NeuReval

A stability-based relative clustering validation method to determine the best number of clusters based on neuroimaging data.

Table of contents

1. Project Overview
2. Installation and Requirements
3. How to use NeuReval
   1. Input structure
   2. Grid-search cross-validation for parameters' tuning
   3. Run NeuReval with opitmized clustering/classifier/preprocessing algorithms
   4. Compute internal measures
   5. External validation
4. Example
5. Notes
6. References

1. Project overview

NeuReval implements a stability-based relative clustering approach within a cross-validation framework to identify the clustering solution that best replicates on unseen data. Compared to commonly used internal measures that rely on the inherent characteristics of the data, this approach has the advantage to identify clusters that are robust and reproducible in other samples of the same population. NeuReval is based on reval Python package (https://github.com/IIT-LAND/reval_clustering) and extends its application to neuroimaging data. For more details about the theoretical background of reval, please see Landi et al. (2021).

This package allows to:

1. Select any classification algorithm from sklearn library;
2. Select a clustering algorithm with n_clusters parameter (i.e., KMeans, AgglomerativeClustering, and SpectralClustering), Gaussian Mixture Models with n_components parameter, and HDBSCAN density-based algorithm;
3. Perform (repeated) k-fold cross-validation to determine the best number of clusters;
4. Test the final model on an hold-out dataset.

The following changes were made to reval to be performed on neuroimaging data:

1. Standardization and covariates adjustement within cross-validation;
2. Combine different kind of neuroimaging data and apply different set of covariates to each neuroimaging modality;
3. Implementation of data reduction techniques (e.g., PCA, UMAP) and optimization of their parameters within cross-validation.

UPDATES NEUREVAL 1.1.0 While the original version of NeuReval was limited to perform different confounds removal only for 2 different types of modalities (e.g., remove the effect of TIV only for grey matter features and not for the DTI ones), the updated version offers more flexibility in the definition and number of modalities and covariates.

2. Installation and Requirements

The most recent version of NeuReval can be installed with pip using the following command:

pip install neureval==1.1.0

Dependencies useful to install NeuReval can be found in requirements.txt

3. How to use NeuReval

i. Input structure

NeuReval requires that input features and covariates are organized as file excel in the following way:

for database with input features (database.xlsx):

• First column: subject ID
• Second column: diagnosis (e.g., patients=1, healthy controls=0). In case NeuReval is run on a single diagnostic group, provide a costant value for all subjects.
• From the third column: features

Example of database structure for input features:

Subject_ID	Diagnosis	Feature_01	Feature_02
sub_0001	0	0.26649221	2.13888054
sub_0002	1	0.32667590	0.67116539
sub_0003	0	0.35406757	2.35572978

for database with covariates (covariates.xlsx):

• First column: subject ID
• Second column: diagnosis (e.g., patients=1, healhty controls=0). In case NeuReval is run on a single diagnostic group, provide a costant value for all subjects.
• From the third column: covariates

Example of database structure for covariates:

Subject_ID	Diagnosis	Age	Sex	TIV
sub_0001	0	54	0	1213.76
sub_0002	1	37	1	1372.93
sub_0003	0	43	0	1285.88

Notes: for external validation, a single data and corresponding covariates file including both training and validation sets should be created, with observations belonging to the validation set placed after those belonging to the training set

Example of data structure with validation set (database_all.xlsx):

Subject_ID	Diagnosis	Feature_01	Feature_02
sub001_tr	0	0.26649221	2.13888054
sub002_tr	1	0.32667590	0.67116539
sub001_ts	0	0.28786749	2.16871673
sub002_ts	0	0.26789256	2.13857829

Example of covariates structure with validation set (covariates_all.xlsx):

Subject_ID	Diagnosis	Age	Sex	TIV
sub001_tr	0	54	0	1213.76
sub002_tr	1	37	1	1372.93
sub001_ts	0	32	0	1224.77
sub002_ts	0	23	1	1224.91

Templates for both datasets are provided in the folder NeuReval/example_data.

ii. Grid-search cross-validation for parameters' tuning

First, parameters for fixed classifier/clustering/preprocessing algorithms can be optimized through a grid-search cross-validation. This can be done with the ParamSelectionConfounds class:

ParamSelectionConfounds(params, cv, s, c, preprocessing, nrand=10, n_jobs=-1, iter_cv=1, strat=None, clust_range=None)

Parameters to be specified:

• params: dictionary of dictionaries of the form {‘s’: {classifier parameter grid}, ‘c’: {clustering parameter grid}} including the lists of classifiers and clustering methods to fit to the data. In case you want to optimize also preprocessing parameters (e.g., PCA or UMAP components), specify {'preprocessing':{preprocessing parameter grid}} within the dictionary.
• cv: cross-validation folds
• s: classifier object
• c: clustering object
• preprocessing: data reduction algorithm object
• nrand: number of random labelling iterations, default 10
• n_jobs: number of jobs to run in parallel, default (number of cpus - 1)
• iter_cv: number of repeated cross-validation, default 1
• clust_range: list with number of clusters, default None
• strat: stratification vector for cross-validation splits, default None

