# An Ensemble Learning Approach Based on Diffusion Tensor Imaging Measures for Alzheimer’s Disease Classification

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## Abstract

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## 1. Introduction

## 2. Diffusion Tensor Imaging

## 3. Materials and Methods

#### 3.1. Data Collection

#### 3.2. Image Processing and Feature Extraction

- 1.
- Application of a nonlinear registration for the alignment of all fractional anisotropy maps to a common registration template: in the present analysis, we used the mean FMRIB58_FA standard target, available with the software, obtained as the average of 58 FA images in the MNI152 standard space. This step was performed for MD, RD and LD maps too.
- 2.
- Affine transformation of the entire aligned dataset to a $1\times 1\times 1$ mm${}^{3}$ standard space: the aligned maps were transformed into the standard space template MNI152.
- 3.
- Extraction of the white matter skeleton: by averaging all the FA maps of the dataset, a mean FA image was obtained, and this result was used to create a mean FA skeleton of WM fiber tracts that were common to all subjects (see Figure 1). A threshold was applied to the mean FA skeleton in order to exclude gray matter and cerebrospinal fluid voxels, and the voxels of the zones characterized by greater inter-subject variability belonging to the outermost part of the cortex.
- 4.
- Projection of all FA maps onto the mean FA skeleton: this allowed us to achieve an alignment among all subjects in the direction orthogonal to the fiber bundle orientation. The same elaboration steps were applied to RD, MD and LD maps.

#### 3.3. Classification Methods

#### 3.4. Learning Experiment

- 1.
- For each group of features in (FA, MD, RD, LD) and their combined feature vector, find the best associated classifier among the three algorithms SVM, RF and MLP, as described in Section 3.3. A 5-fold cross validation grid search procedure should be performed to tune the hyperparameters and evaluate the best performer for each configuration, as shown in Table 2.For instance, for configuration 1-1 the model ${M}_{FA}$ is chosen among SVM${}_{b}^{1-1}$, RF${}_{b}^{1-1}$ and MLP${}_{b}^{1-1}$.
- 2.
- For each possible configuration listed in Table 1, evaluate the performance of the ensemble learning algorithm, based on the combination of the best classifier selected in step 1. The voting scheme is a soft-voting procedure which is based on averaging the probability scores given by the individual classifiers according to the following equation:$$\widehat{y}=\underset{i}{argmax}\sum _{j=1}^{n}{w}_{j}{p}_{ij}$$
- 3.
- Repeat steps 1 and 2 on a balanced dataset obtained from the original one (43 AD vs. 49 HC), removing 6 healthy controls using the instance hardness threshold method (IHT) of Smith et al. [45]. IHT is an under-sampling method for reducing class imbalance based on the removal of the “hard” instances (where instance hardness is the likelihood of being misclassified), while focusing on the majority class samples that overlap the minority class sample space. The balanced dataset is then composed of 43 diseased cases and 43 healthy controls.

## 4. Results

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Coronal, sagittal and axial views of the brain obtained in the FSLeyes image viewer: the mean fractional anisotropy (FA) skeleton (green) is overlaid with the mean FA map. For the following analysis all maps were projected onto the white matter skeleton.

**Figure 2.**(

**a**) Cartoon picture of a SVM classifier with nonlinear kernel: dots of different colors represent instances of two different classes; dotted lines represent the decision boundaries. (

**b**) Example of a multi-layer perceptron with two hidden layers.

**Figure 4.**The case of an imbalanced dataset. (

**a**) Average performance values for each configuration. (

**b**–

**e**) Heatmaps of Mann–Whitney tests. Each square represents the p-value outcome of a one-tail Mann–Whitney test between a configuration on the y-axis and the other on the x-axis. Each p-value in the heatmap was corrected for multiple tests using the Benjamini–Hochberg procedure.

**Figure 5.**The case of a balanced dataset. (

**a**) Average performance values for each configuration. (

**b**–

**e**) Heatmaps of Mann–Whitney tests. Each square represents the p-value outcome of a one-tail Mann–Whitney test between a configuration on the y-axis and the other on the x-axis. Each p-value in a heatmap has been corrected for multiple tests using the Benjamini–Hochberg procedure.

