Microscopic parasite malaria classification using best feature selection based on generalized normal distribution optimization

Research motivation and contribution

Malaria is the most prevalent disease. This illness has affected thousands of people worldwide. People die because of the late diagnosis of this disease. Several approaches for detecting malaria at an early stage are being proposed, but limitations in this domain still exist (Majid et al., 2020). The extraction and selection of features are the most important phases of this process. This research focuses on the suitable selection of features.

The research contribution steps are as follows:

In this article, extensive experimentation is performed individually as well as fusion of PHOG with selected parameters such as 20 bin, $180{}^{\circ }$ angle, two pyramid levels (L), and roi [1; 64; 1; 64] and deep features using pre-trained RasNet-18 and ResNet-50 models for features analysis. Based on experimentation, all extracted features are serially fused and the best features are selected using the generalized normal distribution optimization (GNDO) approach. Finally, the classification is performed based on the selected features using kernels of support vector machine (SVM) and neural network classifiers.

The organization of the articles is as: Related work is described in “Related Work”, proposed technique steps are elaborated in “Proposed Methodology”, achieved outcomes are discussed in “Simulation Results” and “Conclusion” contains a conclusion.

Image smoothing using bilateral filtering

Bilateral filtering is a nonlinear, edge-preserving noise reduction smooth filter (Tomasi & Manduchi, 1998). In this case, pixel intensity is replaced with the average weighted intensity from the neighboring pixels. To preserve the sharpness of edges, this weight could rely on Gaussian distribution, Euclidean distance, and radiometric distance (color intensity, distance in depth). The mathematical Eq. (1) of the bilateral filter is:

(1) $$G^{filtered}\left(x\right)={\displaystyle \frac{1}{{\left(weight\right)}_p}\sum _{x_g\epsilon \mathrm{\Omega }}G\left(x_g\right)f_r\left(\parallel G\left(x_g\right)-G\left(x\right)\parallel \right)t_s\left(\parallel x_g-x\parallel \right),}$$where normalization ${\left(weight\right)}_p$

$${\left(weight\right)}_p=\sum _{x_g\epsilon \mathrm{\Omega }}{f}_r(\parallel G(x_i)-G\left(x\right)\parallel )t_s\left(\parallel x_g-x\parallel \right).$$

Here, $G^{filtered}$ denotes the filtered output image; $G$, the original microscopic image; x, the pixel coordinates; $\mathrm{\Omega }$, the cantered point of the window; $f_r$, range of the pixel values to smooth the image intensity; and $t_s$, a spatial kernel to compute the difference of smoothing among the coordinates. Figure 2 presents the smoothing results of the image.

Deep features extraction

Deep features were derived from smooth images using pre-trained ResNet-18 and ResNet-50 models. The ResNet-18 model consists of 71 layers, which include convolutional (20), ReLU (17), average pool (one), addition (eight), max pooling (one), batch normalization (20), fully connected, softmax and classification. ResNet-50 model has 177 layers, which include 1 input, (53) convolutional, average pool (one), ReLU (49), batch normalization (53), addition (16), softmax, fully connected, and classification.

The proposed method extracts feature from the fully connected layer with the dimension of N × 1,000 from both pre-trained models and serially fused with N × 2,000 dimensions and supplied to GNDO for the most prominent features selection.

Feature extraction using PHOG

The shape level and spatial features were extracted by PHOG from each microscopic malaria image with the dimension of N × 300 (Beulah & Divya Bharathi, 2016). All images are divided into small grids of pyramids, similar to a quadtree, during this procedure. However, each image exhibits a spatial pyramid-like structure. Every small grid in this structure models a different layer. Figure 3, presents HOGs that are computed across each grid. Then, by merging all these HOGs, we obtain PHOG.

In Fig. 3, PHOG provides help in the reorganization of the lesion shape by computing the orientation of the gradient in a local region.

Table 1 presents the selected parameters of the PHOG features.

HOG features with the dimension of N × 300 are fused serially to the deep feature vector dimension of N × 2,000. The final fused feature vector is N × 2,300 in dimension and is put into the GNDO for the selection of more informative features.

