In order to differentiate between normal and abnormal brain tumors in brain MR images, Arunachalam and Savarimuthu [9] suggested a model. They included feature extraction, augmentation, transformation, and classification in their suggested model. First, they used shift- invariant shearlet transform to improve the brain MR image (SIST). The features were then retrieved using the Gabor filter, the discrete wavelet transform (DWT), and the gray level co- occurrence matrix (GLCM). Finally, feed-forward backpropagation neural network was used to acquire a high accuracy rate (99.8%) using these extracted features. Deep learning techniques have been extensively used for brain MRI categorization over the past ten years. The feature extraction and classification stages are integrated into self-learning in the deep learning approach, therefore they do not need to be carefully extracted features manually [10].

Normal and abnormal brain MRI images were categorized into two classes by Shree and Kumar. They applied a probabilistic neural network (PNN) classifier and used GLCM for feature extraction that achieved 95% accuracy [11]. Berkan Ural [12] first applied various image processing methods to improve brain MRI. Additionally, various segmentation techniques have been combined to improve the performance of the system. The PNN approach is additionally used to identify and localize the tumor region in the brain. Their suggested method has a respectable accuracy rate (90%) and a relatively short processing time. A hybrid energy-efficient technique for automatic tumor segmentation and detection was proposed by Rajan and Sundar. Their suggested approach involves seven lengthy phases and a purported 98% accuracy. Their suggested model workflow is its lengthy computation time caused by the employment of various approaches [13].

Preethi and Aishwarya [14] created a strategy to categorize different stages of brain tumors. To create the feature matrix, they combined the GLCM and the wavelet-based methods. With the help of the oppositional flower pollination algorithm (OFPA), the extracted features were further decreased. In order to classify the MR brain images using the chosen features, a deep neural network is used in the end and achieved 92% accuracy. Deepak and Ameer [15] classified three different types of brain tumors with 98% accuracy by using a pre-trained GoogleNet to extract features from brain MR images. To classify data on brain tumor images, Saxena [16] combined transfer learning techniques with Inception V3, ResNet-50, and VGG-16 models. The ResNet-50 model had a 95% accuracy rate, which was the highest.

Several academics have recently confirmed their proposed methods using brain tumor classification datasets and CNNs for brain MRI classification [17,18]. In 2019, Thejaswiniet [22] proposed a model for classifying and detecting brain tumors that combines the Regularized Kernel-based Fuzzy C-Means Clustering (ARKFCM) segmentation method with SVM for feature extraction. Ullah [19] used DWT to extract the level-3 decomposition's approximation and detail coefficients, lowered the coefficient using color moments (CM), and then used a feed- forward ANN to identify between abnormal and normal brain MR images. A multi-pathway CNN design was presented by Francisco [20] for the automatic segmentation of brain tumors like pituitary, meningiomas, and gliomas tumors. Using a T1-weighted, contrast-enhanced MRI dataset that was made accessible to the public, they tested their suggested model and achieved 97.3% accuracy. Their training process is, nevertheless, rather expensive.

Using multiclass datasets, Kang [21] created a CNN-based model for classifying brain cancers. The accuracy is poor (93.72%), though, and the computation time is excessive. For accurate brain tumor MRI classification, Mirza Mumtaz Zahoor and Saddam Hussain Khan [23] suggested a deep residual and regional-based Res-BRNet CNN. Within the redesigned spatial and residual blocks, the developed Res-BRNet applied regional and boundary-based operations in a systematic order. With the help of patterns and edge-related properties, spatial blocks extract the boundary, heterogeneity, and homogeneity of the brain tumor. Furthermore, the remaining blocks effectively represent regional and global changes in brain tumor texture.

