# The Technology-Oriented Pathway for Auxiliary Diagnosis in the Digital Health Age: A Self-Adaptive Disease Prediction Model

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## Abstract

**:**

## 1. Introduction

## 2. Preparation

#### 2.1. Disease Data Description

- They are the common diseases in the real world;
- These disease data are extensively utilized by numerous investigators;
- These disease data have different internal structures and different diagnosis indicators.

#### 2.2. The Base Disease Classifier—Kernel Extreme Learning Machine

_{i}, x

_{j}) indicates the kernel function. In this paper, we adopt the Gaussian kernel function, and the kernel parameter k indicates the kernel width.

#### 2.3. The Base Optimization Tool—Sparrow Search Algorithm

^{th}sparrow individual in the d

^{th}dimensional space when the populations are carrying out the t

^{th}iteration [30], t and i indicate the current iterations and current sparrow individual, respectively. The α, R, and Random are the random parameters set manually, the ST is a warning threshold, the values of which could be set in (0.5, 1) [30]. The Matrix indicates a row vector where each element value is set to 1 and the dimensions are d [30]. Equation (5) describes the location update process of scrounger, the ${posi}_{a}^{t+1}$ indicates the optimal location searched by producer, the posi

_{worst}indicates the worst location in the current iteration [30], the n is the sparrow population size, and the V indicates a row vector where each element value is set to 1 or −1 randomly and the dimensions are d. Equation (6) describes the location update process of detection sparrow, the ${posi}_{best}^{t}$ indicates the optimal location when the populations are carrying out the t

^{th}iteration, and the β, ψ, and ξ indicate adjustment parameters [30].

#### 2.4. The Introduction of Evaluation Metrics

## 3. The Proposed Methodology

#### 3.1. Foraging Strategy of Producers in Hunger-State (PHFS)

_{max}are the parameters set manually. It is clearly shown that Equation (11) has a descending trend and will eventually converge to 0, which means the producers can easily repeat the searching behavior at a certain position with the number of individuals increasing, and eventually fall into a local optimum. By contrast, the HGS has a significant advantage in exploration ability, and the hungry feature function affecting the convergence efficiency is shown in Equation (12):

#### 3.2. Parallel Strategy for Exploration and Exploitation (EEPS)

**δ**indicates a control parameter (it is set to 2), the iter indicates the current number of iterations, and the iter_max indicates the maximum number of iterations.

#### 3.3. Perturbation–Exploration Strategy (PES)

#### 3.4. Parameter Self-Adaptive Strategy (PSAS)

Algorithm 1: MsO-KELM model |

## 4. Results

#### 4.1. Experiment 1: The Performance Analysis of EGSSA

#### 4.1.1. Performance Analysis Based on 23 Classical Benchmark Functions

#### 4.1.2. Statistical Test

#### 4.2. Experiment 2: The Prediction Analysis in Solving Different Disease Datasets

#### 4.2.1. Data Pre-Processing and Parameter Settings

#### 4.2.2. Experiment Results Analysis

## 5. Discussion

#### 5.1. Theoretical Significance

#### 5.2. Practical Significance

#### 5.3. Limitations

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The searching result figures based on Equations (11) and (12). (

**a**) searching processes based on Equation (11); (

**b**) searching processes based on Equation (12).

**Figure 3.**The comparison result figures of searching processes. (

**a**) the original searching process; (

**b**) the searching process based on after-EEPS.

**Figure 4.**The convergence curves of EGSSA and other algorithms. (

**a**) the convergence curves on F5; (

**b**) the convergence curves on F6; (

**c**) the convergence curves on F12; (

**d**) the convergence curves on F13; (

**e**) the convergence curves on F22; (

**f**) the convergence curves on F23.

**Figure 5.**The figure of evaluation metric results on Breast Cancer and Parkinson. (

**a**) the evaluation criterion result on Breast Cancer; (

**b**) the evaluation criterion result on Parkinson.

**Figure 6.**The figure of evaluation metric results on Autistic and Heart Disease. (

**a**) the evaluation criterion result on Autistic; (

**b**) the evaluation criterion result on Heart Disease.

**Figure 7.**The figure of evaluation metric results on Cleveland and Bupa. (

**a**) the evaluation criterion result on Cleveland; (

**b**) the evaluation criterion result on Bupa.

Datasets | Data Volume | Attributes | Missing Values | Positive Volume | Negative Volume |
---|---|---|---|---|---|

Breast cancer | 699 | 9 | 16 | 458 | 241 |

Heart disease | 270 | 13 | 0 | 150 | 120 |

Parkinson | 195 | 23 | 0 | 147 | 48 |

Autistic Spectrum Disorder Screening Data | 292 | 21 | 4 | 141 | 151 |

Cleveland | 303 | 13 | 4 | 139 | 164 |

Bupa | 345 | 6 | 0 | 145 | 200 |

Algorithm | Parameter Values | Reference |
---|---|---|

SSA | ST = 0.8, PD = 20%, SD = 10% | [29] |

PSO | c_{1} = 2, c_{2} = 2, V_{max} = 10 | [42] |

GWO | a = [2, 0] | [43] |

HHO | No input parameters required | [44] |

LSA | ctime = 10 | [45] |

WOA | a = [2 0], a_{2} = [−2 −1], b = 1 | [46] |

FPA | p = 0.5 | [47] |

SCACSSA | ST = 0.8, PD = 20%, SD = 10%, a = 2 | [48] |

HHOHGSO | α = 2, β = 2, K = 1, M_{1} = 0.1, M_{2} = 0.2 | [49] |

**Table 3.**Characteristics of the 23 classical benchmark functions [30].

Function | Function Equationuation | Dim | Range | Optimal | |
---|---|---|---|---|---|

Unimodal | F1 | ${f}_{1}\left(x\right)={\displaystyle \sum}_{i=1}^{n}{x}_{i}^{2}$ | 30 | [−100, 100] | 0 |

F2 | ${f}_{2}\left(x\right)={\displaystyle \sum}_{i=1}^{n}\left|{x}_{i}\right|+{\displaystyle \prod}_{i=1}^{n}\left|{x}_{i}\right|$ | 30 | [−10, 10] | 0 | |

F3 | ${f}_{3}\left(x\right)={\displaystyle \sum}_{i=1}^{n}{\left({\displaystyle \sum}_{j-1}^{i}{x}_{j}\right)}^{2}$ | 30 | [−100, 100] | 0 | |

F4 | ${f}_{4}\left(x\right)=ma{x}_{i}\left\{\left|{x}_{i}\right|,1\le i\le n\right\}$ | 30 | [−100, 100] | 0 | |

F5 | ${f}_{5}\left(x\right)={\displaystyle \sum}_{i=1}^{n-1}\left[100{\left({x}_{i+1}-{x}_{i}{}^{2}\right)}^{2}+{\left({x}_{i}-1\right)}^{2}\right]$ | 30 | [−30, 30] | 0 | |

F6 | ${f}_{6}\left(x\right)={\displaystyle \sum}_{i=1}^{n}{\left(\left[{x}_{i}+0.5\right]\right)}^{2}$ | 30 | [−100, 100] | 0 | |

F7 | ${f}_{7}\left(x\right)={\displaystyle \sum}_{i=1}^{n}i{x}_{i}^{4}+random[0,1)$ | 30 | [−1.28, 1.28] | 0 | |

Multimodal | F8 | ${f}_{8}\left(x\right)={\displaystyle \sum}_{i=1}^{n}-{x}_{i}sin\left(\sqrt{\left|{x}_{i}\right|}\right)$ | 30 | [−500, 500] | −418.9829 × 5 |

F9 | ${f}_{9}\left(x\right)={\displaystyle \sum}_{i=1}^{n}\left[{x}_{i}^{2}-10cos\left(2\pi {x}_{i}\right)+10\right]$ | 30 | [−5.12, 5.12] | 0 | |

F10 | ${f}_{10}\left(x\right)=-20exp\left(-0.2\sqrt{\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}{x}^{i}}\right)-exp\left(\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}cos\left(2\pi {x}_{i}\right)\right)+20+e$ | 30 | [−32, 32] | 0 | |

F11 | ${f}_{11}\left(x\right)=\frac{1}{4000}{\displaystyle \sum}_{i=1}^{n}{x}_{i}^{2}-{\displaystyle \prod}_{i=1}^{n}cos\left(\frac{{x}_{i}}{\sqrt{i}}\right)+1$ | 30 | [−600, 600] | 0 | |

