# Feature Ranking by Variational Dropout for Classification Using Thermograms from Diabetic Foot Ulcers

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Variational Dropout

#### 2.1.1. Stochastic Variational Inference

#### 2.1.2. Feature Selection by Variational Dropout

#### 2.2. Dataset Description

#### Local Dataset

#### 2.3. Feature Extraction

#### 2.4. Feature Selection

## 3. Results

#### 3.1. Feature Selection

#### 3.2. Evaluation of Features by SVM Classifier

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Most relevant features extracted for all the approaches considered and listed according to angiosome. The search for coincidence was restricted to the first 30 ranked features provided for each approach. Features found up to a rank lower than 50 were considered.

Region | Features |
---|---|

MPA | R_MPA_HSE |

L_MPA_skew | |

LPA | R_LPA_min |

LPA_ETD | |

L_LPA_std | |

R_LPA_std | |

MCA | R_MCA_std |

L_MCA_std | |

LCA | R_LCA_std |

R_LCA_kurtosis | |

LCA_ETD | |

Foot | Foot_ETD |

L_kurtosis | |

R_kurtosis |

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**Figure 1.**Dropout as a feature selection method. The variational parameter ${\varphi}_{d}$, where $d\in \left[1.\phantom{\rule{0.166667em}{0ex}}.D\right]$, controls the probability of the input feature ${x}_{d}$ to be dropped out, that is, an estimate of the noise level of ${x}_{d}$. The variational parameters are used for feature ranking.

**Figure 2.**Graphical illustration of the defined angiosomes. The main reference points considered and the proportional foot division are also specified [41,47]. Reference point A was located at the tip of the innermost toe, whereas B at the center of the calcaneal base. Points C and D corresponded to the wider part of the foot. Point E corresponded to the 60% height of the foot.

**Figure 3.**Deep learning architecture used for the feature selection based on variational dropout approaches. The first layer corresponds to variational dropout as a feature selector, illustrated in Figure 1.

**Figure 4.**The sparse rate obtained in the variational feature selector using $\tau >0.9$ as threshold in the different cross-validation iterations.

**Table 1.**Mean temperature values per angiosome in the control group for the INAOE database [47] and the local dataset described in Section 2.2. SD indicates standard deviation.

Angiosome | INAOE | Local | ||
---|---|---|---|---|

$\overline{\mathit{T}}$ (°C) | SD | $\overline{\mathit{T}}$ (°C) | SD | |

MPA | 25.8 | 1.4 | 25.0 | 3.0 |

LPA | 25.7 | 1.3 | 24.5 | 3.1 |

MCA | 26.4 | 1.3 | 24.5 | 2.5 |

LCA | 26.1 | 1.4 | 24.5 | 2.6 |

Class | NTR Class | Interval (°C) | Classmark (°C) |
---|---|---|---|

C${}_{1}$ | NTR_C${}_{1}$ | [18,22) | 20.0 |

C${}_{2}$ | NTR_C${}_{2}$ | [22,26) | 24.0 |

C${}_{3}$ | NTR_C${}_{3}$ | [26,27) | 26.5 |

C${}_{4}$ | NTR_C${}_{4}$ | [27,28) | 27.5 |

C${}_{5}$ | NTR_C${}_{5}$ | [28,29) | 28.5 |

C${}_{6}$ | NTR_C${}_{6}$ | [29,30) | 29.5 |

C${}_{7}$ | NTR_C${}_{7}$ | [30,31) | 30.5 |

C${}_{8}$ | NTR_C${}_{8}$ | [31,32) | 31.5 |

C${}_{9}$ | NTR_C${}_{9}$ | [32,33) | 32.5 |

C${}_{10}$ | NTR_C${}_{10}$ | [33,37) | 35.0 |

**Table 3.**The 30 most relevant features extracted, listed according to rank, for all the approaches considered: LASSO, random forest, and concrete and variational dropout. The 10 first features are highlighted in bold as the most relevant for each method. The nomenclature employed is defined in Section 2.3.

Rank | LASSO | Random Forest | Concrete Dropout | Variational Dropout |
---|---|---|---|---|