Hafiza Akter Munira and Saiful Islam [24] introduced hybrid deep learning methods for CNN and ML classifiers to categorize brain cancers. For the purpose of extracting deep brain features from MRI data, a new 23-layer CNN architecture is created. Then, the CNN model's flattened layer's extracted in-depth features are assessed using SVM and RF classifiers. On multi-class brain MRI datasets, this study applies tuned Inception V3, CNN-SVM, CNN-RF, and CNN deep learning models. For the classification of brain tumors, Majdi Alnowami [25] proposed utilizing densely connected convolutional networks (DenseNets) in 2022. The model is made up of four dense blocks and contains 58 layers. The study has demonstrated that: 1) implementing an intensity normalization preprocessing step significantly improves the performance of the classification model, and 2) the normalization method's effect on classification accuracy.

One of the problems in using the mentioned algorithms is that some of these algorithms are not used directly to classify several classes. Because many real-world applications rely on a large number of parameters and classes, multiclass and multivariate classification issues are crucial to recent advances in machine learning. There are a lot of unresolved difficulties as well, including problems with optimization, overfitting, and high dimensionality [26]. One of the solutions proposed in recent years to solve this problem is the use of group methods with binary techniques such as the decomposition method. One of the analysis methods is the One-Versus-One (OVO) method, in which the data with several classes are divided into the maximum binary subset of classes, and the classification of the subsets is done by binary algorithms, and finally, the output of the classifications of the final class is combined. The use of binary subsets of classes can improve classification in two ways. First, it reduces complexity in classification. Because in multi- class classification, there is more complexity due to the boundaries between classes, and in the second case, it increases the accuracy of the classification in many cases. A classification algorithm provides the most accuracy in the classification, but this does not mean that it can provide the highest accuracy in every subset of classes related to the problem. The combination of pre- processing methods, feature extraction, dimensionality reduction, and classifications has led to the emergence of various algorithms in the field of classification

The Proposed Method

The real data in the field of classification can be objectively used as a suitable tool for checking the efficiency of different algorithms. In this study, in order to create a reliable database, a number of MRI images are collected from the website of Guangzhou Southern Medical University, China. This dataset contains 3064, T1-weighted images collected from 233 patients. Three types of tumors including meningioma, glioma, and pituitary tumor have been identified in these images and thereby three classes have been determined for the images. Due to the limitation of available computer hardware including CPU, GPU, and Ram in using the classification algorithms, 300 images have been selected from each tumor class in MRI images. Also, the size of all images is 227×227 [27]. Therefore, this used dataset includes 900 brain MRI images. The method proposed in this study leads to the diagnosis of brain tumors in MRI images. Based on the steps shown in Figure 1, the suggested algorithm includes four stages pre-processing, feature extraction, dimension reduction, and classification.

Figure 1: The proposed model.

In this research, the histogram equalization method for pre-processing stage, convolution neural network (AlexNet and GoogleNet models) and GLCM for the feature extraction stage, and PCA method for dimensional reduction are used. Finally, a combination of the OVO method and supervised machine learning algorithms was used to classify brain MRI images. At this stage, the classes are separated in binary and therefore classified. Also, in order to divide the images into training and finally test data, the k-fold cross-validation method has been used, in which k is considered equal to 10. The reason for choosing this value is that k=10 in cross-validation has less bias and variance, which is usually recommended [28]. Based on this method, the data are divided into ten separate subsets, in each iteration, one subset of data is considered to test data and nine subsets are considered training data. Finally, the average error of all 10 folds is considered the final classification error. Each step of the proposed method is explained here:

Histogram Equalization

Many imaging applications, including medical image analysis, remote sensing, professional photography, and display technologies, depend on contrast enhancement. Contrast enhancement has been achieved using a variety of image processing methods. Due to its efficiency and simplicity, histogram equalization (HE) is a well-known technique for image improvement [29]. In order to flatten and extend the dynamic range of the histogram, HE first determines the frequency of each intensity value in an image using the probability density function. Then, this method re-distributes the intensity values of pixels in the image. The output image that is produced has a more even distribution of intensities, greatly enhancing the image contrast [30].