F12 | ${f}_{12}\left(x\right)=\frac{\pi}{n}\left\{10sin\left(\pi {y}_{1}\right)+{\displaystyle \sum}_{i=1}^{n-1}{\left({y}_{i}-1\right)}^{2}\left[1+10si{n}^{2}\left(\pi {y}_{i+1}\right)\right]+{\left({y}_{n}-1\right)}^{2}\}+{\displaystyle \sum}_{i=1}^{n}\mu \left({x}_{i},10,100,4\right)\right\}$ | 30 | [−50, 50] | 0 | |

${y}_{i}=1+\frac{{x}_{i}+1}{4}$ | |||||

$\mu \left({x}_{i},a,k,m\right)=\{\begin{array}{c}k{\left({x}_{i}-a\right)}^{m}{x}_{i}a\\ 0-a{x}_{i}a\\ k{\left(-{x}_{i}-a\right)}^{m}{x}_{i}-a\end{array}$ | |||||

F13 | ${f}_{13}\left(x\right)=0.1\left\{si{n}^{2}\left(3\pi {x}_{1}\right)+{\displaystyle \sum}_{i=1}^{n}{\left({x}_{i}-1\right)}^{2}\left[1+si{n}^{2}\left(3\pi {x}_{i}+1\right)\right]+{\left({x}_{n}-1\right)}^{2}\left[1+si{n}^{2}\left(2\pi {x}_{n}\right)\right]\right\}+{\displaystyle \sum}_{i=1}^{n}\mu \left({x}_{i},5,100,4\right)$ | 30 | [−50, 50] | 0 | |

Fixed-dimension multimodal | F14 | ${f}_{14}\left(x\right)={\left(\frac{1}{500}+{\displaystyle \sum}_{j=1}^{25}\frac{1}{j+{{\displaystyle \sum}}_{i=1}^{2}{\left({x}_{i}-{a}_{ij}\right)}^{6}}\right)}^{-1}$ | 2 | [−65, 65] | 1 |

F15 | ${f}_{15}\left(x\right)={\displaystyle \sum}_{i=1}^{11}{\left[{a}_{i}-\frac{{x}_{1}\left({b}_{i}{}^{2}+{b}_{i}{x}_{2}\right)}{{b}_{i}{}^{2}+{b}_{i}{x}_{3}+{x}_{4}}\right]}^{2}$ | 4 | [−5, 5] | 0.00030 | |

F16 | ${f}_{16}\left(x\right)=4{x}_{1}{}^{2}-2.1{x}_{i}{}^{4}+\frac{1}{3}{x}_{1}{}^{6}+{x}_{1}{x}_{2}-4{x}_{2}{}^{2}+4{x}_{2}{}^{4}$ | 2 | [−5, 5] | −1.0316 | |

F17 | ${f}_{17}\left(x\right)={\left({x}_{2}-\frac{5.1}{4{\pi}^{2}}{x}_{1}{}^{2}+\frac{5}{\pi}{x}_{1}-6\right)}^{2}+10\left(1-\frac{1}{8\pi}\right)cos{x}_{1}+10$ | 2 | [−5, 5] | 0.398 | |

F18 | ${f}_{18}\left(x\right)=\left[1+{\left({x}_{1}+{x}_{2}+1\right)}^{2}\left(19-14{x}_{1}+3{x}_{1}{}^{2}-14{x}_{2}+6{x}_{1}{x}_{2}+3{x}_{2}{}^{2}\right)\right]\times \left[30+{\left(2{x}_{1}-3{x}_{2}\right)}^{2}\times \left(18-32{x}_{1}+12{x}_{1}{}^{2}+48{x}_{2}-36{x}_{1}{x}_{2}+27{x}_{2}{}^{2}\right)\right]$ | 2 | [−2, 2] | 3 | |

F19 | ${f}_{19}\left(x\right)=-{\displaystyle \sum}_{i=1}^{4}{c}_{i}exp\left(-{\displaystyle \sum}_{j=1}^{3}{a}_{ij}{\left({x}_{i}-{p}_{ij}\right)}^{2}\right)$ | 3 | [1, 3] | −3.86 | |

F20 | ${f}_{20}\left(x\right)=-{\displaystyle \sum}_{i=1}^{4}{c}_{i}exp\left(-{\displaystyle \sum}_{j=1}^{6}{a}_{ij}{\left({x}_{i}-{p}_{ij}\right)}^{2}\right)$ | 6 | [0, 1] | −3.32 | |

F21 | ${f}_{21}\left(x\right)=-{\displaystyle \sum}_{i=1}^{5}{\left[\left(X-{a}_{i}\right){\left(X-{a}_{i}\right)}^{T}+{c}_{i}\right]}^{-1}$ | 4 | [0, 10] | −10.1532 | |

F22 | ${f}_{22}\left(x\right)=-{\displaystyle \sum}_{i=1}^{7}{\left[\left(X-{a}_{i}\right){\left(X-{a}_{i}\right)}^{T}+{c}_{i}\right]}^{-1}$ | 4 | [0, 10] | −10.4028 | |

F23 | ${f}_{23}\left(x\right)=-{\displaystyle \sum}_{i=1}^{10}{\left[\left(X-{a}_{i}\right){\left(X-{a}_{i}\right)}^{T}+{c}_{i}\right]}^{-1}$ | 4 | [0, 10] | −10.5363 |

EGSSA | SSA | PSO | GWO | HHO | LSA | WOA | FPA | SCACSSA | HHOHGSO | ||
---|---|---|---|---|---|---|---|---|---|---|---|

F1 | avg | 0.00 × 10^{00} | 1.30 × 10^{−49} | 6.25 × 10^{−01} | 1.19 × 10^{−27} | 1.61 × 10^{−93} | 1.11 × 10^{−03} | 7.15 × 10^{−72} | 4.60 × 10^{−01} | 6.17 × 10^{−16} | 5.82 × 10^{−268} |

std | 0.00 × 10^{00} | 7.11 × 10^{−49} | 3.36 × 10^{−01} | 1.64 × 10^{−27} | 8.22 × 10^{−93} | 5.93 × 10^{−03} | 3.90 × 10^{−71} | 1.39 × 10^{−01} | 3.35 × 10^{−15} | 0.00 × 10^{00} | |

F2 | avg | 0.00 × 10^{00} | 5.36 × 10^{−27} | 3.26 × 10^{01} | 1.28 × 10^{−16} | 2.34 × 10^{−48} | 2.48 × 10^{−01} | 9.69 × 10^{−51} | 2.80 × 10^{00} | 1.53 × 10^{−07} | 9.93 × 10^{−160} |

std | 0.00 × 10^{00} | 2.90 × 10^{−26} | 5.50 × 10^{01} | 1.32 × 10^{−16} | 1.25 × 10^{−47} | 3.80 × 10^{−01} | 4.84 × 10^{−50} | 3.64 × 10^{−01} | 6.56 × 10^{−07} | 5.44 × 10^{−159} | |

F3 | avg | 0.00 × 10^{00} | 2.61 × 10^{−29} | 3.37 × 10^{02} | 1.43 × 10^{−05} | 7.32 × 10^{−64} | 1.37 × 10^{02} | 4.99 × 10^{04} | 3.28 × 10^{−01} | 1.76 × 10^{−08} | 2.17 × 10^{−309} |

std | 0.00 × 10^{00} | 1.18 × 10^{−28} | 9.30 × 10^{01} | 3.34 × 10^{−05} | 4.01 × 10^{−63} | 8.69 × 10^{01} | 1.66 × 10^{04} | 1.02 × 10^{−01} | 5.08 × 10^{−08} | 0.00 × 10^{00} | |

F4 | avg | 0.00 × 10^{00} | 3.66 × 10^{−26} | 2.77 × 10^{00} | 7.27 × 10^{−07} | 9.66 × 10^{−49} | 9.62 × 10^{00} | 5.04 × 10^{01} | 3.67 × 10^{−01} | 9.26 × 10^{−26} | 5.81 × 10^{−147} |

std | 0.00 × 10^{00} | 1.99 × 10^{−25} | 4.30 × 10^{−01} | 1.06 × 10^{−06} | 4.89 × 10^{−48} | 4.25 × 10^{00} | 2.86 × 10^{01} | 4.42 × 10^{−02} | 4.86 × 10^{−25} | 3.18 × 10^{−146} | |

