The brain is an inherently dynamic system which both resting-state networks (Hansen et al., 2015) and networks connected to executive cognition requires dynamic reconfiguration of highly evolving networks of brain areas that interact via transient complexity patterns (Bassett et al., 2011; Braun et al., 2015a). To investigate how the brain functionality changes over experimental time, time-varying graphs should be computed as networks that evolve over time with fixed number of nodes but links that change over time. The dynamic approach of brain connectivity is explored by adopting a time-window over experimental time and constructs quasi-static connectivity graphs from the temporal signal segments enclosed within this time-window where various network metrics can be estimated for each window leading to network metric time series (NMTS) (Dimitriadis et al., 2010a, 2012a, 2013a,b, 2015a,c; Sporns, 2011, 2014).

Both static and dynamic graphs can be analyzed either as binary or weighted networks after first applying a thresholding criterion. With both full binary and weighted graphs, every pair of brain areas is directly connected. Many researchers have argued that full-weighted graphs are not “true” networks since brain areas are inter-connected via sparse anatomical connections (Sporns, 2011). A recent study supported that weighted graphs are also less computationally efficient, when someone attempts to analyze large-scale networks like the well-known voxel-based functional connectivity networks (Telesford et al., 2011). Also the overrepresentation of functional connections between brain areas added difficulties to the extraction of significant topological information (Serrano et al., 2009).

To work either with binary or weighted graphs, a large number of topological thresholding schemes can be applied. The list of available thresholding schemes can be divided into arbitrary and data-driven methods. Arbitrary thresholding schemes includes (1) the preservation of the same degree (number of connections per node), k, for each graph, so that the subsequently derived network metrics are comparable across graphs/subjects/conditions (Milo et al., 2002; Sporns and Zwi, 2004; Stam et al., 2007a; Dimitriadis et al., 2009; Micheloyannis et al., 2009), (2) the maintenance of a specific ratio of the strongest edges (sparsity) (Stam et al., 2007a; Rubinov et al., 2009) and (3) the absolute threshold up to a predefined value (between 0 and 1). Each approach has both advantages and disadvantages. The aforementioned thresholding schemes even though are simplified, adds bias for group and task comparisons and moreover, reduce the possibility of the reproducibility of the findings across studies from different research groups but also within the same research group with the extension of recording sessions. Absolute thresholds set a value between 0 and 1 above which the strength of connections survived while below are excluded from further analysis and are set to 0. Proportional thresholds employ a % percentage of the strongest connections (edges), like the top 10% of weighted values in the network. The preservation of the same degree, k, for each graph is more meaningful compared to the two aforementioned approaches since it picks equiprobable strong and weak weights but also assumed that networks have the same mean degree across group and tasks.

Even though connectedness in a node level between groups and conditions could be informative, it restricts both the interpretation and the comparison between various graph measures that vary with the degree (Alexander-Bloch et al., 2013). Additionally, absolute thresholding scheme divides the weights of connections into two groups, weak and strong connections emphasizing either the weak or the strong (van Wijk et al., 2010). A number of studies attempted to diminish the effect and the reproducibility of their results due to the adopted thresholding scheme by presenting various network measures over traditional cumulative thresholding. Specifically, for absolute, sparsity (proportional) and mean degree thresholding schemes, they demonstrated their network-oriented results over a range of values (0–1 for absolute, 2–40% for sparsity, 1-(N-1) for degree preservation where N denotes the number of nodes). Based on correlation coefficient r, a range of thresholds has been applied, e.g., r = 0.1 (Buckner et al., 2009) and r = 0.8 (Tomasi and Volkow, 2010). For sparsity, a range of proportional thresholds have been presented, e.g., from 5 to 40% (e.g., Fornito et al., 2011) or for a narrower range of values in Alzheimer's disease (Stam et al., 2009) and in schizophrenia (Micheloyannis et al., 2006). One of the very first studies that presented network metrics over a range of degree was a MEG resting-state study at both control and Alzheimer's disease group (Stam et al., 2007a) and also in EEG sleep study (Dimitriadis et al., 2009). A few researchers attempted to present their results in narrower range of thresholds in order to support the insensitivity of their results to the arbitrary choice of the threshold (e.g., Cole et al., 2013, 2014, top 2–10%; van den Heuvel et al., 2009, r = 0.3–0.5). However, the above approach will lead to unstable results if the adopted network properties are sensitive to a large range of thresholds, especially in the case where group or task differences in terms of network metrics are reversed within a range of a threshold (e.g., Scheinost et al., 2015). An alternative solution to traditional cumulative thresholding scheme is the alternative windowed thresholding scheme (Bassett et al., 2012) where the connections were binning into 100 bins and finally 100 graphs were created where the first graph encapsulated the 1% of strongest connections, the second graph the 1% of the next strongest connections etc. (Bassett et al., 2012). Finally, a few studies fairly demonstrated their results, e.g., hub detection that is consistent over a range of absolute thresholds (Buckner et al., 2009).

