correctly classified (as class 2). The cell represents TP for class 2.

The accuracy of a model is calculated as the ratio of the number of model’s right predictions to the total number of predictions. So in line with the above confusion matrix notations, accuracy can be defined as:

(6) $$Accuracy={\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}$$where

• TP (true positive): The number of instances in which a model predicted a particular class out of the three classes (Spondylolisthesis or Hernia or normal) correctly.

• TN (true negative): The number of instances in which a model predicted a class as negative which is negative.

• FP (false positive): False positive or type 1 error is the number of cases where a model predicted a class as positive and it is negative. For Example, the number of predictions where persons having no herniation was incorrectly classified as hernia cases.

• FN (false negative): False-negative or Type 2 error is the number of cases where a model predicted a class as negative which is positive. For Example, the number of predictions where persons having herniation was incorrectly classified as another case Le et al. (2020b).

Following the four parameters defined above, accuracy, precision, recall and F₁ score are defined using the following equations (Le & Nguyen, 2019)

(7) $$Precision={\displaystyle \frac{TP}{TP+FP}}$$

(8) $$Recall={\displaystyle \frac{TP}{TP+FN}}$$

(9) $$F_{1}Score=2\times {\displaystyle \frac{Precision\times Recall}{Precision+Recall}}$$

Performance without dataset re-sampling

The selected classification algorithms are initially tested with the imbalanced dataset to analyze the performance. Table 6 shows the results of these models without using data re-sampling approaches. Results indicate that the performance of the RF classifier is superior to other classifiers under investigation. The performance of other classifiers is almost similar regarding accuracy. Similarly, the values for precision, recall, and F₁ scores for these classifiers are very close indicating their similar performance with the imbalanced dataset.

The confusion matrix shown in Fig. 7 indicates that RF gives the highest number of correct predictions than that of other classifiers. RF gives 69 correct predictions out of 78 and only 9 predictions are wrong. The highest number of wrong predictions is given by the AB classifier which gives 14 wrong predictions and 64 correct predictions out of 78 predictions. So, RF is the outperformer while AB is the poor performer while LR, ETC show the same performance concerning the accuracy, recall, and F₁ score but show little difference in precision.

Performance using CC under-sampling technique—strategy 1

In the under-sampling technique, CC has been used to balance the dataset. CC under-sampling resulted in a total of 180 records which were split into 135 and 45 for training and testing, respectively. Table 7 and the confusion matrix in Fig. 8 show the performance results of all models when CC under-sampling is applied to balance the dataset. Results reveal that RF and AB classifiers give the highest accuracy of 0.84. The accuracy of ETC is 0.80, while LR performs poorly with the accuracy of 0.78 in this context. RF and Adaboost are the best performers while ETC is close to them in terms of performance while LR shows the lowest performance.

Overall, the performance of the classifiers has been reduced when trained on under-sampled datasets except for AB whose performance has been slightly improved. Primarily, the less number of records for each class resulted in degraded performance. According to Fig. 8, RF and AB give an equal number of correct predictions when trained and tested with an under-sampled dataset. RF and AB give 38 correct and 7 wrong predictions out of 45 predictions. LR gives 35 correct predictions which are less than all other models and 10 wrong predictions out of 45 predictions.

Performance using ADASYN and SMOTE over-sampling techniques—strategy 1

SMOTE

Besides the under-sampling approach, two over-sampling approaches including ADASYN and SMOTE are also utilized to analyze their efficacy. SMOTE generated 450 records after over-sampling of which 337 and 113 were used for training and testing, respectively. The selected classifiers are trained and tested on the over-sampled dataset and results are given in Table 8. Results suggest that ETC performs the best among the selected classifiers when trained on the over-sampled dataset. For an over-sampled dataset, the accuracy of ETC can go up to 0.90 which is the highest among all classifiers. AB shows poor performance in this scenario as well with an accuracy of 0.76. The performance of classifiers is superior when an over-sampled dataset is used than that of an under-sampled dataset.

Table 8:

Performance results with SMOTE.