F5 | avg | 2.56 × 10^{−02} | 4.61 × 10^{−01} | 6.55 × 10^{02} | 2.73 × 10^{01} | 1.01 × 10^{−02} | 1.21 × 10^{02} | 2.80 × 10^{01} | 7.96 × 10^{01} | 1.03 × 10^{00} | 2.73 × 10^{01} |

std | 9.08 × 10^{−02} | 7.42 × 10^{−01} | 4.83 × 10^{02} | 8.13 × 10^{−01} | 9.64 × 10^{−03} | 1.84 × 10^{02} | 4.42 × 10^{−01} | 1.81 × 10^{01} | 1.56 × 10^{00} | 6.72 × 10^{−01} | |

F6 | avg | 9.24 × 10^{−06} | 3.05 × 10^{−02} | 6.67 × 10^{−01} | 6.92 × 10^{−01} | 2.90 × 10^{−04} | 7.36 × 10^{−05} | 3.94 × 10^{−01} | 1.23 × 10^{00} | 2.35 × 10^{−02} | 1.13 × 10^{−03} |

std | 1.38 × 10^{−05} | 1.64 × 10^{−02} | 3.37 × 10^{−01} | 3.65 × 10^{−01} | 6.00 × 10^{−04} | 3.71 × 10^{−04} | 2.32 × 10^{−01} | 3.99 × 10^{−01} | 1.14 × 10^{−02} | 1.27 × 10^{−03} | |

F7 | avg | 1.11 × 10^{−04} | 7.70 × 10^{−04} | 2.52 × 10^{00} | 2.25 × 10^{−03} | 1.90 × 10^{−04} | 3.05 × 10^{−02} | 3.59 × 10^{−03} | 5.52 × 10^{−01} | 6.41 × 10^{−02} | 9.76 × 10^{−05} |

std | 1.46 × 10^{−04} | 6.79 × 10^{−04} | 2.80 × 10^{00} | 1.12 × 10^{−03} | 2.11 × 10^{−04} | 8.45 × 10^{−03} | 5.59 × 10^{−03} | 2.76 × 10^{−01} | 5.67 × 10^{−02} | 9.71 × 10^{−05} | |

F8 | avg | −8.10 × 10^{03} | −7.79 × 10^{03} | −6.63 × 10^{03} | −5.89 × 10^{03} | −1.26 × 10^{04} | −7.57 × 10^{03} | −1.02 × 10^{04} | −4.26 × 10^{01} | −6.04 × 10^{03} | −1.13 × 10^{04} |

std | 2.23 × 10^{03} | 3.03 × 10^{03} | 7.63 × 10^{02} | 1.07 × 10^{03} | 1.40 × 10^{00} | 7.48 × 10^{02} | 1.70 × 10^{03} | 2.65 × 10^{00} | 7.52 × 10^{02} | 1.19 × 10^{03} | |

F9 | avg | 0.00 × 10^{00} | 0.00 × 10^{00} | 1.43 × 10^{02} | 1.92 × 10^{00} | 0.00 × 10^{00} | 6.92 × 10^{01} | 0.00 × 10^{00} | 4.22 × 10^{01} | 3.46 × 10^{−10} | 0.00 × 10^{00} |

std | 0.00 × 10^{00} | 0.00 × 10^{00} | 3.74 × 10^{01} | 3.27 × 10^{00} | 0.00 × 10^{00} | 1.60 × 10^{01} | 0.00 × 10^{00} | 1.93 × 10^{01} | 1.53 × 10^{−09} | 0.00 × 10^{00} | |

F10 | avg | 8.88 × 10^{−16} | 8.88 × 10^{−16} | 1.85 × 10^{00} | 1.04 × 10^{−13} | 8.88 × 10^{−16} | 2.90 × 10^{00} | 3.85 × 10^{−15} | 1.38 × 10^{00} | 2.35 × 10^{−07} | 8.88 × 10^{−16} |

std | 0.00 × 10^{00} | 0.00 × 10^{00} | 7.06 × 10^{−01} | 1.83 × 10^{−14} | 0.00 × 10^{00} | 8.34 × 10^{−01} | 2.30 × 10^{−15} | 2.31 × 10^{−01} | 1.28 × 10^{−06} | 0.00 × 10^{00} | |

F11 | avg | 0.00 × 10^{00} | 0.00 × 10^{00} | 6.22 × 10^{−02} | 4.49 × 10^{−03} | 0.00 × 10^{00} | 7.22 × 10^{−03} | 5.86 × 10^{−03} | 1.66 × 10^{−02} | 3.20 × 10^{−11} | 0.00 × 10^{00} |

std | 0.00 × 10^{00} | 0.00 × 10^{00} | 4.06 × 10^{−02} | 8.49 × 10^{−03} | 0.00 × 10^{00} | 1.09 × 10^{−02} | 3.21 × 10^{−02} | 5.72 × 10^{−03} | 1.76 × 10^{−10} | 0.00 × 10^{00} | |

F12 | avg | 1.43 × 10^{−07} | 1.00 × 10^{−02} | 1.17 × 10^{00} | 3.97 × 10^{−02} | 1.01 × 10^{−05} | 6.76 × 10^{−01} | 2.70 × 10^{−02} | 6.34 × 10^{−02} | 2.15 × 10^{−03} | 1.00 × 10^{−04} |

std | 1.18 × 10^{−07} | 3.16 × 10^{−02} | 2.30 × 10^{00} | 1.49 × 10^{−02} | 1.27 × 10^{−05} | 1.41 × 10^{00} | 1.61 × 10^{−02} | 2.52 × 10^{−02} | 1.27 × 10^{−03} | 8.86 × 10^{−05} | |

F13 | avg | 6.36 × 10^{−05} | 2.53 × 10^{−01} | 4.69 × 10^{−01} | 7.10 × 10^{−01} | 8.67 × 10^{−05} | 6.36 × 10^{−02} | 5.62 × 10^{−01} | 1.07 × 10^{00} | 1.41 × 10^{−01} | 1.88 × 10^{−02} |

std | 1.74 × 10^{−04} | 1.31 × 10^{−01} | 3.07 × 10^{−01} | 2.93 × 10^{−01} | 1.02 × 10^{−04} | 1.32 × 10^{−01} | 3.28 × 10^{−01} | 3.07 × 10^{−01} | 1.06 × 10^{−01} | 1.72 × 10^{−02} | |

F14 | avg | 9.95 × 10^{00} | 1.09 × 10^{01} | 3.33 × 10^{00} | 4.52 × 10^{00} | 1.26 × 10^{00} | 1.36 × 10^{00} | 3.00 × 10^{00} | 1.27 × 10^{01} | 1.27 × 10^{01} | 1.03 × 10^{00} |

std | 4.04 × 10^{00} | 3.83 × 10^{00} | 2.81 × 10^{00} | 4.22 × 10^{00} | 9.32 × 10^{−01} | 1.02 × 10^{00} | 3.06 × 10^{00} | 1.34 × 10^{−14} | 9.61 × 10^{−11} | 1.81 × 10^{−01} | |

F15 | avg | 3.58 × 10^{−04} | 4.79 × 10^{−04} | 8.90 × 10^{−04} | 3.05 × 10^{−03} | 3.81 × 10^{−04} | 5.94 × 10^{−04} | 1.17 × 10^{−03} | 3.08 × 10^{−04} | 4.85 × 10^{−04} | 4.08 × 10^{−04} |

std | 8.86 × 10^{−05} | 1.46 × 10^{−04} | 1.33 × 10^{−04} | 6.91 × 10^{−03} | 2.13 × 10^{−04} | 3.25 × 10^{−04} | 2.43 × 10^{−03} | 1.19 × 10^{−06} | 2.36 × 10^{−04} | 2.40 × 10^{−04} | |

F16 | avg | −1.03 × 10^{00} | −1.03 × 10^{00} | −1.03 × 10^{00} | −1.03 × 10^{00} | −1.03 × 10^{00} | −1.03 × 10^{00} | −1.03 × 10^{00} | −1.03 × 10^{00} | −1.03 × 10^{00} | −1.03 × 10^{00} |

std | 3.00 × 10^{−10} | 4.74 × 10^{−16} | 5.30 × 10^{−16} | 1.45 × 10^{−08} | 3.95 × 10^{−10} | 6.58 × 10^{−16} | 9.97 × 10^{−10} | 1.53 × 10^{−09} | 2.47 × 10^{−03} | 7.54 × 10^{−13} | |