According to our knowledge, two data-driven thresholding schemes exist in the literature. The first one has as an objective criterion to maximize the formula of cost-efficiency (cost efficiency = global efficiency − cost) of a network vs. its cost (the ratio of the existing edges divided by the total number of possible edges) that typically range between the upper and lower limits of an economical small-world network (Bassett et al., 2008). The basic drawback of this method is that it accumulates edges based on their strength and applying an iteratively absolute threshold searching approach from 0 to 1 without taking into consideration any topological constraint. Additionally, the aforementioned approach completely separate weak from strong connections where in some diseases studying the mixture of both strong and weak connections can improve the designing of reliable connectomic biomarkers (Bassett et al., 2012). The second data-driven thresholding scheme based on the notion of shortest path lengths (SPL) and assumes that the information between brain areas flows via the shortest pathways (Dimitriadis et al., 2010a).

Minimal spanning tree (MST) is a unique representation of a functional brain network and it is a unique acyclic subgraph that connects all nodes and maximizes the synchronization between brain areas. MST has already been applied in human brain networks where both trivial network metrics but also tree-oriented properties have been estimated based on the unique sparse MST-representation of a weighted graph (Vourkas et al., 2014; for a review see Stam, 2014; Stam et al., 2014).

Current approach attempted to maximize the information flow over the network vs. the cost by selecting the connections via the notion of orthogonal minimal spanning trees (OMSTs). OMSTs based on the notion of sampling the full-weighted brain network over consecutive rounds of MST that are orthogonal to each other. Practically, we extracted the 1st MST, then we zeroing their connections and we estimate the 2nd MST based on the rest of the network. With this iteratively approach, we can get orthogonal MST and topologically filtering brain network by optimizing the global efficiency of the network constrained by the cost of keeping its connections.

Therefore, this study sought to introduce a novel data-driven thresholding scheme based on OMSTs that will advance the ability of research neuroimaging centers to compare and analyse large imaging connectomes/connectomics under a common topological filtering framework. This will enforce our ability to compare results from different studies based on the same imaging method and condition and also between different imaging methods in a multimodal imaging approach.

Test-retest reliability of the network metrics derived from functional networks is of significant value in the neuroscience community (Zuo et al., 2012, 2014; Zuo and Xing, 2014; Chen et al., 2015). Many researchers world-wide presented connectomic biomarkers for various brain disorders/diseases and for that reason, their reproducibility should be explored (Kaiser, 2013; Dimitriadis et al., 2015b,c,d, 2016a,b). The choice of the appropriate preprocessing steps to achieve reproducible measurements is more than significant. One significant preprocessing step in the choice of topological filtering scheme to untangle the “true” backbone of a brain network. Therefore, we validated the proposed data-driven topological filtering OMSTs method and the rest in terms of intra-class correlation (ICC) of basic network metrics derived from static functional networks estimated from resting-state BOLD activity. For that reason, we employed an open fMRI database from a single-subject that has been scanned 100 times.

