# White Blood Cells Classification Using Entropy-Controlled Deep Features Optimization

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## Abstract

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## 1. Introduction

- Using a synthetic, real-world, large-scale dataset of five WBC types, transfer learning is performed using two deep CNNs, namely Darknet53 and Densenet201, followed by their feature fusion;
- For feature selection, a nature-inspired meta-heuristic named entropy-controlled marine predators algorithm (ECMPA) is proposed. The proposed algorithm effectively selects only the most dominant features;
- The reduced feature set is classified using various baseline classifiers with multiple kernel settings;
- The proposed feature selection algorithm demonstrates a high accuracy with significant reduction in feature size. The algorithm also achieves a better convergence rate as compared to classical population-based selection methods.

## 2. Materials and Methods

#### 2.1. Dataset Description

#### 2.2. WBCs Classification Pipeline

#### 2.2.1. Preprocessing

- Convert the RGB image into HSI image;
- Obtain the intensity matrix from the HSI image matrix;
- Perform histogram equalization on the intensity matrix;
- Replace the intensity matrix of the HSI image with the histogram-equalized intensity matrix;
- Convert HSI image back to RGB image.

#### 2.2.2. Feature Extraction Using Transfer Learning

**DarkNet53**is a convolutional neural network proposed as a feature extractor in YOLO3 image detection workflow [12]. It is pretrained on more than a million images from ImageNet database [33]. The pretrained network is able to classify up to 1000 categories of image objects. Details about the various layers in the DarkNet CNN architecture are shown in Table 1. The network has an input layer with a size of $256\times 256\times 3$ and is primarily made up of convolution layers with sizes of $1\times 1$ and $3\times 3$, totaling 53 layers, including the final fully connected layer but excluding the residual layer. Each convolutional layer is composed of a Conv2d layer followed by a batch normalization (BN) [34] and LeakyReLU [11] layer. The residual layer is added to solve the gradient disappearance or gradient explosion problems in the network [12]. In Darknet53, a significant reduction in parameters is achieved as compared to its previous version, i.e., Darknet19.

**DenseNet201**. This deep convolutional neural network is 201 layers deep [13]. It is also pre-trained on Imagenet [33] dataset. DenseNet is designed to overcome the vanishing gradient problem in high-level neural networks. In DenseNet, each layer receives new inputs from all preceding levels and passes on its own feature maps to all following layers. Concatenation is utilized. Each layer receives “collective knowledge” from all preceding levels. This results in a thinner and compact network that achieves a high computational efficiency and memory saving. Table 2 shows the layer details of DenseNet201.

#### 2.2.3. Feature Fusion

#### 2.2.4. Feature Selection Using Marine Predators Algorithm

- In low velocity ratio $(v<=0.1)$, the most suitable movement strategy for the MP is Lévy, whereas the prey moves in Brownian or Lévy movement;
- In unit velocity ratio $(v<=1)$, if the prey moves in Lévy, the most suitable movement for MP is Brownian;
- In high velocity ratio $(v>1)$, the best strategy for a predator is not moving at all. In this case, either prey is moving Brownian or Lévy.

**Standard MPA Methodology.**The standard MPA is an iterative, population-based optimization algorithm. The first step is to generate an initial population of solutions. The population matrix of size $n\times d$ is generated as follows:

**Phase 1:**This phase corresponds to the high velocity ratio and happens in the first ${\left(\frac{1}{3}\right)}^{rd}$ of maximum iterations of algorithm where exploration is more significant. The update rule of this phase is given as:

**Phase 2:**This phase corresponds to unit velocity ratio when predator and prey are moving at the same pace. This is the phase which occurs for intermediate ${\left(\frac{1}{3}\right)}^{rd}$ of iterations, where exploration and exploitation matters. The update rules for this phase are given as follows:

**Phase 3:**This phase corresponds to low velocity ratio when predator is moving faster than prey. This scenario happens in the last ${\left(\frac{1}{3}\right)}^{rd}$ iterations of the optimization phase where exploitation matters. The update rules for this phase are given as follows:

#### 2.2.5. Entropy-Controlled MPA for Feature Selection

**Notations:**In Algorithm 1, matrices and vectors are represented as double struck characters (e.g., $\mathbb{F}$) and scalars are represented as normal letters.

Algorithm 1: ECMPA for feature selection. |

#### 2.2.6. Classification

## 3. Results and Discussion

#### Statistical Significance

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

WBC | White blood cell |

CNN | Convolutional neural network |

DNN | Deep neural network |

SVMs | Support vector machines |

MPA | Marine predators algorithm |

ECMPA | Entropy-controlled marine predators algorithm |

KNN | K-nearest neighbors |

TPR | True positive rate |

FNR | False negative rate |

GAN | Generative adversarial network |

GVF | Gradient vector flow |

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**Figure 6.**Classification results of proposed WBCs classification system. Left: Test accuracy achieved by SVM and KNN classifiers with several kernels. Right: Confusion matrix of SVM with quadratic kernel.

