# Large-scale Augmented Granger Causality (lsAGC) for Enhanced Analysis of Brain Connectivity in Autism Spectrum Disorder

Axel Wismüller, Ali Vosoughi, Akhil Kasturi

► To cite this version:

Axel Wismüller, Ali Vosoughi, Akhil Kasturi. Large-scale Augmented Granger Causality (lsAGC) for Enhanced Analysis of Brain Connectivity in Autism Spectrum Disorder. Proceedings of SPIE Medical Imaging 2025, Feb 2025, San Diego (CA), United States. hal-04987642

HAL Id: hal-04987642

https://hal.science/hal-04987642v1

Submitted on 27 Mar 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Large-scale Augmented Granger Causality (lsAGC)
for Enhanced Analysis of Brain Connectivity in
Autism Spectrum Disorder

Axel Wismüller<sup>a,b,c,d</sup>, Ali Vosoughi<sup>b</sup>, and Akhil Kasturi<sup>b</sup>

<sup>a</sup>Department of Imaging Sciences, University of Rochester, NY, USA

<sup>b</sup>Department of Electrical and Computer Engineering, University of Rochester, NY,
USA

<sup>c</sup>Department of Biomedical Engineering, University of Rochester, NY, USA

<sup>d</sup>Faculty of Medicine and Institute of Clinical Radiology, Ludwig Maximilian
University, Munich, Germany

ABSTRACT

We introduce large-scale Augmented Granger Causality (lsAGC) as a novel method for analyzing directed connectivity in high-dimensional neural systems. The lsAGC algorithm integrates invertible dimension reduction with time-series augmentation to overcome the challenges faced by current methods in analyzing connectivity within complex systems. This multivariate approach effectively determines the influence of each time series on others within the context of all time-series in a dynamic system. We applied lsAGC to resting-state fMRI data from the Autism Brain Imaging Data Exchange II (ABIDE II) dataset, with a focus on data from the Olin Neuropsychiatry Research Center. Our method shows improved accuracy in differentiating individuals with Autism Spectrum Disorder (ASD) from healthy controls (HLT). Quantitative evaluation shows that lsAGC achieves a higher AUC of 0.940 ± 0.074 compared to competing methods: correlation (0.890 ± 0.100, -5.32%), local models (0.905 ± 0.108, -3.72%), and antisymmetric correlation (0.882 ± 0.102, -6.17%). Statistical analysis using Wilcoxon signed rank tests confirms significant improvements of lsAGC over all competing methods (p < 10<sup>-4</sup> for all comparisons). Furthermore, lsAGC shows lower entropy values (ASD: 1.563 ± 0.150, HLT: 1.543 ± 0.216) compared to other methods, suggesting that it captures more discriminative features. These results indicate the potential of lsAGC to improve our understanding of brain connectivity patterns in ASD and other neurological conditions. By extracting sparse connectivity matrices, lsAGC can be particularly useful for network analysis in complex systems and could be applicable to clinical fMRI analysis in future research, such as targeting disease-related classification or regression tasks in clinical data.

**Keywords:** machine learning, resting-state fMRI, large-scale Augmented Granger Causality, functional connectivity, autism spectrum disorder

# 1 INTRODUCTION

Assessing the directed transfer of information between interacting brain regions remains a signifi-
cant hurdle in computational neuroscience, especially in systems with high dimensionality. Frequent
simplification techniques often lead to a loss of information and constrain the interpretation of func-
tions of the brain network. Although several approaches for determining directional relationships in
multivariate time series data have been suggested [1, 2], they become increasingly computationally demanding as the dimensions grow [3, 4]. Granger causality, which is equivalent to the transfer entropy for Gaussians [5], encounters difficulties in large-scale problems with limited time series [6].

We have previously introduced the concept of large-scale Granger causality (lsGC), which employs invertible dimension reduction techniques along with backprojection of prediction residuals [6]. Furthermore, we have validated its applicability specifically to the analysis of rs-fMRI data [7]. In addition, we have developed a variant called large-scale extended Granger causality (lsXGC) that uses augmented dimension-reduced time series for the purpose of direct prediction [8, 9].

This study proposes large-scale Augmented Granger Causality (lsAGC), a hybrid methodology that integrates invertible dimension reduction with time-series augmentation. The method utilizes dimension-reduced, augmented time-series to perform predictions within a low-dimensional space and subsequently applies the inversion of the initial dimension reduction.

In the context of clinical research, we analyze connectivity matrices derived from fMRI data pertaining to individuals with autism spectrum disorder (ASD) and neurotypical controls, utilizing the Autism Brain Imaging Data Exchange II (ABIDE II) repository. The results demonstrate the efficacy of lsAGC in discerning connectivity patterns associated with ASD, thus providing valuable information on the neural mechanisms underlying neurodevelopmental disorders. This research initiative represents a component of our collective endeavor to enhance the application of artificial intelligence in biomedical imaging, by leveraging advanced pattern recognition and machine learning methodologies for computational radiology and radiomics. e.g. [10–108].

## 2 DATA

### 2.1 Functional MRI Data for Qualitative Analysis

This section outlines participants and the corresponding data in accordance with the description provided in [109]: The Autism Brain Imaging Data Exchange II (ABIDE II) initiative has made MRI data from multiple sites publicly accessible. For our analysis, we utilized resting-state fMRI data from 59 participants from the ABIDE II online repository

([http://fcon.1000 projects.nitrc.org/indi/abide](http://fcon.1000 projects.nitrc.org/indi/abide)), specifically the data obtained from the Olin Neuropsychiatry Research Center, Institute of Living at Hartford Hospital [110]. This dataset comprises 24 individuals with ASD (aged 18-31 years) and 35 typically developing controls (aged 18-31 years). Autism diagnoses were determined using the cutoff criteria from the Autism Diagnostic Observation Schedule-Generic (ADOS-G). The typically developing controls (TC) were evaluated for autism with the ADOS-G and screened for any psychiatric disorders via the Structured Clinical Interview for DSM-IV Axis I Disorders-Research Version (SCID-I RV) [110].