F17 | avg | 3.98 × 10^{−01} | 3.98 × 10^{−01} | 3.98 × 10^{−01} | 3.98 × 10^{−01} | 3.98 × 10^{−01} | 3.98 × 10^{−01} | 3.98 × 10^{−01} | 7.78 × 10^{00} | 3.98 × 10^{−01} | 3.98 × 10^{−01} |

std | 2.09 × 10^{−04} | 8.68 × 10^{−09} | 0.00 × 10^{00} | 6.52 × 10^{−07} | 2.87 × 10^{−06} | 0.00 × 10^{00} | 1.26 × 10^{−05} | 2.71 × 10^{−15} | 1.23 × 10^{−06} | 2.63 × 10^{−10} | |

F18 | avg | 3.00 × 10^{00} | 3.00 × 10^{00} | 3.00 × 10^{00} | 3.00 × 10^{00} | 3.00 × 10^{00} | 3.00 × 10^{00} | 3.00 × 10^{00} | 3.00 × 10^{00} | 3.00 × 10^{00} | 3.00 × 10^{00} |

std | 2.85 × 10^{−05} | 9.65 × 10^{−15} | 4.41 × 10^{−15} | 4.39 × 10^{−05} | 3.54 × 10^{−07} | 2.56 × 10^{−15} | 9.64 × 10^{−05} | 2.14 × 10^{−10} | 6.60 × 10^{−04} | 1.03 × 10^{−11} | |

F19 | avg | −3.86 × 10^{00} | −3.86 × 10^{00} | −3.86 × 10^{00} | −3.86 × 10^{00} | −3.86 × 10^{00} | −3.86 × 10^{00} | −3.86 × 10^{00} | −3.86 × 10^{00} | −3.86 × 10^{00} | −3.86 × 10^{00} |

std | 1.36 × 10^{−04} | 2.46 × 10^{−05} | 2.36 × 10^{−15} | 1.91 × 10^{−03} | 5.19 × 10^{−03} | 2.67 × 10^{−15} | 7.91 × 10^{−03} | 6.33 × 10^{−09} | 2.77 × 10^{−05} | 1.09 × 10^{−05} | |

F20 | avg | −3.29 × 10^{00} | −3.26 × 10^{00} | −3.27 × 10^{00} | −3.27 × 10^{00} | −3.07 × 10^{00} | −3.27 × 10^{00} | −3.20 × 10^{00} | −3.28 × 10^{00} | −3.25 × 10^{00} | −3.25 × 10^{00} |

std | 5.33 × 10^{−02} | 6.84 × 10^{−02} | 6.03 × 10^{−02} | 7.31 × 10^{−02} | 1.26 × 10^{−01} | 5.92 × 10^{−02} | 1.56 × 10^{−01} | 3.26 × 10^{−02} | 6.29 × 10^{−02} | 8.31 × 10^{−02} | |

F21 | avg | −9.85 × 10^{00} | −8.24 × 10^{00} | −7.14 × 10^{00} | −9.31 × 10^{00} | −5.21 × 10^{00} | −7.72 × 10^{00} | −8.65 × 10^{00} | −5.06 × 10^{00} | −8.79 × 10^{00} | −6.58 × 10^{00} |

std | 5.45 × 10^{−01} | 2.46 × 10^{00} | 3.38 × 10^{00} | 1.92 × 10^{00} | 8.73 × 10^{−01} | 3.13 × 10^{00} | 2.85 × 10^{00} | 2.94 × 10^{−07} | 2.29 × 10^{00} | 2.38 × 10^{00} | |

F22 | avg | −1.02 × 10^{01} | −9.16 × 10^{00} | −6.19 × 10^{00} | −1.02 × 10^{01} | −5.23 × 10^{00} | −8.11 × 10^{00} | −6.97 × 10^{00} | −5.09 × 10^{00} | −8.81 × 10^{00} | −6.68 × 10^{00} |

std | 4.27 × 10^{−01} | 2.29 × 10^{00} | 3.39 × 10^{00} | 9.70 × 10^{−01} | 8.01 × 10^{−01} | 3.34 × 10^{00} | 3.36 × 10^{00} | 2.36 × 10^{−07} | 2.48 × 10^{00} | 2.48 × 10^{00} | |

F23 | avg | −1.02 × 10^{01} | −8.73 × 10^{00} | −8.59 × 10^{00} | −1.01 × 10^{01} | −5.48 × 10^{00} | −7.27 × 10^{00} | −6.77 × 10^{00} | −5.13 × 10^{00} | −9.64 × 10^{00} | −6.39 × 10^{00} |

std | 7.11 × 10^{−01} | 2.59 × 10^{00} | 3.34 × 10^{00} | 1.75 × 10^{00} | 1.34 × 10^{00} | 3.85 × 10^{00} | 3.23 × 10^{00} | 3.42 × 10^{−07} | 2.05 × 10^{00} | 2.33 × 10^{00} |

Algorithm | Better | Equationual | Worst | W+ | W− | p-Value |
---|---|---|---|---|---|---|

EGSSA versus SSA | 16 | 7 | 0 | 136 | 0 | 0.000438 |

EGSSA versus PSO | 18 | 4 | 1 | 176 | 14 | 0.001116 |

EGSSA versus GWO | 17 | 5 | 1 | 155 | 16 | 0.002472 |

EGSSA versus HHO | 13 | 7 | 3 | 95 | 41 | 0.162673 |

EGSSA versus LSA | 18 | 4 | 1 | 176 | 14 | 0.001116 |

EGSSA versus WOA | 16 | 5 | 2 | 140 | 31 | 0.017621 |

EGSSA versus FPA | 19 | 3 | 1 | 209 | 1 | 0.000103 |

EGSSA versus SCACSSA | 19 | 4 | 0 | 190 | 0 | 0.000132 |

EGSSA versus HHOHGSO | 12 | 8 | 3 | 88 | 32 | 0.111769 |

Breast Cancer | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Indicator | Algorithms | Mean | Std | 1# | 2# | 3# | 4# | 5# | 6# | 7# | 8# | 9# | 10# |

ACC | GWO-KELM | 0.93695 | 0.03847 | 0.86765 | 0.95588 | 0.95588 | 0.97059 | 0.92647 | 0.86765 | 0.92647 | 0.98529 | 0.95588 | 0.95775 |

HHO-KELM | 0.92237 | 0.04657 | 0.83824 | 0.92647 | 0.94118 | 0.97059 | 0.95588 | 0.85294 | 0.88235 | 0.98529 | 0.94118 | 0.92958 | |

FPA-KELM | 0.92531 | 0.04580 | 0.85294 | 0.92647 | 0.94118 | 0.98529 | 0.95588 | 0.85294 | 0.88235 | 0.98529 | 0.94118 | 0.92958 | |

WOA-KELM | 0.92237 | 0.04657 | 0.83824 | 0.92647 | 0.94118 | 0.97059 | 0.95588 | 0.85294 | 0.88235 | 0.98529 | 0.94118 | 0.92958 | |

SSA-KELM | 0.92237 | 0.04657 | 0.83824 | 0.92647 | 0.94118 | 0.97059 | 0.95588 | 0.85294 | 0.88235 | 0.98529 | 0.94118 | 0.92958 | |

MsO-KELM | 0.94124 | 0.03785 | 0.85294 | 0.95588 | 0.95588 | 0.97059 | 0.92647 | 0.89706 | 0.94118 | 0.95588 | 0.97059 | 0.98592 | |

Sensitivity | GWO-KELM | 0.92628 | 0.06586 | 0.79412 | 0.92593 | 0.92308 | 1.00000 | 0.96970 | 1.00000 | 0.89474 | 1.00000 | 0.90909 | 0.84615 |

HHO-KELM | 0.88751 | 0.11278 | 0.73529 | 0.92593 | 0.92308 | 0.97368 | 1.00000 | 1.00000 | 0.68421 | 1.00000 | 0.86364 | 0.76923 | |

FPA-KELM | 0.88539 | 0.12182 | 0.76471 | 0.92593 | 0.92308 | 1.00000 | 1.00000 | 1.00000 | 0.68421 | 1.00000 | 0.86364 | 0.69231 | |