Classifier	Accuracy	Class	Precision	Recall	F1 Score
RF	0.86	Hernia	0.79	0.91	0.85
		Normal	0.91	0.71	0.80
		Spondylolisthesis	0.93	1.00	0.96
		Macro avg.	0.88	0.88	0.87
		Weighted Avg.	0.87	0.86	0.86
LR	0.79	Hernia	0.78	0.70	0.74
		Normal	0.71	0.76	0.74
		Spondylolisthesis	0.93	1.00	0.96
		Macro avg.	0.81	0.82	0.81
		Weighted Avg.	0.79	0.79	0.79
ETC	0.90	Hernia	0.83	0.98	0.90
		Normal	0.97	0.76	0.85
		Spondylolisthesis	0.96	1.00	0.98
		Macro avg.	0.92	0.91	0.91
		Weighted Avg.	0.91	0.90	0.90
AB	0.76	Hernia	0.68	0.85	0.76
		Normal	0.77	0.55	0.64
		Spondylolisthesis	0.92	0.96	0.94
		Macro avg.	0.79	0.79	0.78
		Weighted Avg.	0.77	0.76	0.75
SVM	0.89	Hernia	0.85	0.86	0.86
		Normal	0.88	0.85	0.86
		Spondylolisthesis	0.97	0.97	0.97
		Macro avg.	0.90	0.90	0.90
		Weighted Avg.	0.89	0.89	0.89

DOI: 10.7717/peerj-cs.547/table-8

The confusion matrix in Fig. 9 shows that the performance of ETC is superior when the SMOTE technique is used than that of CC and without re-sampling. In the SMOTE case, ETC correctly classifies 104 out of 113 test samples and only 9 predictions are wrong.

ADASYN

Another over-sampling technique ADASYN has been used in this study as well. ADASYN generates 447 instances after the over-sampling of the dataset. Dataset then has been divided into training and testing sets with the same ratio of 75:25 as we did it for SMOTE re-sampling techniques. Consequently, 335 records are used for training the models while 112 are used for model testing. Experimental results are shown in Table 9 which indicate that ADASYN re-sampling technique helps to improve classification accuracy. ETC achieves the highest accuracy of 0.95. Other than that, the performance of RF and AB has been elevated concerning the accuracy and other metrics. The average performance of all the classifiers is higher with the ADASYN over-sampling technique than that of CC under-sampling and SMOTE over-sampling. However, there is no change in the performance of LR.

Table 9:

Performance results using the ADASYN over-sampling technique.

Classifier	Accuracy	Class	Precision	Recall	F1 Score
RF	0.93	Hernia	0.91	0.93	0.92
		Normal	0.95	0.88	0.91
		Spondylolisthesis	0.93	1.00	0.96
		Macro avg.	0.93	0.94	0.93
		Weighted Avg.	0.93	0.93	0.93
LR	0.79	Hernia	0.85	0.63	0.72
		Normal	0.69	0.85	0.76
		Spondylolisthesis	0.93	1.00	0.96
		Macro avg.	0.82	0.83	0.82
		Weighted Avg.	0.81	0.79	0.79
ETC	0.95	Hernia	0.96	0.96	0.96
		Normal	0.93	0.95	0.94
		Spondylolisthesis	0.96	0.92	0.94
		Macro avg.	0.95	0.94	0.95
		Weighted Avg.	0.95	0.95	0.95
AB	0.87	Hernia	0.84	0.91	0.87
		Normal	0.86	0.78	0.82
		Spondylolisthesis	0.92	0.92	0.92
		Macro avg.	0.87	0.87	0.87
		Weighted Avg.	0.87	0.87	0.87
SVM	0.79	Hernia	0.68	0.79	0.73
		Normal	0.76	0.63	0.69
		Spondylolisthesis	0.94	0.97	0.96
		Macro avg.	0.80	0.80	0.79
		Weighted Avg.	0.79	0.79	0.78

DOI: 10.7717/peerj-cs.547/table-9

Figure 10 shows the confusion matrix for selected classifiers. ETC performs very well and correctly classifies 106 samples out of 112. RF also performs well with a 0.93 accuracy score and gives 104 correct predictions. The classifier with the least performance in terms of accuracy and other metrics is LR with an accuracy of 0.79.

Performance using concatenate re-sampling technique—strategy 1

We propose the use of a concatenated re-sampling approach which is a combination of ADASYN, SMOTE, and CC. For the CR approach, the results of ADASYN, SMOTE, and CC techniques have been concatenated which resulted in the enlarged dataset of 1,077 records. Thus, after splitting the dataset into training and testing sets, 807 records are used for the training while 270 are used for testing. Experimental results are shown in Table 10 which indicates the performance of all the classifiers is enhanced. ETC achieves the highest accuracy score of 0.99 and other tree-based models also perform very well. AB achieves its highest accuracy of 0.95 for the current problem and RF also achieves a 0.98 accuracy score. Accuracy of LR is elevated as well from 0.79 in ADASYN re-sampling to 0.85 in CR re-sampling.