The dataset comprises resting-state fMRI scans acquired from all participants utilizing the Siemens Magnetom Skyra Syngo MR D13. The study protocol entailed: (i) high-resolution structural imaging via a T1-weighted magnetization prepared rapid gradient-echo (MPRAGE) sequence with parameters of TE = 2.88 ms, TR = 2200 ms, an isotropic voxel size of 1 mm, and a flip angle of 13°; (ii) resting-state fMRI scans conducted with parameters of TE = 30 ms, TR = 475 ms, a flip angle of 60°, and an isotropic voxel size of 3 mm. The scanning session lasted for 7 minutes and 37 seconds. Pre-processing of the fMRI data was conducted following established methodologies which included motion correction, brain extraction, and adjustment for slice timing acquisitions. Additionally, nuisance regression was employed to mitigate variations arising from head motion
and physiological processes. Each dataset was ultimately registered to the 2 mm MNI standard space through the application of a 12-parameter affine transformation. The functional data were pre-processed using the CONN toolbox (www.nitrc.org/projects/conn) [111].

The time-series data were normalized to have a mean of zero and a standard deviation of one in order to emphasize signal dynamics rather than amplitude [112]. Subsequently, the brain was divided into 116 regions as specified by the Automated Anatomic Labeling (AAL) template [113]. The time-series for each region were represented by averaging the time-series of all voxels within that region. This parcellation process resulted in connectivity matrices of size 116 × 116 for each subject, depicting the functional connectivity between the 116 brain regions. For our simulations and analyses, we utilized these 116 × 116 connectivity matrices across all methods, including correlation, lsAGC, local models, and antisymmetric correlation. This uniform matrix size facilitates direct comparisons between different methods and ensures consistency by anchoring our findings to an identical set of brain regions in all analyses.

## 3 ALGORITHM

The Large-scale Augmented Granger Causality (lsAGC) method has been established on two foundational principles: first, the traditional concept of Granger causality, which measures the causal impact of one time-series $x_s$ on another time-series $x_t$ by evaluating the degree of enhancement in predicting $x_t$ when $x_s$ is present; second, the concept of dimension reduction, which addresses the challenges of an under-determined system, a common issue in fMRI analysis owing to the typically insufficient number of temporal samples for accurate estimation of model parameters.⁷

Consider the ensemble of time-series denoted by $\mathcal{X} \in \mathbb{R}^{N \times T}$, where $N$ represents the number of time-series, also known as Regions Of Interest (ROIs), and $T$ indicates the number of temporal samples. Define $\mathcal{X} = (x_1, x_2, \dots, x_N)^T$ as the entire multidimensional system and $x_i \in \mathbb{R}^{1 \times T}$ as an individual time-series characterized by $i = 1, 2, \dots, N$, with $x_i = (x_i(1), x_i(2), \dots, x_i(T))$ being the relevant condition. To address the issue of underdetermination, $\mathcal{X}$ will initially be decomposed into its first $p$ principal components that exhibit high variance, referred to as $\mathcal{Z} \in \mathbb{R}^{p \times T}$, by employing Principal Component Analysis (PCA), i.e.,

$$ \mathcal{Z} = W\mathcal{X}, \qquad (1) $$

, where $W \in \mathbb{R}^{p \times N}$ denotes the PCA coefficient matrix. Following this, the dimension-reduced ensemble of time-series $\mathcal{Z}$ is augmented by incorporating one original time-series $x_s$, resulting in a dimension-reduced augmented time-series ensemble $\mathcal{Y} \in \mathbb{R}^{(p+1) \times T}$, which is utilized to estimate the influence of $x_s$ on all other time-series.

In subsequent steps, a local prediction of the reduced dimensional representation $\mathcal{Z}$ of the original high-dimensional system $\mathcal{X}$ is executed at every temporal instance $t$, particularly $\mathcal{Z}(t) \in \mathbb{R}^{p \times 1}$, via the computation of an estimate $\hat{\mathcal{Z}}_{x_s}(t)$. To achieve this, an affine model is constructed, utilizing a vector of $m$ containing $m$ temporal instances of $\mathcal{Y}(\tau) \in \mathbb{R}^{(p+1) \times 1}(\tau = t-1, t-2, \dots, t-m)$, referred to as $\mathbf{y}(t) \in \mathbb{R}^{m \times (p+1) \times 1}$, alongside a parameter matrix $\mathcal{A} \in \mathbb{R}^{p \times m \times (p+1)}$ and a constant bias vector $\mathbf{b} \in \mathbb{R}^{p \times 1}$.

$$ \hat{\mathcal{Z}}_{x_s}(t) = \mathcal{A}\mathbf{y}(t) + \mathbf{b}, \quad t = m+1, m+2, \dots, T. \qquad (2) $$

Next, we employ the prediction $\hat{\mathcal{Z}}_{x_s}(t)$ to derive an approximation of $\mathcal{X}$ at time $t$, denoted as $\mathcal{X}(t) \in \mathbb{R}^{N \times 1}$, by reversing the PCA in equation (2). This is given by

$$ \mathcal{X} = W^{\dagger}\mathcal{Z}, \qquad (3) $$
where $W^\dagger \in \mathbb{R}^{N \times p}$ is the inverse PCA coefficient matrix, specifically calculated as the Moore Penrose pseudoinverse of $W$.

The prediction denoted by $\hat{\mathcal{X}}_{\mathbf{x}_s}(t)$, which represents estimating $\mathcal{X}(t)$ excluding the data from $\mathbf{x}_s$, will now be determined. This estimation method mirrors the earlier procedure, except that the augmented time-series $\mathbf{x}_s$ and its associated column in the PCA coefficient matrix $W$ must be excluded.

To calculate the lsAGC index, we compare the variance in prediction errors with and without including $\mathbf{x}_s$. The value $f_{\mathbf{x}_s \to \mathbf{x}_t}$, representing the impact of $\mathbf{x}_s$ on $\mathbf{x}_t$, is determined by the equation:

$$f_{\mathbf{x}_s \to \mathbf{x}_t} = \log \frac{\mathrm{var}(e_s)}{\mathrm{var}(e_{\setminus s})}, \qquad (4)$$

where $e_{\setminus s}$ signifies the prediction error for $\mathbf{x}_t$ without taking $\mathbf{x}_s$ into account, and $e_s$ is the prediction error when $\mathbf{x}_s$ is included. Following initial analyses, we chose $p = 7$ and $m = 3$ for this study.