WOA-KELM | 0.88751 | 0.11278 | 0.73529 | 0.92593 | 0.92308 | 0.97368 | 1.00000 | 1.00000 | 0.68421 | 1.00000 | 0.86364 | 0.76923 | |

SSA-KELM | 0.88751 | 0.11278 | 0.73529 | 0.92593 | 0.92308 | 0.97368 | 1.00000 | 1.00000 | 0.68421 | 1.00000 | 0.86364 | 0.76923 | |

MsO-KELM | 0.94434 | 0.06814 | 0.76471 | 0.96296 | 0.92308 | 0.97368 | 0.9697 | 1.00000 | 0.89474 | 1.00000 | 0.95455 | 1.00000 | |

Specificity | GWO-KELM | 0.94212 | 0.04838 | 0.94118 | 0.97561 | 0.97619 | 0.93333 | 0.88571 | 0.82692 | 0.93878 | 0.98246 | 0.97826 | 0.98276 |

HHO-KELM | 0.93944 | 0.04847 | 0.94118 | 0.92683 | 0.95238 | 0.96667 | 0.91429 | 0.80769 | 0.95918 | 0.98246 | 0.97826 | 0.96552 | |

FPA-KELM | 0.94117 | 0.04965 | 0.94118 | 0.92683 | 0.95238 | 0.96667 | 0.91429 | 0.80769 | 0.95918 | 0.98246 | 0.97826 | 0.98276 | |

WOA-KELM | 0.93944 | 0.04847 | 0.94118 | 0.92683 | 0.95238 | 0.96667 | 0.91429 | 0.80769 | 0.95918 | 0.98246 | 0.97826 | 0.96552 | |

SSA-KELM | 0.93944 | 0.04847 | 0.94118 | 0.92683 | 0.95238 | 0.96667 | 0.91429 | 0.80769 | 0.95918 | 0.98246 | 0.97826 | 0.96552 | |

MsO-KELM | 0.94539 | 0.03753 | 0.94118 | 0.95122 | 0.97619 | 0.96667 | 0.88571 | 0.86538 | 0.95918 | 0.94737 | 0.97826 | 0.98276 | |

MCC | GWO-KELM | 0.86068 | 0.07295 | 0.74338 | 0.90771 | 0.90635 | 0.94163 | 0.85652 | 0.72748 | 0.82083 | 0.94899 | 0.89852 | 0.85542 |

HHO-KELM | 0.82433 | 0.09736 | 0.69128 | 0.84779 | 0.87546 | 0.94035 | 0.91548 | 0.70501 | 0.69626 | 0.94899 | 0.86440 | 0.75824 | |

FPA-KELM | 0.82916 | 0.09867 | 0.71714 | 0.84779 | 0.87546 | 0.97051 | 0.91548 | 0.70501 | 0.69626 | 0.94899 | 0.86440 | 0.75053 | |

WOA-KELM | 0.82433 | 0.09736 | 0.69128 | 0.84779 | 0.87546 | 0.94035 | 0.91548 | 0.70501 | 0.69626 | 0.94899 | 0.86440 | 0.75824 | |

SSA-KELM | 0.82433 | 0.09736 | 0.69128 | 0.84779 | 0.87546 | 0.94035 | 0.91548 | 0.70501 | 0.69626 | 0.94899 | 0.86440 | 0.75824 | |

MsO-KELM | 0.87099 | 0.071906 | 0.71714 | 0.90886 | 0.90635 | 0.94035 | 0.85652 | 0.77589 | 0.85392 | 0.86276 | 0.93281 | 0.95528 |

Parkinson | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Indicator | Algorithms | Mean | Std | 1# | 2# | 3# | 4# | 5# | 6# | 7# | 8# | 9# | 10# |

ACC | GWO-KELM | 0.81000 | 0.06633 | 0.75000 | 0.75000 | 0.80000 | 0.75000 | 0.90000 | 0.85000 | 0.80000 | 0.95000 | 0.75000 | 0.80000 |

HHO-KELM | 0.82667 | 0.08206 | 0.80000 | 0.65000 | 0.80000 | 0.95000 | 0.85000 | 0.80000 | 0.90000 | 0.75000 | 0.90000 | 0.86667 | |

FPA-KELM | 0.82833 | 0.06103 | 0.75000 | 0.80000 | 0.90000 | 0.75000 | 0.80000 | 0.80000 | 0.80000 | 0.85000 | 0.90000 | 0.93333 | |

WOA-KELM | 0.81667 | 0.05164 | 0.85000 | 0.85000 | 0.80000 | 0.80000 | 0.85000 | 0.75000 | 0.85000 | 0.85000 | 0.70000 | 0.86667 | |

SSA-KELM | 0.80333 | 0.08021 | 0.90000 | 0.85000 | 0.90000 | 0.65000 | 0.85000 | 0.70000 | 0.80000 | 0.85000 | 0.80000 | 0.73333 | |

MsO-KELM | 0.84167 | 0.07042 | 0.85000 | 0.95000 | 0.85000 | 0.90000 | 0.75000 | 0.85000 | 0.70000 | 0.80000 | 0.90000 | 0.86667 | |

Sensitivity | GWO-KELM | 0.85991 | 0.09367 | 0.75000 | 0.75000 | 0.84615 | 0.76471 | 1.00000 | 0.92308 | 0.78571 | 1.00000 | 0.93333 | 0.84615 |

HHO-KELM | 0.88423 | 0.10233 | 0.88235 | 0.80000 | 0.76471 | 1.00000 | 0.93333 | 0.92857 | 0.93333 | 0.66667 | 0.93333 | 1.00000 | |

FPA-KELM | 0.88071 | 0.09250 | 0.76923 | 0.81250 | 0.92857 | 0.70588 | 0.87500 | 0.92857 | 0.84615 | 0.94118 | 1.00000 | 1.00000 | |

WOA-KELM | 0.86809 | 0.10697 | 0.93750 | 0.82353 | 1.00000 | 0.69231 | 0.92857 | 0.81250 | 1.00000 | 0.88235 | 0.68750 | 0.91667 | |

SSA-KELM | 0.86521 | 0.10720 | 0.93750 | 1.00000 | 0.93750 | 0.66667 | 0.93750 | 0.73333 | 0.93750 | 0.92857 | 0.82353 | 0.75000 | |

MsO-KELM | 0.89596 | 0.068495 | 0.87500 | 0.93333 | 0.84615 | 0.88889 | 0.80000 | 0.87500 | 0.80000 | 1.00000 | 0.94118 | 1.00000 | |

Specificity | GWO-KELM | 0.65286 | 0.17666 | 0.75000 | 0.75000 | 0.71429 | 0.66667 | 0.60000 | 0.71429 | 0.83333 | 0.80000 | 0.20000 | 0.50000 |

HHO-KELM | 0.64417 | 0.27719 | 0.33333 | 0.20000 | 1.00000 | 0.87500 | 0.60000 | 0.50000 | 0.80000 | 1.00000 | 0.80000 | 0.33333 | |

FPA-KELM | 0.65119 | 0.18505 | 0.71429 | 0.75000 | 0.83333 | 1.00000 | 0.50000 | 0.50000 | 0.71429 | 0.33333 | 0.66667 | 0.50000 | |

WOA-KELM | 0.67500 | 0.18703 | 0.50000 | 1.00000 | 0.42857 | 1.00000 | 0.66667 | 0.50000 | 0.57143 | 0.66667 | 0.75000 | 0.66667 | |

SSA-KELM | 0.61500 | 0.14092 | 0.75000 | 0.70000 | 0.75000 | 0.60000 | 0.50000 | 0.60000 | 0.25000 | 0.66667 | 0.66667 | 0.66667 | |

MsO-KELM | 0.67571 | 0.24685 | 0.75000 | 1.00000 | 0.85714 | 1.00000 | 0.60000 | 0.75000 | 0.60000 | 0.20000 | 0.66667 | 0.33333 | |

MCC | GWO-KELM | 0.50579 | 0.19972 | 0.41931 | 0.41931 | 0.56044 | 0.33612 | 0.72761 | 0.66339 | 0.57907 | 0.86603 | 0.19245 | 0.29417 |

HHO-KELM | 0.53338 | 0.24618 | 0.21569 | 0.00000 | 0.57248 | 0.89872 | 0.57735 | 0.49099 | 0.73333 | 0.57735 | 0.73333 | 0.53452 | |