Layer Type | Filters | Filter Size | Stride Size | Repeat | Output Size |
---|---|---|---|---|---|

Input | - | - | - | - | $224\times 256$ |

Convolutional | 32 | $3\times 3$ | 1 | 1 | $256\times 256$ |

Convolutional | 64 | $3\times 3$ | 2 | 1 | $128\times 128$ |

Convolutional | 32 | $1\times 1$ | 1 | 1 | |

Convolutional | 64 | $3\times 3$ | 1 | ||

Residual | $128\times 128$ | ||||

Convolutional | 128 | $3\times 3$ | 2 | 1 | $64\times 64$ |

Convolutional | 64 | $1\times 1$ | 1 | 2 | |

Convolutional | 128 | $3\times 3$ | 1 | ||

Residual | $64\times 64$ | ||||

Convolutional | 256 | $3\times 3$ | 2 | 1 | $32\times 32$ |

Convolutional | 128 | $1\times 1$ | 1 | 8 | |

Convolutional | 256 | $3\times 3$ | 1 | ||

Residual | $32\times 32$ | ||||

Convolutional | 512 | $3\times 3$ | 2 | 1 | $16\times 16$ |

Convolutional | 256 | $1\times 1$ | 1 | 8 | |

Convolutional | 512 | $3\times 3$ | 1 | ||

Residual | $16\times 16$ | ||||

Convolutional | 1024 | $3\times 3$ | 2 | 1 | $8\times 8$ |

Convolutional | 512 | $1\times 1$ | 1 | 4 | |

Convolutional | 1024 | $3\times 3$ | 1 | ||

Residual | $8\times 8$ | ||||

GlobalAvgPool | |||||

Fully Connected | 1000 | ||||

Softmax |

Layer Type | Composition | Repeat | OutSize |
---|---|---|---|

Input | – | – | $224\times 224$ |

Convolution | Conv($7\times 7$), stride 2 | $112\times 112$ | |

MaxPool | ($3\times 3$), stride 2 | $56\times 56$ | |

Dense Block 1 | Conv($1\times 1$) | 6 | |

Conv($3\times 3$ ) | $56\times 56$ | ||

Transition Layer 1 | Conv($1\times 1$) | 1 | $56\times 56$ |

Avg Pool($2\times 2$), Stride 2 | $28\times 28$ | ||

Dense Block 2 | Conv($1\times 1$) | 12 | |

Conv($3\times 3$ ) | $28\times 28$ | ||

Transition Layer 2 | Conv($1\times 1$) | 1 | $28\times 28$ |

Avg Pool($2\times 2$), Stride 2 | $14\times 14$ | ||

Dense Block 3 | Conv($1\times 1$) | 48 | |

Conv($3\times 3$ ) | $14\times 14$ | ||

Transition Layer 3 | Conv($1\times 1$) | 1 | $14\times 14$ |

Avg Pool($2\times 2$), Stride 2 | $7\times 7$ | ||

Dense Block 4 | Conv($1\times 1$) | 32 | |

Conv($3\times 3$ ) | $7\times 7$ | ||

Classification Layer | $7\times 7$ Global Avg. Pool | ||

1000D fully Connected, softmax | $1\times 1$ |

Property | Value | Property | Value |
---|---|---|---|

Kernel | sdgm | Initial Learning Rate | $1\times $${10}^{-4}$ |

Execution Environment | Auto | MiniBatch Size | 20 |

MaxEpochs | 5 | Validation Frequency | 30 |

Dropout rate | 0.1 | Stride Size | 1 |

**Table 4.**Performance Comparison of proposed method with some existing works. ×: Not done, N.A: Information not available.

Work | Deep Learning Model | Feature Selection | Feature Vector Size | Classifier | Accuracy % |
---|---|---|---|---|---|

[40] | GoogleNet, ResNet-50 | Maximal Information Coefficient, Ridge Regression Model | 755 | Quadratic Discriminant Analysis | 97.95 |

[41] | AlexNet | × | 1000 | CNN | 98.4 |

[42] | PatternNet fused ensemble of CNNs | × | N.A | CNN | 99.90 |

[43] | ResNet and Inception | Hierarchical Approach | N.A | ResNet and Inception | 99.84 |

This Work | DenseNet201 and DartkNet53 | ECMPA | 76 | SVM and KNN | 99.6 |

V-Source | SS | df | MSE | F-Statistics | p-Value |
---|---|---|---|---|---|

Between | 7.0812 $\times {10}^{-5}$ | 2 | 3.6333 $\times {10}^{-5}$ | 0.37 | 0.705 |

Within | 5.9123 $\times {10}^{-4}$ | 6 | 9.8222 $\times {10}^{-5}$ | - | - |

Total | 6.6232 $\times {10}^{-4}$ | 8 | - | - | - |

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## Share and Cite

**MDPI and ACS Style**

Ahmad, R.; Awais, M.; Kausar, N.; Akram, T.
White Blood Cells Classification Using Entropy-Controlled Deep Features Optimization. *Diagnostics* **2023**, *13*, 352.
https://doi.org/10.3390/diagnostics13030352

**AMA Style**

Ahmad R, Awais M, Kausar N, Akram T.
White Blood Cells Classification Using Entropy-Controlled Deep Features Optimization. *Diagnostics*. 2023; 13(3):352.
https://doi.org/10.3390/diagnostics13030352

**Chicago/Turabian Style**

Ahmad, Riaz, Muhammad Awais, Nabeela Kausar, and Tallha Akram.
2023. "White Blood Cells Classification Using Entropy-Controlled Deep Features Optimization" *Diagnostics* 13, no. 3: 352.
https://doi.org/10.3390/diagnostics13030352