# 4 RESULTS

Figure 1 illustrates the average connectivity matrices obtained through the application of lsAGC, correlation, local models, and antisymmetric correlation for both individuals with Autism Spectrum Disorder (ASD) and healthy controls (HLT) within the OLIN ASD dataset. Each methodological approach uncovers unique connectivity patterns. We utilize a Multivariate Pattern Analysis (MVPA) methodology to quantitatively examine the differences in connectivity between the cohorts. The efficacy of classification is evaluated using the Area Under the Receiver Operating Characteristic Curve (AUC), accuracy, and F1-score. An AUC score of 1 indicates perfect classification, whereas an AUC value of 0.5 signifies random classification.

Following initial analyses, two principal component analysis (PCA) components were selected for retention within the lsAGC algorithm, alongside the establishment of a model order of four for the multivariate vector autoregression function. The graphical representations in Fig. 2 illustrate that the lsAGC algorithm surpasses alternative methodologies concerning the optimal number of features for each respective method.

We conducted an analysis using feature sets comprising 300, 500, and 700 features, utilizing 100 cross-validation shuffles for each method. Upon averaging the results for each feature set, it was observed that lsAGC consistently surpassed the alternative methods, achieving a mean AUC of $0.940 \pm 0.074$, a mean accuracy of $0.870 \pm 0.083$, and a mean F1-score of $0.832 \pm 0.121$.

When compared, correlation resulted in an AUC of $0.890 \pm 0.100$ on average, with accuracy reaching $0.819 \pm 0.106$ on average, and a mean F1-score of $0.776 \pm 0.143$. Local models achieved an average AUC of $0.905 \pm 0.108$, accuracy of $0.817 \pm 0.112$, and an F1-score mean of $0.786 \pm 0.147$. For the antisymmetric correlation method, the average AUC was $0.882 \pm 0.102$, the mean accuracy was $0.820 \pm 0.097$, and the mean F1-score was $0.785 \pm 0.129$. Statistical evaluation through Wilcoxon signed-rank tests revealed significant differences between lsAGC and the other methods: correlation ($p = 2.64 \times 10^{-7}$), local models ($p = 4.73 \times 10^{-5}$), and antisymmetric correlation ($p = 9.72 \times 10^{-6}$), affirming the enhanced performance of lsAGC.

An evaluation of entropy has demonstrated that the lsAGC method resulted in reduced values (ASD: $1.563 \pm 0.150$, HLT: $1.543 \pm 0.216$) relative to those observed in correlation (ASD: $4.070 \pm 0.080$, HLT: $4.062 \pm 0.089$), local models (ASD: $4.054 \pm 0.148$, HLT: $4.044 \pm 0.166$), and
<figure><img src="image_2.png" /><figcaption>Figure 1: The average connectivity matrices for healthy control participants and individuals with Autism Spectrum Disorder (ASD) are derived employing four distinct methodologies: lsAGC, correlation, local models, and antisymmetric correlation. Illustrated herein are examples corresponding to the lsAGC and correlation methods: the top left panel presents the mean connectivity matrix for healthy control participants via lsAGC, whereas the top right panel depicts the mean connectivity matrix for ASD patients using lsAGC. Similarly, the bottom left panel demonstrates the mean connectivity matrix for healthy control participants utilizing correlation, while the bottom right panel shows the mean connectivity matrix for ASD patients employing correlation. The application of these disparate methods reveals unique connectivity features, with noticeable differences in connectivity patterns discernible between healthy individuals and ASD patients across different methodologies.</figcaption></figure>

antisymmetric correlation (ASD: 2.617 ± 0.075, HLT: 2.605 ± 0.063). These results suggest that lsAGC possesses an enhanced capability to discern distinctive characteristics when compared to alternative methodologies.

# 5 CONCLUSIONS

In this study, we present large-scale Augmented Granger Causality (lsAGC) as an innovative approach for the analysis of directed connectivity in neural systems of high dimensionality. The lsAGC algorithm integrates invertible dimension reduction with time-series augmentation to overcome the limitations of current methodologies. We applied lsAGC to resting-state fMRI data from the ABIDE II dataset, specifically analyzing data from the Olin Neuropsychiatry Research Center. Our method exhibited superior efficacy in classifying individuals with Autism Spectrum Disorder (ASD) compared to healthy controls, achieving a mean AUC of 0.940 ± 0.074. This performance substantially exceeded that of competing methods: correlation (0.890 ± 0.100), local models (0.905 ± 0.108), and antisymmetric correlation (0.882 ± 0.102). Statistical analyses confirmed significant advantages of lsAGC over these alternative methods ($p < 10^{-4}$ for all comparisons). Additionally, lsAGC displayed lower entropy values, indicating that it captures more discriminative features. These findings suggest the potential of lsAGC to enhance our understanding of brain connectivity patterns in ASD
<figure><img src="image_3.png" /><figcaption>Figure 2: The performance of large-scale Augmented Granger Causality (lsAGC) was compared with other methods, namely correlation, local models, and antisymmetric correlation, in the classification of individuals with Autism Spectrum Disorder (ASD) versus healthy control subjects. This analysis utilized functional connectivity data from the OLIN ASD functional magnetic resonance imaging (fMRI) dataset. Each point in the graph corresponds to the mean, while the terminal bars denote the 95% confidence interval for the area under the curve (AUC), accuracy, and F1 score. Notably, lsAGC consistently demonstrates superior performance across all evaluated metrics. The results are derived from feature sets ranging from 300 to 700, with 100 shuffles in cross-validation for each feature set.</figcaption></figure>

and other neurological conditions. By deriving sparse connectivity matrices, lsAGC may be par-
ticularly advantageous for network analysis in complex systems and could be pertinent to various
clinical fMRI analyses in future research, such as for disease-related classification or regression tasks.

ACKNOWLEDGMENTS

This research was partially funded by the American College of Radiology (ACR) Innovation Award
"AI-PROBE: A Novel Prospective Randomized Clinical Trial Approach for Investigating the Clin-
ical Usefulness of Artificial Intelligence in Radiology" (PI: Axel Wismüller). This work was con-
ducted as a Practice Quality Improvement (PQI) project related to the American Board of Radi-
ology (ABR) Maintenance of Certificate (MOC) for A.W.

REFERENCES

[1] Schreiber, T., "Measuring information transfer," *Physical review letters* **85**(2), 461 (2000).

[2] Kraskov, A., Stögbauer, H., and Grassberger, P., "Estimating mutual information," *Physical review E* **69**(6), 066138 (2004).