FPA-KELM | 0.54365 | 0.14232 | 0.47076 | 0.49099 | 0.76190 | 0.51450 | 0.37500 | 0.49099 | 0.56044 | 0.32673 | 0.76376 | 0.68139 | |

WOA-KELM | 0.53987 | 0.12579 | 0.49010 | 0.64169 | 0.57248 | 0.66375 | 0.62994 | 0.28868 | 0.68139 | 0.49010 | 0.35722 | 0.58333 | |

SSA-KELM | 0.47749 | 0.18407 | 0.68750 | 0.73380 | 0.68750 | 0.23570 | 0.49010 | 0.30261 | 0.25000 | 0.62994 | 0.40423 | 0.35355 | |

MsO-KELM | 0.57140 | 0.14677 | 0.57735 | 0.88192 | 0.68474 | 0.66667 | 0.37796 | 0.57735 | 0.40825 | 0.39736 | 0.60784 | 0.53452 |

**Table 8.**The prediction results on disease dataset Autistic Spectrum Disorder Screening Data for Children.

Autistic Spectrum Disorder Screening Data for Children | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Indicator | Algorithms | Mean | Std | 1# | 2# | 3# | 4# | 5# | 6# | 7# | 8# | 9# | 10# |

ACC | GWO-KELM | 0.88665 | 0.04423 | 0.89655 | 0.93103 | 0.89655 | 0.82759 | 0.86207 | 0.89655 | 0.93103 | 0.79310 | 0.89655 | 0.93548 |

HHO-KELM | 0.88643 | 0.04925 | 0.89655 | 0.89655 | 0.82759 | 0.93103 | 0.86207 | 0.86207 | 0.79310 | 0.89655 | 0.93103 | 0.96774 | |

FPA-KELM | 0.89377 | 0.06262 | 0.86207 | 0.93103 | 0.82759 | 0.79310 | 0.93103 | 1.00000 | 0.96552 | 0.89655 | 0.82759 | 0.90323 | |

WOA-KELM | 0.89422 | 0.05088 | 0.96552 | 0.89655 | 0.86207 | 0.89655 | 0.93103 | 0.89655 | 0.89655 | 0.96552 | 0.79310 | 0.83871 | |

SSA-KELM | 0.84917 | 0.05838 | 0.86207 | 0.93103 | 0.79310 | 0.96552 | 0.82759 | 0.79310 | 0.79310 | 0.86207 | 0.79310 | 0.87097 | |

MsO-KELM | 0.91079 | 0.05621 | 0.89655 | 0.96552 | 0.89655 | 0.93103 | 0.96552 | 0.93103 | 0.93103 | 0.75862 | 0.89655 | 0.93548 | |

Sensitivity | GWO-KELM | 0.98606 | 0.02807 | 1.00000 | 0.92308 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 0.93750 | 1.00000 | 1.00000 |

HHO-KELM | 0.91786 | 0.08472 | 0.93750 | 0.92857 | 0.80000 | 1.00000 | 0.78947 | 0.92308 | 0.80000 | 1.00000 | 1.00000 | 1.00000 | |

FPA-KELM | 0.98619 | 0.02764 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 0.92857 | 1.00000 | 1.00000 | 1.00000 | 0.93333 | 1.00000 | |

WOA-KELM | 0.91246 | 0.08829 | 0.93750 | 0.92857 | 0.90909 | 0.93333 | 1.00000 | 0.86667 | 0.85714 | 1.00000 | 0.69231 | 1.00000 | |

SSA-KELM | 0.84079 | 0.09657 | 0.83333 | 1.00000 | 0.72222 | 1.00000 | 0.87500 | 0.71429 | 0.75000 | 0.81250 | 0.81818 | 0.88235 | |

MsO-KELM | 0.98424 | 0.03198 | 0.90909 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 0.93333 | |

Specificity | GWO-KELM | 0.78695 | 0.09798 | 0.82353 | 0.93750 | 0.78571 | 0.64286 | 0.71429 | 0.76923 | 0.86667 | 0.61538 | 0.85714 | 0.85714 |

HHO-KELM | 0.86932 | 0.05986 | 0.84615 | 0.86667 | 0.85714 | 0.87500 | 1.00000 | 0.81250 | 0.78571 | 0.83333 | 0.86667 | 0.95000 | |

FPA-KELM | 0.80771 | 0.10983 | 0.77778 | 0.84615 | 0.70588 | 0.64706 | 0.93333 | 1.00000 | 0.93333 | 0.75000 | 0.71429 | 0.76923 | |

WOA-KELM | 0.87851 | 0.07869 | 1.00000 | 0.86667 | 0.83333 | 0.85714 | 0.87500 | 0.92857 | 0.93333 | 0.92857 | 0.87500 | 0.68750 | |

SSA-KELM | 0.86322 | 0.05392 | 0.88235 | 0.89474 | 0.90909 | 0.92857 | 0.76923 | 0.86667 | 0.82353 | 0.92308 | 0.77778 | 0.85714 | |

MsO-KELM | 0.83379 | 0.11179 | 0.88889 | 0.93333 | 0.83333 | 0.88889 | 0.93333 | 0.83333 | 0.71429 | 0.56250 | 0.81250 | 0.93750 | |

MCC | GWO-KELM | 0.78620 | 0.08291 | 0.81168 | 0.86058 | 0.80917 | 0.69437 | 0.75094 | 0.80484 | 0.87082 | 0.59433 | 0.78954 | 0.87574 |

HHO-KELM | 0.77964 | 0.09857 | 0.79130 | 0.79524 | 0.65714 | 0.87082 | 0.75094 | 0.73207 | 0.58571 | 0.80917 | 0.87082 | 0.93318 | |

FPA-KELM | 0.80578 | 0.10725 | 0.75523 | 0.86726 | 0.70588 | 0.65679 | 0.86190 | 1.00000 | 0.93333 | 0.79844 | 0.66696 | 0.81200 | |

WOA-KELM | 0.79398 | 0.10018 | 0.93303 | 0.79524 | 0.72436 | 0.79427 | 0.87082 | 0.79524 | 0.79427 | 0.93303 | 0.58146 | 0.71807 | |

SSA-KELM | 0.69917 | 0.11668 | 0.71569 | 0.86349 | 0.61301 | 0.93303 | 0.65052 | 0.58943 | 0.57353 | 0.73207 | 0.58146 | 0.73950 | |

MsO-KELM | 0.82899 | 0.08910 | 0.78616 | 0.93333 | 0.80917 | 0.86726 | 0.93333 | 0.86349 | 0.80917 | 0.60467 | 0.81250 | 0.87083 |

Heart Disease | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Indicator | Algorithms | Mean | Std | 1# | 2# | 3# | 4# | 5# | 6# | 7# | 8# | 9# | 10# |

ACC | GWO-KELM | 0.69630 | 0.08733 | 0.66667 | 0.59259 | 0.81481 | 0.70370 | 0.70370 | 0.59259 | 0.66667 | 0.81481 | 0.81481 | 0.59259 |

HHO-KELM | 0.69259 | 0.08772 | 0.66667 | 0.59259 | 0.85185 | 0.66667 | 0.70370 | 0.59259 | 0.66667 | 0.81481 | 0.81481 | 0.59259 | |

FPA-KELM | 0.70741 | 0.07115 | 0.70370 | 0.66667 | 0.77778 | 0.70370 | 0.74074 | 0.66667 | 0.66667 | 0.81481 | 0.77778 | 0.55556 | |

WOA-KELM | 0.70370 | 0.09799 | 0.66667 | 0.62963 | 0.81481 | 0.74074 | 0.70370 | 0.59259 | 0.66667 | 0.77778 | 0.88889 | 0.55556 | |

SSA-KELM | 0.66296 | 0.07305 | 0.59259 | 0.59259 | 0.77778 | 0.66667 | 0.66667 | 0.59259 | 0.62963 | 0.66667 | 0.81481 | 0.62963 | |

MsO-KELM | 0.72222 | 0.07813 | 0.70370 | 0.70370 | 0.85185 | 0.77778 | 0.74074 | 0.66667 | 0.70370 | 0.81481 | 0.70370 | 0.55556 | |

Sensitivity | GWO-KELM | 0.57690 | 0.15682 | 0.60000 | 0.42857 | 0.90000 | 0.57143 | 0.57143 | 0.25000 | 0.63636 | 0.63636 | 0.63636 | 0.53846 |