The confusion matrix in Fig. 11 shows the performance of learning models with the CR re-sampling technique. ETC gives the highest number of correct predictions as compared to other models. Out of 270 test samples, ETC provides 267 correct predictions and only 3 wrong predictions. The proportion of the number of correct predictions shows how effective CR re-sampling is on small and imbalanced datasets. ETC and RF are the best performers while Adaboost is close to them in terms of performance. Results show that collectively the tree-based models are more effective in the given scenario.

Performance using re-sampling technique—strategy 2

For strategy 2, the data re-sampling is carried once the data are split into training and testing data. Table 11 shows the accuracy, precision, recall, and F1 score of all the classifiers using CC undersampling. Results show change in the accuracy of different classifiers, e.g., RF from 0.84 to 0.81, LR 0.78 to 0.84, ETC 0.80 to 0.81, Adaboost 0.84 to 0.79, and SVM 0.82 to 0.90 using strategy 2. Consequently, the performance of LR and SVM has been elevated substantially.

The performance of the classifiers using SMOTE is shown in Table 12. Results indicate that the performance of the classifiers has been changed slightly. For example, the accuracy of RF, ETC has been reduced to 0.81, and 0.85 from 0.86, and 0.90, respectively. However, the performance of LR and Adaboost is boosted when following strategy 2.

Similarly, Table 13 shows the results for performance evaluation parameters when predictions are made using ADASYN oversampling approach. Results suggest that the performance of RF, ETC, and Adaboost has been degraded substantially when strategy 2 is adopted. On the other hand, the performance of LR and SVM has been improved following this strategy. Using sampling before data split may result in having duplicate samples in both the training and test datasets which could overstate the performance of the classifiers. So when the data split is performed before the resampling, the performance is reduced slightly.

In the end, the experiments are performed using the proposed CR resampling approach to analyze if the results are affected when strategy 2 is adopted. Results shown in Table 14 prove that the accuracy of all the classifiers has been changed. For example, the accuracy of RF has been degraded substantially from 0.98 to 0.86 when strategy 2 is adopted. Similarly, the performance of ETC and Adaboost is reduced as well. Conversely, the performance of LR is greatly improved and the same is true for SVM. Despite the change in the accuracy of different classifiers, the overall performance of the classifiers is better when used with the proposed CR resampling approach.

Performance comparison with other approaches

The efficacy of the proposed approach is analyzed by comparing its performance to several other similar approaches. For example, the study (Unal, Polat & Kocer, 2014) uses a combination of pairwise fuzzy C-means based feature weighting and SVM to classify samples into three classes of hernia, normal, and spondylolisthesis and achieves 96.4% accuracy. Similarly, the authors classified samples into normal and abnormal classes for vertebral column disorder in Unal, Polat & Kocer (2016) and achieved an accuracy of 99.3%. The classification has been done using the combination of MSCBAW (mean shift clustering-based attribute weighting) and RBDNN (radial basis function–neural network) in the study. To compare the performance of the proposed approach with Unal, Polat & Kocer (2016), ETC is trained on two classes with concatenated re-sampling. Hernia and spondylolisthesis class samples are merged into one class called, ‘abnormal’ while samples of healthy people belong to the ‘normal’ class. ETC achieves an accuracy of 99.5% when tested with two classes.

Performance results are given in Table 15. Results indicate that the proposed approach which comprises of ETC with CR re-sampling approach outperforms the state-of-the-art approaches for vertebral pathologies. The proposed approach can successfully classify the given samples into three classes of hernia, normal, and spondylolisthesis with high accuracy. So, the approach possesses the potential to assist medical experts in the accurate diagnosis of vertebral pathologies.

To further corroborate the findings of this study performs a statistical T-test on the results of machine learning models and shows the significances of our proposed CR technique. We perform a T-test for both scenarios as follows:

1. Resampling before splitting

2. Splitting before resampling

We compare the model’s results to check that which technique is statistically significant for data resampling. To evaluate the T-test we take two hypotheses as:

1. Null hypothesis (NHo): The model results are statistically significant after apply CR as compare to SMOTE, ADASYN, and CC.

2. Alternative hypothesis (AHa): The model results are not statistically significant after apply CR as compare to SMOTE, ADASYN, and CC.

In the first scenario, tree-based models such as ETC, RF accept the NHo and reject AHa which means their performance is statistically significant after applying resampling techniques. On the other hand, for the second scenario, LR performs statically significant after applying CR as compared to other re-sampling techniques because it accepts the NHo hypothesis. These statistical T-test results show that the CR technique is better as compared to other individual re-sampling techniques.

Due to the lack of a similar dataset, cross-validation is used to confirm the performance of the proposed approach. Table 16 shows the results of 10-fold cross-validation which indicates the performance of the proposed resampling approach with all the selected classifiers.