[3] Mozaffari, M. and Yilmaz, Y., "Online multivariate anomaly detection and localization for high-dimensional settings," *arXiv preprint arXiv:1905.07107* (2019).

[4] Mozaffari, M. and Yilmaz, Y., "Online anomaly detection in multivariate settings," in [*2019 IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)*], 1-6, IEEE (2019).

[5] Barnett, L., Barrett, A. B., and Seth, A. K., "Granger causality and transfer entropy are equivalent for Gaussian variables," *Physical review letters* **103**(23), 238701 (2009).

[6] Wismüller, A., DSouza, A. M., Vosoughi, M. A., and Abidin, A. Z., "Large-scale nonlinear Granger causality: A data-driven, multivariate approach to recovering directed networks from short time-series data," *arXiv preprint arXiv:2009.04681* (2020).

[7] DSouza, A. M., Abidin, A. Z., Leistritz, L., and Wismüller, A., "Exploring connectivity with large-scale Granger causality on resting-state functional MRI," *Journal of neuroscience methods* **287**, 68-79 (2017).

[8] Vosoughi, M. A. and Wismüller, A., "Large-scale extended Granger causality for classification of marijuana users from functional MRI," *arXiv preprint arXiv:2101.01832* (2021).

[9] Wismüller, A. and Vosoughi, M. A., "Classification of Schizophrenia from Functional MRI Using Large-scale Extended Granger Causality," (2021). working paper or preprint.

[10] Nattkemper, T. W. and Wismüller, A., "Tumor feature visualization with unsupervised learning," *Medical Image Analysis* **9**(4), 344-351 (2005).
[11] Then Bergh, F., Kümpfel, T., Schumann, E., Held, U., Schwan, M., Blazevic, M., Wismüller, A., Holsboer, F., Yassouridis, A., Uhr, M., et al., "Monthly intravenous methylprednisolone in relapsing-remitting multiple sclerosis-reduction of enhancing lesions, t2 lesion volume and plasma prolactin concentrations," *BMC neurology* **6**, 1–9 (2006).

[12] Wismüller, A., Vietze, F., and Dersch, D. R., "Segmentation with neural networks," in [*Handbook of medical imaging*], 107–126, Academic Press, Inc. (2000).

[13] Leinsinger, G., Schlossbauer, T., Scherr, M., Lange, O., Reiser, M., and Wismüller, A., "Cluster analysis of signal-intensity time course in dynamic breast mri: does unsupervised vector quantization help to evaluate small mammographic lesions?," *European radiology* **16**, 1138–1146 (2006).

[14] Wismüller, A., Vietze, F., Behrends, J., Meyer-Baese, A., Reiser, M., and Ritter, H., "Fully automated biomedical image segmentation by self-organized model adaptation," *Neural Networks* **17**(8-9), 1327–1344 (2004).

[15] Wismüller, A., "Exploratory morphogenesis (XOM): a novel computational framework for self-organization," *Ph.D. thesis*, Technical University of Munich, Department of Electrical and Computer Engineering (2006).

[16] Wismüller, A., Dersch, D. R., Lipinski, B., Hahn, K., and Auer, D., "A neural network approach to functional mri pattern analysis—clustering of time-series by hierarchical vector quantization," in [*ICANN 98: Proceedings of the 8th International Conference on Artificial Neural Networks, Skövde, Sweden, 2–4 September 1998*], 857–862, Springer London (1998).

[17] Wismüller, A., Vietze, F., Dersch, D. R., Behrends, J., Hahn, K., and Ritter, H., "The deformable feature map-a novel neurocomputing algorithm for adaptive plasticity in pattern analysis," *Neurocomputing* **48**(1-4), 107–139 (2002).

[18] Behrends, J., Hoole, P., Leinsinger, G. L., Tillmann, H. G., Hahn, K., Reiser, M., and Wismüller, A., "A segmentation and analysis method for mri data of the human vocal tract," in [*Bildverarbeitung für die Medizin 2003: Algorithmen—Systeme—Anwendungen, Proceedings des Workshops vom 9.–11. März 2003 in Erlangen*], 186–190, Springer Berlin Heidelberg (2003).

[19] Wismüller, A. and Dersch, D., "Neural network computation in biomedical research/neuronale netze in der medizinischen forschung," *Theory in Biosciences-Theorie in den Biowissenschaften* **116**(3) (1997).

[20] Wismüller, A., Vietze, F., Dersch, D. R., Hahn, K., and Ritter, H., "The deformable feature map—adaptive plasticity for function approximation," in [*ICANN 98: Proceedings of the 8th International Conference on Artificial Neural Networks, Skövde, Sweden, 2–4 September 1998*], 123–128, Springer London (1998).

[21] Wismüller, A., "The exploration machine-a novel method for data visualization," in [*International Workshop on Self-Organizing Maps*], 344–352, Springer (2009).

[22] Wismüller, A., "Method, data processing device and computer program product for processing data," (July 28 2009). US Patent 7,567,889.

[23] Meyer-Bäse, A., Jancke, K., Wismüller, A., Foo, S., and Martinetz, T., "Medical image compression using topology-preserving neural networks," *Engineering Applications of Artificial Intelligence* **18**(4), 383–392 (2005).

[24] Wismüller, A., "The exploration machine: a novel method for analyzing high-dimensional data in computer-aided diagnosis," in [*Medical Imaging 2009: Computer-Aided Diagnosis*], **7260**, 143–149, SPIE (2009).

[25] Bunte, K., Hammer, B., Villmann, T., Biehl, M., and Wismüller, A., "Neighbor embedding xom for dimension reduction and visualization," *Neurocomputing* **74**(9), 1340–1350 (2011).

[26] Meyer-Bäse, A., Lange, O., Wismüller, A., and Ritter, H., "Model-free functional mri analysis using topographic independent component analysis," *International journal of neural systems* **14**(04), 217–228 (2004).

[27] WISMÜLLER, A., "Exploration-organized morphogenesis (xom): A general framework for learning by self-organization," *Forschungsberschteil- Institut für Phonetik und Sprachliche Kommunikation der Universität München* "(37), 205–239 (2001).

[28] Wismüller, A., "A computational framework for exploratory data analysis," in [*ESANN*], (2009).