HHO-KELM | 0.56976 | 0.15853 | 0.60000 | 0.42857 | 0.90000 | 0.50000 | 0.57143 | 0.25000 | 0.63636 | 0.63636 | 0.63636 | 0.53846 | |

FPA-KELM | 0.63198 | 0.13636 | 0.70000 | 0.57143 | 0.80000 | 0.64286 | 0.64286 | 0.33333 | 0.54545 | 0.72727 | 0.81818 | 0.53846 | |

WOA-KELM | 0.60937 | 0.16683 | 0.60000 | 0.50000 | 0.90000 | 0.64286 | 0.57143 | 0.25000 | 0.63636 | 0.63636 | 0.81818 | 0.53846 | |

SSA-KELM | 0.42951 | 0.07305 | 0.40000 | 0.35714 | 0.70000 | 0.50000 | 0.50000 | 0.16667 | 0.54545 | 0.27273 | 0.54545 | 0.30769 | |

MsO-KELM | 0.68853 | 0.11780 | 0.80000 | 0.64286 | 0.80000 | 0.78571 | 0.64286 | 0.41667 | 0.63636 | 0.72727 | 0.81818 | 0.61538 | |

Specificity | GWO-KELM | 0.80042 | 0.09743 | 0.70588 | 0.76923 | 0.76471 | 0.84615 | 0.84615 | 0.86667 | 0.68750 | 0.93750 | 0.93750 | 0.64286 |

HHO-KELM | 0.80042 | 0.09743 | 0.70588 | 0.76923 | 0.82353 | 0.84615 | 0.84615 | 0.86667 | 0.68750 | 0.93750 | 0.93750 | 0.64286 | |

FPA-KELM | 0.77350 | 0.09368 | 0.70588 | 0.76923 | 0.76471 | 0.76923 | 0.84615 | 0.93333 | 0.75000 | 0.87500 | 0.75000 | 0.57143 | |

WOA-KELM | 0.78702 | 0.10368 | 0.70588 | 0.76923 | 0.76471 | 0.84615 | 0.84615 | 0.86667 | 0.68750 | 0.87500 | 0.93750 | 0.57143 | |

SSA-KELM | 0.85548 | 0.09534 | 0.70588 | 0.84615 | 0.82353 | 0.84615 | 0.84615 | 0.93333 | 0.68750 | 0.93750 | 1.00000 | 0.92857 | |

MsO-KELM | 0.75307 | 0.12057 | 0.64706 | 0.76923 | 0.88235 | 0.76923 | 0.84615 | 0.86667 | 0.75000 | 0.87500 | 0.62500 | 0.50000 | |

MCC | GWO-KELM | 0.39037 | 0.17811 | 0.30062 | 0.20966 | 0.64242 | 0.43207 | 0.43207 | 0.14924 | 0.32024 | 0.61751 | 0.61751 | 0.18232 |

HHO-KELM | 0.38385 | 0.17766 | 0.30062 | 0.20966 | 0.70314 | 0.36690 | 0.43207 | 0.14924 | 0.32024 | 0.61751 | 0.61751 | 0.18232 | |

FPA-KELM | 0.41245 | 0.14183 | 0.39445 | 0.34642 | 0.54880 | 0.41437 | 0.49728 | 0.34112 | 0.30062 | 0.61281 | 0.55874 | 0.10989 | |

WOA-KELM | 0.40322 | 0.20024 | 0.30062 | 0.27857 | 0.64242 | 0.49728 | 0.43207 | 0.14924 | 0.32024 | 0.53300 | 0.76890 | 0.10989 | |

SSA-KELM | 0.32280 | 0.15446 | 0.10847 | 0.23179 | 0.52353 | 0.36690 | 0.36690 | 0.15811 | 0.23295 | 0.29077 | 0.64466 | 0.30390 | |

MsO-KELM | 0.44557 | 0.15081 | 0.43207 | 0.41437 | 0.68235 | 0.55495 | 0.49728 | 0.32127 | 0.38636 | 0.61281 | 0.43823 | 0.11602 |

Cleveland | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Indicator | Algorithms | Mean | Std | 1# | 2# | 3# | 4# | 5# | 6# | 7# | 8# | 9# | 10# |

ACC | GWO-KELM | 0.67862 | 0.09806 | 0.70000 | 0.50000 | 0.76667 | 0.70000 | 0.73333 | 0.60000 | 0.76667 | 0.83333 | 0.60000 | 0.58621 |

HHO-KELM | 0.67862 | 0.09806 | 0.70000 | 0.50000 | 0.76667 | 0.70000 | 0.73333 | 0.60000 | 0.76667 | 0.83333 | 0.60000 | 0.58621 | |

FPA-KELM | 0.68506 | 0.09372 | 0.60000 | 0.63333 | 0.70000 | 0.63333 | 0.86667 | 0.66667 | 0.76667 | 0.76667 | 0.70000 | 0.51724 | |

WOA-KELM | 0.68839 | 0.09241 | 0.60000 | 0.63333 | 0.70000 | 0.66667 | 0.86667 | 0.66667 | 0.76667 | 0.76667 | 0.70000 | 0.51724 | |

SSA-KELM | 0.64517 | 0.08481 | 0.60000 | 0.63333 | 0.60000 | 0.63333 | 0.83333 | 0.63333 | 0.7000 | 0.73333 | 0.53333 | 0.55172 | |

MsO-KELM | 0.70184 | 0.08741 | 0.70000 | 0.60000 | 0.70000 | 0.70000 | 0.86667 | 0.66667 | 0.76667 | 0.80000 | 0.66667 | 0.55172 | |

Sensitivity | GWO-KELM | 0.67421 | 0.12466 | 0.72727 | 0.50000 | 0.92857 | 0.66667 | 0.69231 | 0.57143 | 0.78571 | 0.72727 | 0.64286 | 0.50000 |

HHO-KELM | 0.67421 | 0.12466 | 0.72727 | 0.50000 | 0.92857 | 0.66667 | 0.69231 | 0.57143 | 0.78571 | 0.72727 | 0.64286 | 0.50000 | |

FPA-KELM | 0.59256 | 0.15431 | 0.45455 | 0.57143 | 0.71429 | 0.40000 | 0.69231 | 0.64286 | 0.85714 | 0.54545 | 0.71429 | 0.33333 | |

WOA-KELM | 0.59923 | 0.14712 | 0.45455 | 0.57143 | 0.71429 | 0.46667 | 0.69231 | 0.64286 | 0.85714 | 0.54545 | 0.71429 | 0.33333 | |

SSA-KELM | 0.45252 | 0.14078 | 0.27273 | 0.42857 | 0.50000 | 0.33333 | 0.61538 | 0.57143 | 0.71429 | 0.45455 | 0.35714 | 0.27778 | |

MsO-KELM | 0.63519 | 0.11134 | 0.54545 | 0.57143 | 0.71429 | 0.53333 | 0.69231 | 0.64286 | 0.85714 | 0.63636 | 0.71429 | 0.44444 | |

Specificity | GWO-KELM | 0.68668 | 0.10728 | 0.68421 | 0.50000 | 0.62500 | 0.73333 | 0.76471 | 0.62500 | 0.75000 | 0.89474 | 0.56250 | 0.72727 |

HHO-KELM | 0.68668 | 0.10728 | 0.68421 | 0.50000 | 0.62500 | 0.73333 | 0.76471 | 0.62500 | 0.75000 | 0.89474 | 0.56250 | 0.72727 | |

FPA-KELM | 0.77013 | 0.11023 | 0.68421 | 0.68750 | 0.68750 | 0.86667 | 1.00000 | 0.68750 | 0.68750 | 0.89474 | 0.68750 | 0.81818 | |

WOA-KELM | 0.77013 | 0.11023 | 0.68421 | 0.68750 | 0.68750 | 0.86667 | 1.00000 | 0.68750 | 0.68750 | 0.89474 | 0.68750 | 0.81818 | |

SSA-KELM | 0.81800 | 0.12426 | 0.78947 | 0.81250 | 0.68750 | 0.93333 | 1.00000 | 0.68750 | 0.68750 | 0.89474 | 0.68750 | 1.00000 | |

MsO-KELM | 0.75906 | 0.11886 | 0.78947 | 0.62500 | 0.68750 | 0.86667 | 1.00000 | 0.68750 | 0.68750 | 0.89474 | 0.62500 | 0.72727 | |