Once the ParamSelectionConfounds class is initialized, the fit(data_tr, mod_tr, cov_tr, nclass=None) class method can be used to run grid-search cross-validation. It returns the optimal number of clusters (i.e., minimum normalized stability), the corresponding normalized stability, and the selected classifier/clustering/preprocessing parameters.

iii. Run NeuReval with opitmized clustering/classifier/preprocessing algorithms

After the selection of the best clustering/classifier/preprocessing parameters through grid-search cross-vallidation, we can initalize the FindBestClustCVConfounds class to assess the normalized stability associated to the best clustering solution and the corresponding clusters' labels

FindBestClustCVConfounds(s, c, preprocessing=None, nrand=10, nfold=2, n_jobs=-1, nclust_range=None)

Parameters to be specified:

• s: classifier object (with opitmized parameters)
• c: clustering object (with optimized parameters)
• preprocessing: data reduction algorithm object (with optimized parameters), default None
• nrand: number of random labelling iterations, default 10
• nfold: number of cross-validation folds, default 2
• n_jobs: number of jobs to run in parallel, default (number of cpus - 1)
• clust_range: list with number of clusters, default None

Once the class has been initialized, the best_nclust_confounds(data, modalities, covariates, iter_cv=1, strat_vect=None) method can be used to obtain the normalized stability, the number of clusters associated to the optimal clustering solution, and clusters' labels. It returns:

• metrics: normalized stability
• bestncl: best number of clusters
• tr_lab: clusters' labels

iv. Compute internal measures

Together with normalized stability, NeuReval also allows to compute internal measures for comparisons between the stability-based relative validation and internal validation approaches. This can be done with the neureval.internal_baselines_confounds method and the function select_best to select the best number of clusters that maximize/minimize the selected internal measure:

neureval.internal_baselines_confounds.select_best(data, modalities, covariates, c, int_measure, preprocessing=None, select='max', nclust_range=None)

Parameters to be specified:

• data: features dataset
• covariates: covariates dataset
• c: clustering algorithm class (with optimized parameters)
• int_measure: internal measure function (e.g., silhouette score, Davies-Bouldin score)
• preprocessing: data reduction algorithm object (with optimized parameters), default None
• select: it can be ‘min’, if the internal measure is to be minimized or ‘max’ if the internal measure should be maximized
• nclust_range: range of clusters to consider, default None

Notes: in case Gaussian Mixture Model was implemented as clustering algorithm, the select_best_bic_aic function can be used to compute Akaike and Bayesian Information Criterion (AIC, BIC) and used them for model's selection.

v. External validation

To test the replicability of clustering solutions in an external dataset, the evaluate_confounds function within the neureval.best_nclust_cv_confounds method can be used:

neureval.best_nclust_cv_confounds.evaluate_confounds(data, modalities, covariates, tr_idx, val_idx, nclust=None, tr_lab=None)

Parameters to be specified:

• data : complete dataset with both training and hold-out sets
• modalities : dictionary specifying the datasets for each type of input feature
• covariates: dictionary specifying the covariates for each type of input feature
• tr_idx: index specifying the training dataset
• val_idx: index specifying the validation dataset
• nclust: best number of clusters, default None.
• tr_lab: clustering labels for the training set. If not None the clustering algorithm is not performed and the classifier is fitted. Available for clustering methods without n_clusters parameter. Default None

It returns accuracies in both training and validation sets and cluster labels in for the validation set

4. Example

An example of how to perform NeuReval can be found in the folder NeuReval/scripts. These codes show the application of NeuReval using Gaussian Mixture Model as clustering algorithm, Support Vector Machine as classifier, and UMAP as dimensionality reduction algorithm:

• 01_grid_search: code to perform grid-search cross-validation for clustering/classifier/preprocessing parameters tuning
• 02_run_findbestclustcv: code to perform NeuReval with the optimized clustering/classifier/preprocessing algorithms. This script also provides codes to compute different kind of internal measures and external validation in an hold-out dataset
• 03_visualization: code to create a plot for clusters' representation

5. Notes

NeuReval was developed in Python 3.8.10 and tested on ubuntu 20.04. In case of any issues in running NeuReval on other operating systems (i.e., Windows), you can send an email at the following address: fcolombo.italia@gmail.com

6. References

Landi, I., Mandelli, V., & Lombardo, M. V. (2021). reval: A Python package to determine best clustering solutions with stability-based relative clustering validation. Patterns, 2(4), 100228.