[29] Wismüller, A., "A computational framework for nonlinear dimensionality reduction and clustering," in [*International Workshop on Self-Organizing Maps*], 334–343, Springer Berlin Heidelberg Berlin, Heidelberg (2009).

[30] Leinsinger, G., Teipel, S., Pruessner, J., Hampel, H., Wismueller, A., Born, C., Meindl, T., Flatz, W., Schoenberg, S., and Reiser, M., "Volumetric mri for evaluation of regional pattern and progression of neocortical degeneration in alzheimer's disease; mr-volumetrie zur darstellung von verteilung und zeitlicher abfolge neokortikaler degeneration bei morbus alzheimer," *Der Radiologe* **43** (2003).

[31] Meyer-Bäse, A., Auer, D., and Wismueller, A., "Topographic independent component analysis for fmri signal detection," in [*Proceedings of the International Joint Conference on Neural Networks, 2003.*], 1, 601–605, IEEE (2003).

[32] Wismüller, A., "The exploration machine-a novel method for structure-preserving dimensionality reduction," in [*ESANN*], (2009).

[33] Meyer-Bäse, A., Schlossbauer, T., Lange, O., and Wismüller, A., "Small lesions evaluation based on unsupervised cluster analysis of signal-intensity time courses in dynamic breast mri," *International journal of biomedical imaging* **2009** (2009).

[34] Wismüller, A., Lange, O., Auer, D., and Leinsinger, G., "Model-free functional mri analysis for detecting low-frequency functional connectivity in the human brain," in [*Medical Imaging 2010: Computer-Aided Diagnosis*], **7624**, 473–478, SPIE (2010).

[35] Meyer-Bäse, A., Saalbach, A., Lange, O., and Wismüller, A., "Unsupervised clustering of fmri and mri time series," *Biomedical Signal Processing and Control* **2**(4), 295–310 (2007).

[36] Huber, M. B., Nagarajan, M. B., Leinsinger, G., Eibel, R., Ray, L. A., and Wismüller, A., "Performance of topological texture features to classify fibrotic interstitial lung disease patterns," *Medical Physics* **38**(4), 2035–2044 (2011).

[37] Wismüller, A., Leinsinger, G., Dersch, D., Lange, O., Scherr, M., and Hahn, K., "Neural network image processing in contrast-enhanced mri mammography-unsupervised cluster analysis of signal dynamics time-series by deterministic annealing," in [*RADIOLOGICAL SOC NORTH AMER 20TH AND NORTHAMPTON, STS, EASTON, PA 18042 USA* (2000).

[38] Meyer-Bäse, A., Lange, O., Wismüller, A., and Hurdal, M. K., "Analysis of dynamic susceptibility contrast MRI time series based on unsupervised clustering methods," *IEEE Transactions on Information Technology in Biomedicine* **11**(5), 563–573 (2007).

[39] Wismueller, A., Behrends, J., Hoole, P., Leinsinger, G. L., Reiser, M. F., and Westesson, P.-L., "Human vocal tract analysis by in vivo 3d mri during phonation: a complete system for imaging, quantitative modeling, and speech synthesis," in [*Medical Image Computing and Computer-Assisted Intervention–MICCAI 2008: 11th International Conference, New York, NY, USA, September 6-10, 2008, Proceedings, Part II*], 306–312, Springer Berlin Heidelberg (2008).

[40] Wismüller, A., Lange, O., Dersch, D. R., Hahn, K., and Leinsinger, G. L., "Neural network analysis of dynamic contrast-enhanced mri mammography," in [*Artificial Neural Networks—ICANN 2001: International Conference Vienna, Austria, August 21–25, 2001 Proceedings*], 1000–1005, Springer Berlin Heidelberg (2001).

[41] Wismüller, A., Dersch, D. R., Lipinski, B., Hahn, K., and Auer, D., "Hierarchical clustering of functional mri time-series by deterministic annealing," in [*Medical Data Analysis: First International Symposium, ISMDA 2000 Frankfurt, Germany, September 29–30, 2000 Proceedings*], 49–54, Springer Berlin Heidelberg (2000).

[42] Wismüller, A., "Method and device for representing multichannel image data," (November 2015). US Patent 9,189,846.

[43] Huber, M. B., Bunte, K., Nagarajan, M. B., Biehl, M., Ray, L. A., and Wismüller, A., "Texture feature ranking with relevance learning to classify interstitial lung disease patterns," *Artificial intelligence in medicine* **56**(2), 91–97 (2012).

[44] Wismüller, A., Meyer-Bäse, A., Lange, O., Reiser, M., and Leinsinger, G., "Cluster analysis of dynamic cerebral contrast-enhanced perfusion mri time-series," *Medical Imaging, IEEE Transactions on* **25**(1), 62–73 (2006).

[45] Twellmann, T., Saalbach, A., Muller, C., Nattkemper, T. W., and Wismüller, A., "Detection of suspicious lesions in dynamic contrast enhanced mri data," in [*The 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society*], 1, 454–457, IEEE (2004).
[46] Schlossbauer, T., Leinsinger, G., Wismuller, A., Lange, O., Scherr, M., Meyer-Baese, A., and Reiser, M., "Classification of small contrast enhancing breast lesions in dynamic magnetic resonance imaging using a combination of morphological criteria and dynamic analysis based on unsupervised vector-quantization," *Investigative radiology* 43(1), 56–64 (2008).

[47] Otto, T. D., Meyer-Baese, A., Hurdal, M., Sumners, D., Auer, D., and Wismuller, A., "Model-free functional mri analysis using cluster-based methods," in [*Intelligent Computing: Theory and Applications*], 5103, 17–24, SPIE (2003).

[48] Varini, C., Nattkemper, T. W., Degenhard, A., and Wismuller, A., "Breast mri data analysis by lle," in [*2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No. 04CH37541)*], 3, 2449–2454, IEEE (2004).

[49] Meyer-Baese, A., Lange, O., Wismuller, A., and Leinsinger, G., "Computer-aided diagnosis in breast mri based on ica and unsupervised clustering techniques," in [*Independent Component Analyses, Wavelets, Unsupervised Smart Sensors, and Neural Networks III*], 5818, 38–49, SPIE (2005).

[50] Meyer-Base, A., Pilyugin, S. S., and Wismuller, A., "Stability analysis of a self-organizing neural network with feedforward and feedback dynamics," in [*2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No. 04CH37541)*], 2, 1505–1509, IEEE (2004).