Therefore, by equalizing the histogram, the brightness of the background and textures are adjusted and the processing is done correctly. This algorithm makes it possible that if the devices are different and the images are produced with different brightness levels, this will not affect the efficiency of the algorithm and the images will be delivered to the processor algorithm in the same way. Histogram equalization is calculated for each pixel by equation (1).

where h(v) is the value of the histogram, cdf(v) is the value of the cumulative distribution function associated with pixel v, cdfmin is the minimum value of the cumulative distribution function, w is the image width, h is the image height, and L is the value of the gray level used and, in most cases, equals 256.

Feature Extraction

The process of feature extraction starts with feature selection. The complexity and effectiveness of the analysis and pattern categorization procedure will largely depend on the features that are chosen. The features are initially chosen based on the specifications of the application and the developer's expertise [31]. In order to extract features, a combination of a traditional technique GLCM and two pre-trained ANN models named GoogleNet and AlexNet have been used.

Gray Level Co-occurrence Matrix (GLCM)

GLCM is a matrix that contains information pertinent to the relationship between the values of adjacent pixels in an image and the number of rows and columns which is equal to the number of gray levels in the image. This means that if the number of gray levels of an image is G, then the dimensions of the desired GLCM matrix are equal to a G×G matrix [32]. Features such as energy, correlation, contrast, etc. are extracted from this matrix, which is found to have a significant impact on image classification and recognition. For instance, cancerous glands have a contrasting color compared to their surroundings. This feature is a good choice in describing the variation of the gray level around the desired pixel. At this stage, applying the co-occurrence matrix technique, 22 features are extracted from brain MRI images, and those features along with the relevant formula are shown in Table 2.

Table 2: Descriptions related to extracted features from the GLCM.

p(i, j): (i,j)th entry in a normalized gray-tones spatial-dependence matrix, p_x(i): ith entry in a marginal-probability matrix obtained by summing the rows of  means of p_x, u_y: means of  standard deviations of  standard deviations of p_y n_g: number of distinct gray levels in the quantized image, c(i, j): the co-occurrence probability between grey levels i and j j, G: GLCM matrix 

Finally, the output of features extracted using the GLCM method according to the 900 studied images, includes a matrix with 900 rows and 22 columns.        

Convolutional Neural Networks (CNNs)

Deep learning is a set of techniques based on neural networks that allow us to learn features automatically from input data [33]. In deep learning, CNNs are considered a class of ANNs that are mostly used for image analysis and to extract features and better accuracy in the classification. The purpose of designing CNNs is to accurately model the function of the human visual system and its connection with the visual part of the brain, which is responsible for automatically extracting key features, learning images, and removing possible additional features. A CNN consists of numerous convolutional and pooling layers. The input layer of a CNN is usually an image with arbitrary dimensions and its output layer is a feature vector with high resolution and corresponds to different classes. The hidden layers in this network are composed of the convolution layer, pooling layer, and full connection layer [34]. The structure of CNN is shown in Figure 2.

Figure 2: Simple structure of CNN.

It should be noted that convolutional layers perform very well in finding features in images. If some of these layers are placed one after the other, they learn a hierarchy of non-linear features. That is, in the initial layers of the network, parts of the image such as corners, lines, and edges are learned, and in the later stages, the features of higher levels (Figure 3) are learned. For instance, if the input image is an image of a person's face; features such as eyes, nose, cheeks, and face are learned in the higher layers. Finally, the final layers of the generated features are also used for classification.

Figure 3: Learning stages and feature extraction in CNN [35].

Two models of CNN models, which are used in the proposed algorithm in this study, are the AlexNet and GoogleNet models. The AlexNet model was introduced in 2012 to train and classify ImageNet data in an article entitled "ImageNet classification using deep CNNs". ImageNet contains 1.2 million 256x256 images divided into 1000 subsets. According to Figure 4, There are eight learnable layers in the AlexNet. The Rectified Linear Unit (ReLU) activation is used in each of the five levels of the model, with the exception of the output layer, which uses max pooling followed by three fully connected layers. They discovered that the training process was nearly six times faster when the ReLU was used as an activation function. Additionally, they made use of dropout layers, which stopped their model from overfitting. The database used by the AlexNet network includes 15 million photos in 22 thousand groups [36].