1 | R_LPA_min | L_MPA_min | R_LPA_min | R_LPA_min |

2 | L_LPA_std | R_LPA_min | R_MCA_std | R_MPA_HSE |

3 | Foot_ETD | L_MPA_NTR_C${}_{3}$ | Foot_ETD | MCA_ETD |

4 | L_MPA_min | R_MCA_std | R_LCA_kurtosis | L_kurtosis |

5 | L_MPA_skew | R_LPA_std | R_LPA_std | L_MPA_skew |

6 | L_LCA_NTR_C${}_{4}$ | L_MPA_std | L_MPA_min | L_MCA_skew |

7 | R_LPA_NTR_C${}_{3}$ | L_LPA_NTR_C${}_{2}$ | LPA_ETD | R_LCA_kurtosis |

8 | R_MPA_NTR_C${}_{4}$ | L_LPA_std | L_LPA_std | R_LPA_std |

9 | L_MPA_HSE | R_LCA_NTR_C${}_{2}$ | L_MCA_skew | L_MPA_NTR_C${}_{4}$ |

10 | R_MCA_std | R_MPA_NTR_C${}_{2}$ | L_MPA_HSE | L_LCA_std |

11 | LCA_ETD | R_MPA_std | R_LCA_skew | R_LPA_HSE |

12 | MCA_ETD | R_LCA_mean | MCA_ETD | R_LCA_std |

13 | R_LCA_kurtosis | L_MCA_min | L_MCA_std | Foot_ETD |

14 | R_MPA_NTR_C${}_{3}$ | L_LCA_NTR_C${}_{2}$ | MPA_ETD | R_MCA_std |

15 | R_LCA_NTR_C${}_{3}$ | L_MCA_mean | LCA_ETD | LPA_ETD |

16 | L_kurtosis | R_MPA_ET | R_MCA_skew | L_MCA_std |

17 | R_std | R_std | L_MPA_skew | R_MCA_skew |

18 | R_LCA_HSE | L_MCA_NTR_C${}_{2}$ | R_kurtosis | L_MCA_NTR_C${}_{5}$ |

19 | R_skew | L_LPA_ET | R_HSE | R_MCA_HSE |

20 | L_HSE | L_LPA_NTR_C${}_{1}$ | L_LCA_kurtosis | R_kurtosis |

21 | R_LPA_NTR_C${}_{5}$ | L_LCA_NTR_C${}_{3}$ | R_LCA_std | LCA_ETD |

22 | L_max | Foot_ETD | L_MPA_std | R_LCA_skew |

23 | L_MCA_std | LPA_ETD | L_LCA_std | R_MPA_std |

24 | L_LPA_NTR_C${}_{4}$ | L_MPA_NTR_C${}_{4}$ | R_LCA_HSE | R_MPA_NTR_C${}_{4}$ |

25 | L_MCA_NTR_C${}_{3}$ | L_NTR_C${}_{3}$ | R_skew | L_MPA_NTR_C${}_{3}$ |

26 | LPA_ETD | L_std | R_MPA_NTR_C${}_{4}$ | L_LPA_NTR_C${}_{2}$ |

27 | R_MCA_HSE | L_kurtosis | R_MPA_HSE | R_LCA_HSE |

28 | L_MCA_skew | R_MPA_NTR_C${}_{3}$ | L_MCA_kurtosis | L_MPA_HSE |

29 | L_LPA_NTR_C${}_{5}$ | L_MCA_std | L_LCA_NTR_C${}_{4}$ | L_MCA_HSE |

30 | R_NTR_C${}_{5}$ | L_LCA_max | L_kurtosis | L_skew |

**Table 4.**Most relevant features that coincided in all the approaches considered, listed according to rank.

Rank | Features in Coincidence |
---|---|

Rank < 10 | R_LPA_min |

Rank < 20 | R_MCA_std |

Rank < 30 | Foot_ETD |

LPA_ETD | |

L_MCA_std | |

L_kurtosis | |

Rank < 50 | L_LPA_std |

R_kurtosis | |

R_LCA_std | |

R_LCA_kurtosis |

Input Dataset | Accuracy | Precision | Recall | F1 Score |
---|---|---|---|---|

All features | 0.9099 ± 0.0613 | 0.9473 ± 0.0705 | 0.8535 ± 0.1016 | 0.8965 ± 0.0837 |

**Table 6.**Performance metrics of the approaches considered, according to the selected input features, in each experimental setting. The highest value for each performance metric is highlighted in bold.

Input Dataset | Approach | Accuracy | Precision | Recall | F1 Score |
---|---|---|---|---|---|

First 10 features | LASSO | 0.8975 ± 0.073 | 0.9533 ± 0.079 | 0.8361 ± 0.130 | 0.8908 ± 0.107 |

Random Forest | 0.8893 ± 0.070 | 0.9703 ± 0.080 | 0.8033 ± 0.118 | 0.8789 ± 0.103 | |

Concrete dropout | 0.9098 ± 0.069 | 0.9808 ± 0.057 | 0.8361 ± 0.131 | 0.9027 ± 0.104 | |

Variational dropout | 0.8934 ± 0.054 | 0.9615 ± 0.049 | 0.8197 ± 0.104 | 0.8850 ± 0.081 | |

First 10 features in coincidence | LASSO, random forest, concrete and variational dropout | 0.9057 ± 0.066 | 0.9626 ± 0.052 | 0.8442 ± 0.135 | 0.8995 ± 0.102 |

Selected features from [18] | Pearson, chi square, RFE, logistics, random forest, and LightGBM | 0.7951 ± 0.075 | 0.8750 ± 0.136 | 0.6885 ± 0.089 | 0.7706 ± 0.103 |

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**MDPI and ACS Style**

Hernandez-Guedes, A.; Arteaga-Marrero, N.; Villa, E.; Callico, G.M.; Ruiz-Alzola, J.
Feature Ranking by Variational Dropout for Classification Using Thermograms from Diabetic Foot Ulcers. *Sensors* **2023**, *23*, 757.
https://doi.org/10.3390/s23020757

**AMA Style**

Hernandez-Guedes A, Arteaga-Marrero N, Villa E, Callico GM, Ruiz-Alzola J.
Feature Ranking by Variational Dropout for Classification Using Thermograms from Diabetic Foot Ulcers. *Sensors*. 2023; 23(2):757.
https://doi.org/10.3390/s23020757

**Chicago/Turabian Style**

Hernandez-Guedes, Abian, Natalia Arteaga-Marrero, Enrique Villa, Gustavo M. Callico, and Juan Ruiz-Alzola.
2023. "Feature Ranking by Variational Dropout for Classification Using Thermograms from Diabetic Foot Ulcers" *Sensors* 23, no. 2: 757.
https://doi.org/10.3390/s23020757