To validate its potentiality, a large EEG study of resting-state activity was used in order to increase the recognition accuracy of each subject over the rest of the database based on nodal network metric time series (nNMTS) using well-known network metrics (Dimitriadis et al., 2010a). The EEG database is a free available dataset repository as part of PhysioNet BCI Database¹. The whole analysis based on dynamic functional brain connectivity and a set of nNMTS over frequencies and topology (EEG sensors) which were used as the unique brain fingerprinting of each subject (Finn et al., 2015). Our method was compared to various thresholding schemes based on the recognition accuracy of each individual based on the nNMTS signature to the rest of cohort. Additionally, since the EEG dataset based on a single-trial, we accessed the reliability of the current method and the derived network metrics from a free available dataset of a case study of fMRI resting-state recordings repeated over 100 scans (Poldrack et al., 2015). The fMRI dataset from the single-case long term study can be downloaded and preprocessed with available code from the author's website².

On this section, we described both free available neuroimaging datasets (EEG and fMRI) with the adopted preprocessing steps. The main goal with EEG resting-state dataset was to demonstrate the superiority of the proposed topological filtering scheme to filter dynamic networks using as validation criterion the recognition accuracy of each subject to the rest of the cohort. Using multiple scans of fMRI, we demonstrated the superiority of the topological filtering method to increase the reliability of trivial network metrics across scans.

For each of the aforementioned thresholding schemes (absolute, proportional, mean degree, shortest-path edges selection and the maximization of global cost efficiency) and the proposed one based on OMSTs, we estimated nodal global efficiency across time based on the thresholding versions of dynamic 4D ^TViPLV arrays across subjects and frequency bands. This approach results to subject and frequency specific nNMTS^GE from GE which will then be used as possible brain fingerprinting features.

To access the recognition accuracy of each node and network metric over the eight frequency bands, we split each nNMTS^GE into two equal segments and we employed Wald-Wolfowitz (WW) test as a similarity index to each target nNMTS^GE from the database. On the next section, we described how WW test was used.

All the threshold schemes were implemented in an in-house software toolbox using MATLAB environment and will be available from the author's website after acceptance of this manuscript. http://users.auth.gr/~stdimitr/software.html, from researchgate (https://www.researchgate.net/profile/Stavros_Dimitriadis), and from the github website (https://github.com/stdimitr/topological_filtering_networks). A webpage in scholarpedia is under construction for the promotion of the whole approach.

Last years, an increasing amount of human brain research based on functional imaging methods (EEG/MEG/fMRI) have adopted a more dynamic approach for exploring how brain connectivity fluctuates at resting-state and during tasks (Laufs et al., 2003; Mantini et al., 2007; Chang and Glover, 2010; Dimitriadis et al., 2010a, 2012a,c, 2013a,b, 2015a,b,c,d, 2016a,b; Bassett et al., 2011; Allen et al., 2012; Handwerker et al., 2012; Ioannides et al., 2012; Hutchison et al., 2013; Liu and Duyn, 2013; Braun et al., 2015b; Mylonas et al., 2015; Toppi et al., 2015; Yang and Lin, 2015; Calhoun and Adali, 2016, for reviews see Calhoun et al., 2014). Innovative techniques for manipulating the large number of graphs estimated via dynamic functional connectivity analysis (DFCA) have just arisen (Sakoğlu et al., 2010; Dimitriadis et al., 2013a, 2015a, 2016b; Leonardi et al., 2013; Keilholz, 2014; Leonardi and Van De Ville, 2014; Betzel et al., 2016). A crucial step in brain connectivity analysis is the application of a statistical thresholding scheme to capture the most significant connections within a graph and also the selection of a topological filtering where the most significant connections can be extracted leading to meaningful topologies. Especially, in the case of (DFCA), a data-driven approach is important in order to avoid any pitfalls in the interpretations of the results and also to enhance the reproducibility of the results of a current study under a common data-driven thresholding framework.