Best feature selection using GNDO

In this research, a feature vector dimension of N × 2,300 is supplied to the GNDO, and the optimum feature dimension of N × 468 is selected. GNDO is based on the normal distribution theory. The normal distribution theory is employed to identify and describe significant natural occurrences. Let a variable x follow a probability distribution location $\mu$, and scale parameters are defined in Eq. (2):

(2) $$f(x)=\frac{1}{\sqrt{2\pi \sigma }}ex{p}^{-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}}.$$

Here, x is a normal random variable, and this is referred to as the normal distribution. Equation (2) shows two normal distribution parameters, namely, the location variable $\mu$ and the scaling variables. The location variable $\mu$ denotes the mean value, and the scale variable $\sigma$ denotes the variance. When $\sigma$ remains constant, the probability density curve will shift to either a high or low mean value. However, when the mean value remains constant, the curve will shift toward an increase in the variance. The population-based optimization search process is categorized into three stages. The scattered distribution leads to a global optimum solution, which is then gathered around to achieve the optimum solution. The position of an individual in a normal distribution can be thought of as a random variable. The standard deviation of an individual’s position in the initial stage is high because the mean value and optimal position value are significantly far off at this point. In the next stage, the mean and the optimal position are much closer to the previous stage. The GNDO model was trained on the pre-trained GNDO parameters with a positive effect on malaria cell classification, as presented in Table 2.

The selected GNDO parameters provide help in determining the optimal fitness values and convergence points. Figure 4 presents a graphical representation of the convergence of the GNDO model over a hundred training epochs.

Visualization of extracted features using tSNE

tSNE is applied for dimensionality reduction and visualization of high dimensional data. In this article manifold learning method is applied for dimensionality reduction and the complete process is presented in Fig. 5.

In the proposed method, a bilateral filter is used to enhance the image quality. The feature analysis is performed using hand-crafted (PHOG) and deep features (ResNet-18 and ResNet-50). The classification is performed based on the linear SVM using individual features of PHOG, ResNet-18, and ResNet-50 as well as based on fused features of ResNet-18 and ResNet-50 models. Finally, to improve the classification results, hand-crafted (PHOG) and deep features such as ResNet-18 and ResNet-50 are fused serially, and prominent features are selected using GNDO. The selected features are used for further experimentation based on SVM linear, SVM quadratic, SVM cubic, NN-narrow, NN-wide, and NN-medium classifiers. To authenticate the classification results, the statistical inference test is performed in terms of mean and standard deviation.

Experiment-1: classification of the malaria cells

The classification outcomes are calculated on deep and hand-crafted features separately and fusion of both types of features. The detailed experiment of this research work is mentioned in Table 4.

Table 4 provides the details of features extraction, fusion, and selection along with their dimension. The experiment is performed individually based on ResNet-18, ResNet-50, PHOG, Fusion of ResNet-18, and ResNet-50 features, and selected features using GNDO after fusion of PHOG, ResNet-18, and ResNet-50 features. The outcomes are detailed in Table 5.

In Table 5, malaria cells were classified using manual features and deep features individually based on a linear SVM classifier. Which achieved an accuracy is 0.89 on PHOG, 0.87 on ResNet-18, 0.82 on Res-Net-50, and 0.90 on fusion of the ResNet-18+ Res-Net-50 features.

In the subsequent experiments, the best features are chosen using GNDO by combining features from various sources, including PHOG, ResNet-18, and ResNet-50. The outcomes of these experiments are detailed in Table 6.

Visual representation of the deep feature learning patterns

Gradient class-weighted activation mapping (Grad-CAM) must explain the capability that could be used to facilitate prediction understanding through the neural network. Grad-CAM is a generalization method that computes the neuron significance in the model prediction using gradients as a target. It measures gradient output differently, such as the class score connected to convolutional layer features. The importance of the neuron weights is discovered using a pooled spatial gradient. These weights are used to integrate linear maps of the activation and determine which features played a vital role in the model prediction.