[51] Wismüller, A., Dersch, D., Lipinski, B., Hahn, K., and Auer, D., "Hierarchical clustering of fmri time-series by deterministic annealing," *Neuroimage* 7(4), S593 (1998).

[52] Meyer-Baese, A., Lange, O., Schlossbauer, T., and Wismuller, A., "Computer-aided diagnosis and visualization based on clustering and independent component analysis for breast mri," in [*2008 15th IEEE International Conference on Image Processing*], 3000–3003, IEEE (2008).

[53] Wismüller, A., Meyer-Bäse, A., Lange, O., Schlossbauer, T., Kallergi, M., Reiser, M. F., and Leinsinger, G., "Segmentation and classification of dynamic breast magnetic resonance image data," *Journal of Electronic Imaging* 15(1), 013020–013020 (2006).

[54] Wismüller, A., De, T., Lochmüller, E., Eckstein, F., and Nagarajan, M. B., "Introducing anisotropic minkowski functionals and quantitative anisotropy measures for local structure analysis in biomedical imaging," in [*Medical Imaging 2013: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 8672, 112–119, SPIE (2013).

[55] Bhole, C., Pal, C., Rim, D., and Wismüller, A., "3d segmentation of abdominal ct imagery with graphical models, conditional random fields and learning," *Machine vision and applications* 25, 301–325 (2014).

[56] Nagarajan, M. B., Coan, P., Huber, M. B., Diemoz, P. C., Glaser, C., and Wismüller, A., "Computer-aided diagnosis in phase contrast imaging x-ray computed tomography for quantitative characterization of ex vivo human patellar cartilage," *IEEE Transactions on Biomedical Engineering* 60(10), 2896–2903 (2013).

[57] Wismüller, A., Behrends, J., Dersch, D., Leinsinger, G., Vietze, F., and Hahn, K., "Automatic segmentation of cerebral contours in multispectral mri data sets of the human brain by self-organizing neural networks," in [*Radiology*], 221, 461–461, RADIOLOGICAL SOC NORTH AMERICA 820 JORIE BLVD, OAK BROOK, IL 60523 USA (2001).

[58] Wismüller, A., Meyer-Bäse, A., Lange, O., Auer, D., Reiser, M. F., and Sumners, D., "Model-free functional mri analysis based on unsupervised clustering," *Journal of Biomedical Informatics* 37(1), 10–18 (2004).

[59] Wismüller, A., Vietze, F., Dersch, D., Leinsinger, G., Ritter, H., and Hahn, K., "Adaptive self-organized template matching of the gray-level feature space for automatic segmentation of multispectral mri data of the human brain," *Radiology* 213, 364–364 (1999).

[60] Meyer-Baese, A., Wismüller, A., Lange, O., and Leinsinger, G., "Computer-aided diagnosis in breast mri based on unsupervised clustering techniques," in [*Intelligent Computing: Theory and Applications II*], 5421, 29–37, SPIE (2004).

[61] Nagarajan, M. B., Coan, P., Huber, M. B., Diemoz, P. C., Glaser, C., and Wismüller, A., "Computer-aided diagnosis for phase-contrast x-ray computed tomography: quantitative characterization of human patellar cartilage with high-dimensional geometric features," *Journal of digital imaging* 27, 98–107 (2014).

[62] Pester, B., Leistritz, L., Witte, H., and Wismüller, A., "Exploring effective connectivity by a granger causality approach with embedded dimension reduction," *Biomedical Engineering/Biomedizinische Technik* 58(SI-1-Track-G), 000010151520134172 (2013).

[63] Nagarajan, M. B., Huber, M. B., Schlossbauer, T., Leinsinger, G., Krol, A., and Wismüller, A., "Classification of small lesions on dynamic breast mri: Integrating dimension reduction and out-of-sample extension into cadx methodology," *Artificial intelligence in medicine* 60(1), 65–77 (2014).

[64] Yang, C.-C., Nagarajan, M. B., Huber, M. B., Carballido-Gamio, J., Bauer, J. S., Baum, T. H., Eckstein, F., Lochmüller, E.-M., Majumdar, S., Link, T. M., et al., "Improving bone strength prediction in human proximal femur specimens through geometrical characterization of trabecular bone microarchitecture and support vector regression," *Journal of electronic imaging* 23(1), 013013 (2014).

[65] Wismüller, A., Nagarajan, M. B., Witte, H., Pester, B., and Leistritz, L., "Pair-wise clustering of large scale granger causality index matrices for revealing communities," in [*Medical Imaging 2014: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 9038, 442–449, SPIE (2014).

[66] Wang, X., Nagarajan, M. B., Conover, D., Ning, R., O'Connell, A., and Wismüller, A., "Investigating the use of texture features for analysis of breast lesions on contrast-enhanced cone beam ct," in [*Medical Imaging 2014: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 9038, 507–514, SPIE (2014).

[67] Nagarajan, M. B., De, T., Lochmüller, E.-M., Eckstein, F., and Wismüller, A., "Using anisotropic 3d minkowski functionals for trabecular bone characterization and biomechanical strength prediction in proximal femur specimens," in [*Medical Imaging 2014: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 9038, 499–506, SPIE (2014).

[68] Wismüller, A., Wang, X., DSouza, A. M., and Nagarajan, M. B., "A framework for exploring non-linear functional connectivity and causality in the human brain: mutual connectivity analysis (mca) of resting-state functional mri with convergent cross-mapping and non-metric clustering," *arXiv preprint arXiv:1407.3809 X*.

[69] Meyer-Bäse, A., Pilyugin, S., Wismüller, A., and Foo, S., "Local exponential stability of competitive neural networks with different time scales," *Engineering Applications of Artificial Intelligence* 17(3), 227–232 (2004).

[70] Schmidt, C., Pester, B., Nagarajan, M., Witte, H., Leistritz, L., and Wismüller, A., "Impact of multivariate Granger causality analyses with embedded dimension reduction on network modules," in [*2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society*], 2797–2800, IEEE (2014).

[71] Nagarajan, M. B., Coan, P., Huber, M. B., Diemoz, P. C., and Wismüller, A., "Integrating dimension reduction and out-of-sample extension in automated classification of ex vivo human patellar cartilage on phase contrast x-ray computed tomography," *Plos one* 10(2), e011757 (2015).