The majority of neuroimaging studies that followed a connectivity analysis (static or dynamic) adopted an arbitrary threshold that in many cases can vary the results in terms of group comparisons. Additionally, it restricts the usability of the results across different research groups but also within the group by adding more samples in the initial analysis. The instability of the functional network measures over different thresholds have been recently demonstrated (Garrison et al., 2015). With the increased number of open neuroimaging repositories (Sharing the wealth:Brain Imaging Repositories in 2015), it is crucial to adopt more sophisticated data-driven techniques within brain network analysis in order to aggregate the effort given by hundreds of research groups all over the world for a better understanding of how the brain functions.

In the present study, we demonstrated the superiority of a novel data-driven thresholding scheme based on OMSTs compared to the rest well-known thresholds to accurate identifies individuals in a large EEG database. The recognition accuracy was the highest in both eyes-open and eyes-closed condition compared to the rest of thresholding schemes. As unique features of this EEG biometric evaluation approach, a set of nNMTS^GE were used across the sensors and frequency bands. The location of the selected nNMTS^GE highly overlapped with the topography of the EEG spectrum related to the default mode network (DMN) of the brain (Chen et al., 2008). In δ band, there is a more prefrontal selection of the NMTS^GE and a more fronto-central for the θ frequency. In both α₁ and α₂ selected sensors were distributed at posterior parietal brain regions. In both β₁ selected sensors were located at posterior parieto-occipital brain regions while in β₂, γ₁, and γ₂ selected sensors were distributed anteriorly (Figure 8). Overall, the set of NMTS^GE from the whole repertoire of the eight frequency bands can be seen as the unique subject-specific brain signature of the DMN.

MST is a unique acyclic subgraph that connects all nodes with a minimal cost and also maximizes the information flow between brain regions since it captures the backbone of all shortest path lengths. One of the basic disadvantages of the MST is that it gives a sparse representation of a full-weighted functional graph. Especially, for a brain network up to or larger than 100 nodes, MST-oriented representation of the functional brain network is too sparse to get robust network metrics for characterizing the connectivity matrix. For that reason, the method of OMSTs with the objective criterion of maximizing the information flow with the restriction of the wiring cost presents a more robust approach. Here, we demonstrated the superiority of OMSTs over the existing methods of an EEG dynamic functional connectivity analysis at resting-state with the main scope to maximizing the identification accuracy within a database.

The basic explanation of the superiority of the proposed algorithm over the rest and especially the data-driven techniques (Bassett and Bullmore, 2006) is the sampling of weighted connections with main constrain to connect all the nodes with minimal cost without ranking connections according to their strength. The algorithm presented by Bassett et al., searches over the network by windowing the range of the weights which are often between 0 and 1 starting from 0 up to 1 with a small stepping criterion (e.g., 0.01; Bassett and Bullmore, 2006). This option separates strongest from weakest connections obliviously also if the network is connected. It seems that MST and especially multiple rounds of OMSTs is a reliable sampling approach for the selection of the subgraph that better described the functionality of the studying brain topology. A recent study combined MST with an arbitrary proportional threshold to get the sparse representations of brain networks (Song et al., 2015).

One significant observation of our method is that using the penalty term of wiring cost, part of information flows via non-shortest path lengths compared to the notion of shortest path lengths (see Figure 6; Van Mieghem and Wang, 2009; Dimitriadis et al., 2010a, 2012b). Our previous data-driven algorithm based on shortest-path lengths have already been reported as the Union of Shortest Path Trees (USPL; Van Mieghem and Wang, 2009) and applied to functional brain networks (Meier et al., 2015).

It is important to mention here that our main goal was to present the superiority of our method overall the existing thresholding schemes in a large EEG database by adopting a dynamic functional connectivity analysis. The objective criterion to validate the proposed data-driven thresholding scheme based on OMSTs was the identification accuracy of each individual further supporting recent efforts over functional connectome brain fingerprinting (Finn et al., 2015). Additionally, previous attempts have already demonstrated high classification accuracy based on power spectrum and coherence on static graphs on the same database (La Rocca et al., 2014). Our approach improves current efforts over EEG-based biometric systems by extracting meaningful temporal graph-oriented features supporting and validating the proposed data-driven threshold algorithm (OMSTs) via the notion of brain fingerprinting. Finally, we demonstrated its temporal stability in terms of recognition accuracy and the number of selected features over three different widths of temporal windows.