The classification models with $y^c$ output denotes class score c and Grad-CAM (Selvaraju et al., 2017) mapping on each convolutional layer with the k number of feature channels, ${{\mathrm{A}}_{\mathrm{i},\mathrm{j}}}^{\mathrm{k}}$, in which i and j specify the pixel indices. The weight of a neuron’s importance is defined in Eq. (3).

(3) $${\alpha }^{channel}{}_k=\frac{1}{N}{\displaystyle \sum _i{\displaystyle \sum _j\frac{\underset{}{\underbrace{\frac{\vartheta y^c}{\vartheta A_{i,j}{}^k}}}}{Gradientbybackpropagation}}}.$$

Here, N denotes the total pixels, and a weighted combination of feature mapping with ReLU is explained in Eq. (4)

(4) $$ReLU=\left({\sum }_k{{\alpha }^{channel}}_k{A}^k\right).$$

The activation function ReLU returns the positive features to a given class, and the output is presented in the form of a heatmap of a specified class of the same size as the feature mapping. The Grad-CAM mapping is unsampled to the input size. Figure 6 presents the learning patterns.

The classification outcomes are presented in Fig. 7.

The classification outcomes are calculated on SVM and NN, as demonstrated in Table 6 and Fig. 8.

Table 6 presents the malaria classification outcomes using two family classifiers: geometric and neural networks. On the geometric family, linear, quadratic, and cubic SVM are used to compute classification results with accuracies of 95.71%, 97.38%, and 99.05%, respectively. On the neural network family, narrow, medium, and wide neural network kernels were used, yielding accuracies of 99.34%, 99.45%, and 99.48, respectively. In this experimental analysis, we observed that the neural network’s wide kernel provides maximum accuracy.

Statistical inference test for malaria classification

The proposed classification method is statistically analyzed on selected kernels, such as (linear, quadratic, cubic), (narrow, medium, and wide) of SVM and neural network classifiers, as presented in Figs. 10 and 11.

Tables 7 and 8 present the quantitative classification results.

In this experiment, the cubic kernel of the SVM classifier produces a mean ROC of 0.97 $\pm$ 0.01, whereas the linear and quadratic kernels of SVM produce mean ROCs of 0.93 $\pm$ 0.02 and 0.96 $\pm$ 0.01, respectively. Figure 9 presents the malaria classification results using NN. Table 8 presents the quantitative evaluation of NN.

In Table 8, the wide kernel of NN provides a maximum mean ROC of 0.98 $\pm$ 0.00 on the neural network classifier. Table 9 presents the proposed testing results in terms of ROC using different kernels of NN and SVM classifiers.

Table 9, depicts classification results that are computed on different kernels of NN and SVM classifiers which we achieved using NN 0.98 $\pm$ 0.00 ROC on wide kernel and 0.97 $\pm$ 0.01 ROC on SVM quadratic. Table 10 provides a detailed comparison of classification outcomes with the existing methods.

In Table 10, five recent works are considered for comparison with the proposed method. Traditional techniques are employed to obtain the classical features, which are then passed to the SVM classifier. This work provided an accuracy of 93.13% (Vijayalakshmi, 2020). The features are derived from classical handcrafted techniques and achieved a 91% accuracy by using a naïve Bayes classifier (Maqsood et al., 2021). In this work, the features were extracted using different handcrafted methods and achieved an accuracy of 98.35% (Elangovan & Nath, 2021). The fusion of CNN and handcrafted features gives an accuracy of 88% (Sadafi et al., 2021). The features in this work are derived from the handcrafted method and then classified with 92% accuracy using the SVM classifier.

This research provides an improved classification model, as compared with existing work, by fusing derived deep and handcrafted features using the ResNet18 model, ResNet50 pre-trained model, and PHOG handcrafted feature extraction method and then selecting the most prominent features using GNDO for the classification of malaria cells.

Limitations and future work

This work is limited to binary classification of the parasite malaria microscopic images. In the future, this research may be extended for multiclassification of parasite malaria using real patient data from several acquisition sources. Nowadays quantum computing gaining more importance as compared to machine/deep learning. Therefore, this work may also be extended using quantum machine learning for the multi-classification of parasite malaria cells.