For image recognition and classification, extracting key features from images is one of the most important steps. Before, people tried to extract features from images by hand, but manually extracting features needs a lot of time and energy, and the results were not very satisfactory. The continuous development of machine learning in computers [17] has been applied to image classification and achieved great success. A sea number of CNN models have been proposed, such as AlexNet, VGG, MobileNet, ResNet, and so on. Scholars use these CNN models to classify and segment brain tumors. Nevertheless, there are some problems: (i) These proposed CNN models are generally tested on large data sets. However, brain tumors’ data sets are relatively small, which can lead to overfitting problems. (II) CNN model contains many layers and parameters, so it may take a long time to complete the training. Our team proposes a novel model (RBEBT) to deal with these problems as mentioned above. The pipeline of the proposed model is shown in Fig. 2.

In the RBEBT, we use fine-tuned ResNet18 to extract the features of brain tumor images. The RBEBT is different from the traditional CNN models in that the randomized neural network (RNN) is selected as the classifier. The training time of RNN is shorter than that of the CNN models because of the simpler structure of RNN. What’s more, it is not easy to produce overfitting problems on small data sets in RNN. However, it may also cause some other problems because the parameters in the RNN are random, such as redundant nodes. We use the bat algorithm (BA) to optimize it to get the ideal parameters. The five-fold cross-validation is chosen to verify the superiority of the RBEBT.

Scholars hope that the increasing number of layers in the CNN models could improve the performance. However, the increase in the number of layers leads to the problem of gradient explosion. Many methods have been proposed to alleviate such problems, such as batch normalization (BN). However, gradient degradation has not been well solved. He et al. [18] coped with the gradient degradation problem by the residual connection, as shown in Fig. 3. The formula of the residual connection is as follows:

(1)R(x)=T(x)−xwhere x is the input, T(x) is the learned feature, and R(x) is learned from the residual connection. The conversion of the above formula is shown as:

(2)T(x)=R(x)+x

The data set in this paper is classified into two categories, but the output nodes of the pre-trained ResNet18 are 1000. In this paper, our team classifies this public data set into two categories. Therefore, we fine-tune the ResNet18, as given in Fig. 4. Fully connected and batch normalization are abbreviated as FC and BN, respectively. Then, we replace the last five layers of fine-tuned ResNet18 (ReLU, BN, FC2, Softmax, and Classification layer) with the RNN.

This paper chooses the RNN as the classifier. The advantages of RNN are to shorten the training time and avoid the overfitting problem. RNN used in this paper is the extreme learning machine (ELM). The structure of ELM is presented in Fig. 5.

Given a data set with the i-th sample as (xi, yi), the calculation steps of ELM are as follows:

(3)xi=(xi1,…,xin)T∈Rn,i=1,…,N,

(4)yi=(Oi1,…,Oim)T∈Rm,i=1,…,N,where n, m represents the input and output dimension, respectively.

The formula of the output matrix of the hidden layer is shown as:

(5)QELM(i)=∑j=1rf(wjxi+bj),i=1,…,N.where r is the number of hidden nodes, the weight vector is given as wj, the bias of the j-th hidden node is bj, and f is the sigmoid function.

The calculation of final output weight (v) is as follows:

(6)v=QELM+Y,

However, the parameters assigned at random may not be the optimal solution. Our team selects the bat algorithm (BA) to optimize it. Suppose the velocity of the u-th bat is lut and the position is put at the time t.

(7)fu=fmin+(fmax−fmin)α

(8)lut+1=lut+(put−p∗)fu

(9)put+1=put+lutwhere fmax, fmin, and fu, are the maximum, minimum, and current frequency, respectively, α∈[0,1] is randomized, p∗ is the best position at present.

The optimal position will be updated as:

(10)pnew=pold+βstwhere β∈[0,1] is randomized, the loudness is st.

The emission rate and loudness will be generated when the u-th bat gets the prey:

(11)sut+1=0.9sut

(12)hut=hu0(1−e−0.99t)

Five-fold cross-validation is chosen to verify the superiority of the RBEBT. In this paper, the abnormal brain and the normal brain are defined as the positive and the negative, respectively. Five indexes are selected in this paper, which are accuracy (ACC), specificity (SPE), precision (PRE), sensitivity (SEN), and F1-score (F1). Their equations are shown as below:

(13){ACC=TP+TNTP+TN+FP+FNSPE=TNTN+FPPRE=TPTP+FPSEN=TPTP+FNF1=2×TP2TP+FP+FN,

The five-fold cross-validation is chosen to verify the superiority of the RBEBT, as shown in Tab. 1. Average and standard deviation are abbreviated as Avr and Std, respectively. The ACC, SPE, PRE, SEN, and F1 are 99.00%, 95.00%, 99.00%, 100.00%, and 100.00%. The results of the RBEBT are greater than 95%, which can prove that the RBEBT is an effective model to classify brain tumors.

In this paper, we test five different backbone models, which are ResNet18, AlexNet, MobileNet, ResNet50, and VGG. The results are shown in Tab. 1 and Fig. 6. ResNet18 as the backbone model can obtain the best results than the other four backbone models.

The ResNet18 can deal with the problem of gradient explosion by residual connection. Other backbone models may meet the problem of gradient explosion. Therefore, our model can achieve the best performance than other models.

To prove the superiority of our network, we compare the proposed RBEBT with the fine-tuned model and the model with only RNN. The results are shown in Tab. 1. The comparison figure is given in Fig. 7. We can conclude that the optimized network (RBEBT) will achieve better classification performance through comparison.

The ELM can get better classification performance in small data set because of its simpler structure. What’s more, the BA is selected to optimize the ELM. Based on these reasons, the RBEBT can get better results than the fine-tuned ResNet18 and ResNet18-ELM.

The proposed RBEBT is compared with seven other state-of-the-art methods, which are 3D-CNN [1], SVM-CNN [2], KNN-CNN [5], 2D-CNN [7], BPNN [11], LVQNN [12], and LRC [13], as shown in Tab. 2. In conclusion, the classification performance of our network is better than the other seven methods, which proves the superiority of our network.

In the RBEBT, we use fine-tuned ResNet18 to extract the features of brain tumor images and select ELM as the classifier. The fine-tuned ResNet18 can extract features accurately and ELM has good performance in small data sets. Therefore, the RBEBT can produce better classification performance than other methods.