MCC | GWO-KELM | 0.36245 | 0.19057 | 0.39747 | 0.00000 | 0.57309 | 0.40089 | 0.45701 | 0.19643 | 0.53452 | 0.63585 | 0.20536 | 0.22391 |

HHO-KELM | 0.36245 | 0.19057 | 0.39747 | 0.00000 | 0.57309 | 0.40089 | 0.45701 | 0.19643 | 0.53452 | 0.63585 | 0.20536 | 0.22391 | |

FPA-KELM | 0.37742 | 0.17392 | 0.13876 | 0.26068 | 0.40089 | 0.30151 | 0.74863 | 0.33036 | 0.54833 | 0.47969 | 0.40089 | 0.16449 | |

WOA-KELM | 0.38364 | 0.17219 | 0.13876 | 0.26068 | 0.40089 | 0.36370 | 0.74863 | 0.33036 | 0.54833 | 0.47969 | 0.40089 | 0.16449 | |

SSA-KELM | 0.30108 | 0.17525 | 0.07087 | 0.26245 | 0.19094 | 0.33333 | 0.68958 | 0.26068 | 0.40089 | 0.39796 | 0.04725 | 0.35681 | |

MsO-KELM | 0.40608 | 0.16562 | 0.34238 | 0.19643 | 0.40089 | 0.42426 | 0.74863 | 0.33036 | 0.54833 | 0.55849 | 0.33929 | 0.17172 |

Liver Disorders | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Indicator | Algorithms | Mean | Std | 1# | 2# | 3# | 4# | 5# | 6# | 7# | 8# | 9# | 10# |

ACC | GWO-KELM | 0.65571 | 0.12527 | 0.34286 | 0.74286 | 0.68571 | 0.71429 | 0.54286 | 0.62857 | 0.82857 | 0.68571 | 0.68571 | 0.70000 |

HHO-KELM | 0.67810 | 0.04583 | 0.65714 | 0.74286 | 0.74286 | 0.71429 | 0.71429 | 0.62857 | 0.65714 | 0.60000 | 0.65714 | 0.66667 | |

FPA-KELM | 0.66429 | 0.10405 | 0.42857 | 0.74286 | 0.68571 | 0.71429 | 0.54286 | 0.65714 | 0.82857 | 0.65714 | 0.68571 | 0.70000 | |

WOA-KELM | 0.68095 | 0.04349 | 0.65714 | 0.74286 | 0.74286 | 0.71429 | 0.71429 | 0.65714 | 0.65714 | 0.60000 | 0.65714 | 0.66667 | |

SSA-KELM | 0.66714 | 0.07286 | 0.54286 | 0.77143 | 0.68571 | 0.71429 | 0.62857 | 0.65714 | 0.74286 | 0.54286 | 0.68571 | 0.70000 | |

MsO-KELM | 0.70476 | 0.05216 | 0.68571 | 0.71429 | 0.77143 | 0.77143 | 0.65714 | 0.65714 | 0.77143 | 0.62857 | 0.65714 | 0.73333 | |

Sensitivity | GWO-KELM | 0.84923 | 0.09508 | 0.80000 | 0.72727 | 0.94444 | 0.72414 | 0.94118 | 0.90909 | 0.92308 | 0.94444 | 0.70370 | 0.87500 |

HHO-KELM | 0.80101 | 0.08283 | 0.80000 | 0.72727 | 0.83333 | 0.72414 | 1.00000 | 0.81818 | 0.76923 | 0.72222 | 0.74074 | 0.87500 | |

FPA-KELM | 0.84368 | 0.09089 | 0.80000 | 0.72727 | 0.94444 | 0.72414 | 0.94118 | 0.90909 | 0.92308 | 0.88889 | 0.70370 | 0.87500 | |

WOA-KELM | 0.81010 | 0.08898 | 0.80000 | 0.72727 | 0.83333 | 0.72414 | 1.00000 | 0.90909 | 0.76923 | 0.72222 | 0.74074 | 0.87500 | |

SSA-KELM | 0.80546 | 0.10156 | 0.80000 | 0.75758 | 0.77778 | 0.72414 | 1.00000 | 0.90909 | 0.88462 | 0.61111 | 0.77778 | 0.81250 | |

MsO-KELM | 0.82133 | 0.07947 | 0.80000 | 0.69697 | 0.88889 | 0.79310 | 0.94118 | 0.90909 | 0.84615 | 0.72222 | 0.74074 | 0.87500 | |

Specificity | GWO-KELM | 0.51041 | 0.21830 | 0.26667 | 1.00000 | 0.41176 | 0.66667 | 0.16667 | 0.50000 | 0.55556 | 0.41176 | 0.62500 | 0.50000 |

HHO-KELM | 0.55407 | 0.18497 | 0.63333 | 1.00000 | 0.64706 | 0.66667 | 0.44444 | 0.54167 | 0.33333 | 0.47059 | 0.37500 | 0.42857 | |

FPA-KELM | 0.52458 | 0.20896 | 0.36667 | 1.00000 | 0.41176 | 0.66667 | 0.16667 | 0.54167 | 0.55556 | 0.41176 | 0.62500 | 0.50000 | |

WOA-KELM | 0.55407 | 0.18497 | 0.63333 | 1.00000 | 0.64706 | 0.66667 | 0.44444 | 0.54167 | 0.33333 | 0.47059 | 0.37500 | 0.42857 | |

SSA-KELM | 0.53247 | 0.19378 | 0.50000 | 1.00000 | 0.58824 | 0.66667 | 0.27778 | 0.54167 | 0.33333 | 0.47059 | 0.37500 | 0.57143 | |

MsO-KELM | 0.59423 | 0.16648 | 0.66667 | 1.00000 | 0.64706 | 0.66667 | 0.38889 | 0.54167 | 0.55556 | 0.52941 | 0.37500 | 0.57143 | |

MCC | GWO-KELM | 0.33546 | 0.13057 | 0.05338 | 0.36364 | 0.42397 | 0.31030 | 0.16941 | 0.39304 | 0.52298 | 0.42397 | 0.28566 | 0.40825 |

HHO-KELM | 0.30891 | 0.13465 | 0.30641 | 0.36364 | 0.49010 | 0.31030 | 0.52899 | 0.33757 | 0.10256 | 0.19944 | 0.10758 | 0.34247 | |

FPA-KELM | 0.33780 | 0.11549 | 0.12287 | 0.36364 | 0.42397 | 0.31030 | 0.16941 | 0.42714 | 0.52298 | 0.34381 | 0.28566 | 0.40825 | |

WOA-KELM | 0.31786 | 0.13916 | 0.30641 | 0.36364 | 0.49010 | 0.31030 | 0.52899 | 0.42714 | 0.10256 | 0.19944 | 0.10758 | 0.34247 | |

SSA-KELM | 0.29871 | 0.11377 | 0.21073 | 0.38925 | 0.37341 | 0.31030 | 0.39675 | 0.42714 | 0.25275 | 0.08251 | 0.14678 | 0.39747 | |

MsO-KELM | 0.36706 | 0.11544 | 0.33333 | 0.34082 | 0.55437 | 0.38357 | 0.39286 | 0.42714 | 0.40171 | 0.25672 | 0.10758 | 0.47246 |

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## Share and Cite

**MDPI and ACS Style**

Hao, Z.; Ma, J.; Sun, W. The Technology-Oriented Pathway for Auxiliary Diagnosis in the Digital Health Age: A Self-Adaptive Disease Prediction Model. *Int. J. Environ. Res. Public Health* **2022**, *19*, 12509.
https://doi.org/10.3390/ijerph191912509

**AMA Style**

Hao Z, Ma J, Sun W. The Technology-Oriented Pathway for Auxiliary Diagnosis in the Digital Health Age: A Self-Adaptive Disease Prediction Model. *International Journal of Environmental Research and Public Health*. 2022; 19(19):12509.
https://doi.org/10.3390/ijerph191912509

**Chicago/Turabian Style**

Hao, Zhiyuan, Jie Ma, and Wenjing Sun. 2022. "The Technology-Oriented Pathway for Auxiliary Diagnosis in the Digital Health Age: A Self-Adaptive Disease Prediction Model" *International Journal of Environmental Research and Public Health* 19, no. 19: 12509.
https://doi.org/10.3390/ijerph191912509