Label | Configuration | Label | Configuration |
---|---|---|---|

1-1 | $\mathcal{E}\left({M}_{\mathrm{FA}}\right)$ | 2-5 | $\mathcal{E}({M}_{\mathrm{LD}}$, ${M}_{\mathrm{RD}})$ |

1-2 | $\mathcal{E}\left({M}_{\mathrm{MD}}\right)$ | 2-6 | $\mathcal{E}({M}_{\mathrm{MD}}$, ${M}_{\mathrm{RD}})$ |

1-3 | $\mathcal{E}\left({M}_{\mathrm{RD}}\right)$ | 3-1 | $\mathcal{E}({M}_{\mathrm{FA}}$, ${M}_{\mathrm{LD}}$, ${M}_{\mathrm{MD}})$ |

1-4 | $\mathcal{E}\left({M}_{\mathrm{LD}}\right)$ | 3-2 | $\mathcal{E}({M}_{\mathrm{FA}}$, ${M}_{\mathrm{LD}}$, ${M}_{\mathrm{RD}})$ |

2-1 | $\mathcal{E}({M}_{\mathrm{FA}}$, ${M}_{\mathrm{LD}})$ | 3-3 | $\mathcal{E}({M}_{\mathrm{FA}}$, ${M}_{\mathrm{MD}}$, ${M}_{\mathrm{RD}})$ |

2-2 | $\mathcal{E}({M}_{\mathrm{FA}}$, ${M}_{\mathrm{MD}})$ | 3-4 | $\mathcal{E}({M}_{\mathrm{LD}}$, ${M}_{\mathrm{MD}}$, ${M}_{\mathrm{RD}})$ |

2-3 | $\mathcal{E}({M}_{\mathrm{FA}}$, ${M}_{\mathrm{RD}})$ | 4-1 | $\mathcal{E}({M}_{\mathrm{FA}}$, ${M}_{\mathrm{MD}}$, ${M}_{\mathrm{RD}}$, ${M}_{\mathrm{LD}})$ |

2-4 | $\mathcal{E}({M}_{\mathrm{LD}}$, ${M}_{\mathrm{MD}})$ | 5-1 | $\mathcal{E}\left({M}_{\mathrm{FA},\mathrm{MD},\mathrm{RD},\mathrm{LD}}\right)$ |

_{i}is the best classification method associated with the i-th feature group and $\mathcal{E}$(M

_{1}, M

_{2}, …, M

_{j}) is the ensemble learning method based on the combination of best classifiers M

_{1}, M

_{2}, …, M

_{j}. The ensemble of a singleton corresponds to the best classifier, i.e., $\mathcal{E}$(M

_{i}) ≡ M

_{i}. Finally, configuration 5-1 refers to the best classifier trained on a single high-dimensional vector concatenating all feature groups.

1-1 | 1-2 | 1-3 | 1-4 | 5-1 | |
---|---|---|---|---|---|

5-fold SVM best | SVM${}_{b}^{1-1}$ | SVM${}_{b}^{1-2}$ | SVM${}_{b}^{1-3}$ | SVM${}_{b}^{1-4}$ | SVM${}_{b}^{5-1}$ |

5-fold RF best | RF${}_{b}^{1-1}$ | RF${}_{b}^{1-2}$ | RF${}_{b}^{1-3}$ | RF${}_{b}^{1-4}$ | RF${}_{b}^{5-1}$ |

5-fold MLP best | MLP${}_{b}^{1-1}$ | MLP${}_{b}^{1-2}$ | MLP${}_{b}^{1-3}$ | MLP${}_{b}^{1-4}$ | MLP${}_{b}^{5-1}$ |

Best Classifier | ${M}_{\mathrm{FA}}$ | ${M}_{\mathrm{MD}}$ | ${M}_{\mathrm{RD}}$ | ${M}_{\mathrm{LD}}$ | ${M}_{5-1}$ |

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**MDPI and ACS Style**

Lella, E.; Pazienza, A.; Lofù, D.; Anglani, R.; Vitulano, F. An Ensemble Learning Approach Based on Diffusion Tensor Imaging Measures for Alzheimer’s Disease Classification. *Electronics* **2021**, *10*, 249.
https://doi.org/10.3390/electronics10030249

**AMA Style**

Lella E, Pazienza A, Lofù D, Anglani R, Vitulano F. An Ensemble Learning Approach Based on Diffusion Tensor Imaging Measures for Alzheimer’s Disease Classification. *Electronics*. 2021; 10(3):249.
https://doi.org/10.3390/electronics10030249

**Chicago/Turabian Style**

Lella, Eufemia, Andrea Pazienza, Domenico Lofù, Roberto Anglani, and Felice Vitulano. 2021. "An Ensemble Learning Approach Based on Diffusion Tensor Imaging Measures for Alzheimer’s Disease Classification" *Electronics* 10, no. 3: 249.
https://doi.org/10.3390/electronics10030249