[72] Wang, X., Nagarajan, M. B., Abidin, A. Z., DSouza, A., Hobbs, S. K., and Wismüller, A., "Investigating the use of mutual information and non-metric clustering for functional connectivity analysis on resting-state functional mri," in [*Medical Imaging 2015: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 9417, 451–459, SPIE (2015).

[73] Wismüller, A., Abidin, A. Z., D'Souza, A. M., Wang, X., Hobbs, S. K., Leistritz, L., and Nagarajan, M. B., "Nonlinear functional connectivity network recovery in the human brain with mutual connectivity analysis (mca): convergent cross-mapping and non-metric clustering," in [*Medical Imaging 2015: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 9417, 158–166, SPIE (2015).

[74] Nagarajan, M. B., Checefsky, W. A., Abidin, A. Z., Tsai, H., Wang, X., Hobbs, S. K., Bauer, J. S., Baum, T., and Wismüller, A., "Characterizing trabecular bone structure for assessing vertebral fracture risk on volumetric quantitative computed tomography," in [*Medical Imaging 2015: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 9417, 383–390, SPIE (2015).

[75] Abidin, A. Z., Nagarajan, M. B., Checefsky, W. A., Coan, P., Diemoz, P. C., Hobbs, S. K., Huber, M. B., and Wismüller, A., "Volumetric characterization of human patellar cartilage matrix on phase contrast x-ray computed tomography," in [*Medical Imaging 2015: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 9417, 391–399, SPIE (2015).

[76] Wismüller, A., Krol, A., and O'Connell, A., "Method and device for preserving and imaging specimens while retaining information on the spatial orientation of specimens with respect to reference objects," (Aug. 15 2017). US Patent 9,733,167.
<footnote>[77] Pester, B., Schmidt, C., Schmid-Hertel, N., Witte, H., Wismüller, A., and Leistritz, L., "Identification of whole-brain network modules based on a large scale granger causality approach," in [*2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)*], 5380-5383, IEEE (2015).</footnote>

<footnote>[78] Wismüller, A., Abidin, A. Z., DSouza, A. M., and Nagarajan, M. B., "Mutual connectivity analysis (mca) for nonlinear functional connectivity network recovery in the human brain using convergent cross-mapping and non-metric clustering," in [*Advances in Self-Organizing Maps and Learning Vector Quantization: Proceedings of the 11th International Workshop WSOM 2016, Houston, Texas, USA, January 6-8, 2016*], 217-226, Springer International Publishing (2016).</footnote>

<footnote>[79] Checefsky, W. A., Abidin, A. Z., Nagarajan, M. B., Bauer, J. S., Baum, T., and Wismüller, A., "Assessing vertebral fracture risk on volumetric quantitative computed tomography by geometric characterization of trabecular bone structure," in [*Medical Imaging 2016: Computer-Aided Diagnosis*], 9785, 39-46, SPIE (2016).</footnote>

<footnote>[80] Abidin, A. Z., D'Souza, A. M., Nagarajan, M. B., and Wismüller, A., "Investigating changes in brain network properties in hiv-associated neurocognitive disease (hand) using mutual connectivity analysis (mca)," in [*Medical Imaging 2016: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 9788, 485-492, SPIE (2016).</footnote>

<footnote>[81] DSouza, A. M., Abidin, A. Z., Leistritz, L., and Wismüller, A., "Large-scale granger causality analysis on resting-state functional mri," in [*Proceedings of Spie-the International Society for Optical Engineering*], 9788, 97880L (2016).</footnote>

<footnote>[82] Schmidt, C., Pester, B., Schmid-Hertel, N., Witte, H., Wismüller, A., and Leistritz, L., "A multivariate granger causality concept towards full brain functional connectivity," *PloS one* 11(4), e0153105 (2016).</footnote>

<footnote>[83] Abidin, A. Z., Jameson, J., Molthen, R., and Wismüller, A., "Classification of micro-ct images using 3d characterization of bone canal patterns in human osteogenesis imperfecta," in [*Medical Imaging 2017: Computer-Aided Diagnosis*], 10134, 270-277, Spie (2017).</footnote>

<footnote>[84] Abidin, A. Z., Chockanathan, U., DSouza, A. M., Inglise, M., and Wismüller, A., "Using large-scale Granger causality to study changes in brain network properties in the clinically isolated syndrome (CIS) stage of multiple sclerosis," in [*Medical Imaging 2017: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 101371B, International Society for Optics and Photonics (2017).</footnote>

<footnote>[85] DSouza, A. M., Abidin, A. Z., Leistritz, L., and Wismüller, A., "Exploring connectivity with large-scale granger causality on resting-state functional mri," *Journal of neuroscience methods* 287, 68-79 (2017).</footnote>

<footnote>[86] Abidin, A. Z., DSouza, A. M., Nagarajan, M. B., Wang, L., Qiu, X., Schifitto, G., and Wismüller, A., "Alteration of brain network topology in hiv-associated neurocognitive disorder: A novel functional connectivity perspective," *NeuroImage: Clinical* 17, 768-777 (2018).</footnote>

<footnote>[87] Chockanathan, U., Abidin, A. Z., DSouza, A. M., Schifitto, G., and Wismüller, A., "Resilient modular small-world directed brain networks in healthy subjects with large-scale granger causality analysis of resting-state functional mri," in [*Medical Imaging 2018: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 10578, 68-75, SPIE (2018).</footnote>

<footnote>[88] DSouza, A. M., Abidin, A. Z., Chockanathan, U., Schifitto, G., and Wismüller, A., "Mutual connectivity analysis of resting-state functional MRI data with local models," *NeuroImage* 178, 210-223 (2018).</footnote>

<footnote>[89] Chockanathan, U., DSouza, A. M., Abidin, A. Z., Schifitto, G., and Wismüller, A., "Automated diagnosis of HIV-associated neurocognitive disorders using large-scale Granger causality analysis of resting-state functional MRI," *Computers in Biology and Medicine* 106, 24-30 (2019).</footnote>

<footnote>[90] DSouza, A. M., Abidin, A. Z., and Wismüller, A., "Automated identification of thoracic pathology from chest radiographs with enhanced training pipeline," in [*Medical Imaging 2019: Computer-Aided Diagnosis*], 10950, 855-861, SPIE (2019).</footnote>