Figure 4: AlexNet CNN [36].

In 2014, Szegedy et al. introduced GoogleNet in an article entitled "Going deeper with convolutions", which is deeper and more complex than the AlexNet model, and in fact, it is the deepest network among common models. The network consists of 22 layers and the error rate of this network is 6.7%. For the first time, the structure of this network deviated from the common structures of CNNs that predicted convolution and pooling layers on top of each other as a sequential structure. In this model, the authors introduced a new concept called inception. Each inception consists of six convolution layers and one pooling layer. According to Figure 5, it can be seen that the GoogleNet model includes two convolution layers, three pooling layers, and nine inception layers. In comparison to shallower and less wide networks, this method's key benefit is a large quality gain with a relatively small increase in processing needs. A further indication of the power of the Inception architecture is the fact that detection work was competitive despite not using context nor performing bounding box regression [37].

Figure 5: GoogleNet Convolution Neural Network [37].

Ensemble learning combines several deep learning methods. This is carried out to improve predictions, classifications, or other deep learning model functions. The combined functionality of various deep learning models could be used in ensemble learning to construct new models. Compared to training a new model from scratch, it has advantages including saving time, using less computing power, having a model with higher accuracy, and more capabilities [37]. Because of the several benefits of ensemble learning, in this research, GoogleNet and AlexNet networks have been used to extract image features using pre-trained CNN methods. Through the AlexNet network, we will have 4096 features, the output of which will be a matrix with 900 rows and 4096 columns. Furthermore, 1000 features are extracted through the GoogleNet network, the output of which will be a matrix with 900 rows and 100 columns. Ultimately, from the feature extraction techniques introduced in advance, we have three feature matrices including the GLCM feature matrix with 900 rows and 22 columns, the AlexNet feature matrix with 900 rows and 4096 columns, and last the GoogleNet feature matrix with 900 rows and 1000 columns.

Dimension Reduction

It is quite obvious that the vectors extracted from the AlexNet and GoogleNet methods as features are quite large and thereby increase the amount of complexity in the calculations and accordingly increase the calculation time in the classification, and to sum up, generally, all these features are not used in the classification. In essence, there is no need to use all these features. As an example, to better understand this issue, imagine if we are looking to find the face of a certain person among several images with a blue background, the features of the face are considered, not the background of the image. The use of dimension reduction methods makes it possible to select the optimal and effective features that have achieved the highest percentage of correct detection in the samples (correct classification) from the obtained features [38]. Among these methods, the PCA method is used in this study because of the small amount of data displayed. In the mathematical definition, PCA is an orthogonal linear transformation that places the data into a new coordinate system. So that the largest data variance is placed on the first coordinate axis, the second largest data variance is placed on the second coordinate axis, and the same is done for the rest of the data. PCA retains the components of the dataset that contribute the most variance. One of the advantages of the principal components analysis method compared with the components analysis method is to reduce the computational complexity and find special vectors with more influence [39]. By using the PCA method to reduce the number of features, in order to reduce the complexity in calculations, decrease the calculation time and optimal use of the effective features, from the number of 22 features obtained by the GLCM technique, 4096 features obtained using AlexNet and 1000 features obtained from GoogleNet, the number of 10, 100, and 100 features are obtained, respectively. That is, reducing the dimensions using the PCA method which leads to a reduction in the number of image features from 5118 to 210 new features. Therefore, by reducing the features of the previous matrices and aggregating the remaining features, we come by a feature matrix with 900 rows and 210 columns.

Table 4: Comparison of our proposed work and related studies in terms of performance metrics.