<footnote>[91] Abidin, A. Z., Dar, I., D'Souza, A. M., Lin, E. P., and Wismüller, A., "Investigating a quantitative radiomics approach for brain tumor classification," in [*Medical imaging 2019: biomedical applications in molecular, structural, and functional imaging*], 10953, 36-45, SPIE (2019).</footnote>

<footnote>[92] DSouza, A. M., Abidin, A. Z., and Wismüller, A., "Classification of autism spectrum disorder from resting-state fmri with mutual connectivity analysis," in [*Medical Imaging 2019: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 10953, 292-299, SPIE (2019).</footnote>

<footnote>[93] DSouza, A. M., Abidin, A. Z., Schifitto, G., and Wismüller, A., "A multivoxel pattern analysis framework with mutual connectivity analysis investigating changes in resting state connectivity in patients with hiv associated neurocognitve disorder," *Magnetic resonance imaging* 62, 121-128 (2019).</footnote>

<footnote>[94] Abidin, A. Z., DSouza, A. M., Schifitto, G., and Wismüller, A., "Detecting cognitive impairment in hiv-infected individuals using mutual connectivity analysis of resting state functional mri," *Journal of neurovirology* 26, 188-200 (2020).</footnote>

<footnote>[95] Wismüller, A. and Stockmaster, L., "A prospective randomized clinical trial for measuring radiology study reporting time on artificial intelligence-based detection of intracranial hemorrhage in emergent care head ct," in [*Medical Imaging 2020: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 11317, 144-150, SPIE (2020).</footnote>

<footnote>[96] Saboksayr, S. S., Foxe, J. J., and Wismüller, A., "Attention-deficit/hyperactivity disorder prediction using graph convolutional networks," in [*Medical imaging 2020: computer-aided diagnosis*], 11314, 430-437, SPIE (2020).</footnote>

<footnote>[97] Wismüller, A., Foxe, J. J., Geha, P., and Saboksayr, S. S., "Large-scale extended Granger causality (lsxgc) for classification of autism spectrum disorder from resting-state functional MRI," in [*Medical Imaging 2020: Computer-Aided Diagnosis*], 11314, 113141Y, International Society for Optics and Photonics (2020).</footnote>

<footnote>[98] Vosoughi, M. A. and Wismuller, A., "Large-scale kernelized granger causality to infer topology of directed graphs with applications to brain networks," *arXiv preprint arXiv:1101.08261* (2020).</footnote>

<footnote>[99] Vosoughi, M. A. and Wismüller, A., "Large-scale extended granger causality for classification of marijuana users from functional mri," in [*Medical Imaging 2021: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 11600, 72-84, SPIE (2021).</footnote>

<footnote>[100] Wismüller, A. and Vosoughi, M. A., "Classification of schizophrenia from functional mri using large-scale extended granger causality," in [*Medical Imaging 2021: Computer-Aided Diagnosis*], 11597, 337-350, SPIE (2021).</footnote>

<footnote>[101] Wismüller, A. and Vosoughi, M. A., "Large-scale augmented granger causality (lsagc) for connectivity analysis in complex systems: From computer simulations to functional mri (fmri)," in [*Medical Imaging 2021: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 11600, 43-57, SPIE (2021).</footnote>

<footnote>[102] Wismüller, A., DSouza, A. M., Vosoughi, M. A., and Abidin, A., "Large-scale nonlinear granger causality for inferring directed dependence from short multivariate time-series data," *Scientific reports* 11(1), 7817 (2021).</footnote>

<footnote>[103] Vosoughi, M. A. and Wismüller, A., "Leveraging pre-images to discover nonlinear relationships in multivariate environments," in [*2021 29th European Signal Processing Conference (EUSIPCO)*], 1456-1460, IEEE (2021).</footnote>

<footnote>[104] Wismüller, A., Vosoughi, M. A., DSouza, A., and Abidin, A. Z., "Exploring directed network connectivity in complex systems using large-scale augmented granger causality (lsagc)," in [*Medical Imaging 2022: Computer-Aided Diagnosis*], 12033, 182-191, SPIE (2022).</footnote>

<footnote>[105] Vosoughi, M. A. and Wismüller, A., "Large-scale kernelized granger causality (lsxgc) for inferring topology of directed graphs in brain networks," in [*Medical Imaging 2022: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 12036, 1203603, SPIE (2022).</footnote>

<footnote>[106] Vosoughi, A., DSouza, A., Abidin, A., and Wismüller, A., "Relation discovery in nonlinearly related large-scale settings," in [*ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)*], 5103-5107, IEEE (2022).</footnote>

<footnote>[107] Wismüller, A., DSouza, A. M., Abidin, A. Z., Ali Vosoughi, M., Gange, C., Cortopassi, I. O., Bozovic, G., Bankier, A. A., Batra, K., Chodakiewitz, Y., et al., "Early-stage covid-19 pandemic observations on pulmonary embolism using nationwide multi-institutional data harvesting," *NPJ Digital Medicine* 5(1), 120 (2022).</footnote>

<footnote>[108] Villmann, T., Seiffert, U., and Wismüller, A., "Theory and applications of neural maps.," in [ESANN], 25-38 (2004).</footnote>

<footnote>[109] DSouza, A. M., Abidin, A. Z., and Wismüller, A., "Classification of autism spectrum disorder from resting-state fmri with mutual connec- tivity analysis," in [*Medical Imaging 2019: Biomedical Applications in Molecular, Structural, and Functional Imaging*], 10953, 109531D, International Society for Optics and Photonics (2019).</footnote>
[110] First, M., Spitzer, R., Gibbon, M., and Williams, J., "Structured clinical interview for dsm-iv axis i disorders (scid). new york, new york state psychiatric institute," *Biometrics Research* (1995).

[111] Whitfield-Gabrieli, S. and Nieto-Castanon, A., "Conn: a functional connectivity toolbox for correlated and anticorrelated brain networks," *Brain connectivity* 2(3), 125-141 (2012).

[112] Wismüller, A., Lange, O., Dersch, D. R., Leinsinger, G. L., Hahn, K., Pütz, B., and Auer, D., "Cluster analysis of biomedical image time-series," *International Journal of Computer Vision* 46(2), 103-128 (2002).

[113] Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., and Joliot, M., "Automated anatomical labeling of activations in spm using a macroscopic anatomical parcellation of the mni MRI single-subject brain," *Neuroimage* 15(1), 273-289 (2002).