Finally, the proposed data-driven thresholding scheme based on OMSTs demonstrates the need of a data-driven approach for topological filtering of brain networks. Complementary, it shows that sampling the connections in weighted brain network using orthogonal MSTs is a superior approach compared to taking into consideration only their strength (Bassett and Bullmore, 2006). Additionally, the wiring cost is a significant attribute of a brain network while it was proved its key role to the evolution of hierarchy and modularity by its direct link to sparsity (Mengistu et al., 2016). Further studies should validate the superiority of this approach to multimodal imaging and to the design of reliable connectomic biomarkers for various brain disorders/diseases.

The analysis of functional brain networks derived from resting-state recordings or task-related via graph theory has been proven to be a powerful tool to characterize both globally and locally the architecture of functional connectivity in the human brain (Van Dijk et al., 2010). Due to the increment of research studies that expanded their results based on network analysis to daily clinical use (Savitz et al., 2013), it is significant to provide data-driven solutions of preprocessing steps in order to increase the reproducibility of the network metrics (Zuo and Xing, 2014; Zuo et al., 2014; Chen et al., 2015). Here, we investigated how the different topological filtering scheme (data-driven vs. arbitrary algorithms) can alter the reliability of basic network metrics estimated via ICC score. Apart from the choice of topological filtering scheme of functional brain network, the selection of the connectivity estimator can also affect the reliability of the network metrics (Garcés et al., 2016). The effect of both the connectivity estimator and the selection of filtering schemes has been recently demonstrated (Jalili, 2016) and we will present the reproducibility of network metrics based on brain connectivity on the source level with both EEG and MEG recordings in a next upcoming journal paper.

Employing a second fMRI case study dataset and following a static network analysis, we demonstrated the superiority of the proposed topological filtering scheme to increase the test-retest reliability of the network metrics across different scans/sessions (Deuker et al., 2009). The reliability of network metrics across trials is an important issue in order to make general conclusions for a targeted group (e.g., Alzheimer) or a task (e.g., resting-state, n-back memory etc.).

To further validate the proposed thresholding scheme over the highly used thresholds, it is important to apply it also on EEG and MEG source level (Ioannides et al., 2012) and also to fMRI experimental paradigms where the spatial resolution is higher compared to the scalp-recorded EEG activity. Additionally, it is significant to compare nNMTS between resting-state and tasks in both control and disease groups (Damaraju et al., 2014) but also during the developmental time (Dimitriadis et al., 2015a). Finally, by adopting multivariate estimators like Granger causality or partial direct coherence (Omidvarnia et al., 2013) in a dynamic fashion with the proposed algorithm may further shed light on the importance of data-driven approaches in neuroimaging.

It will be interesting in the future to generate brain network models of the human connectome (Betzel et al., 2016) based on the notion of OMSTs using a distance geometric penalty (e.g., Euclidean distance between ROIs in 3-dimensional space). It seems that geometry is crucial in the studying of structural connectome (Roberts et al., 2016), an observation that should be further validated if it contributes to the network topology in functional connectome at source space.

We showed that a data-driven thresholding scheme based on OMSTs implies a unique description of each individual brain activity based on the notion of nodal network metrics times series and namely the global efficiency (nNMTS^GE). The proposed technique overcame the rest of highly used thresholding schemes in terms of human brain distinctiveness employing a dynamic functional connectivity approach. Moreover, we demonstrated its effectiveness to increase the reliability of network metrics in a multi-scan fMRI dataset. The novel method has practical significance over the existing thresholding schemes, in that it represents a model-free framework for identifying the significant connections over which the information flow between the brain areas is maximized with the constraints of the wiring cost. Current approach could be of greater neuroinformatic importance especially in the direction of reproducibility of brain connectivity results across different data repositories based on various imaging methods like EEG,MEG and fMRI. Especially, in a simultaneous recording of different imaging methods (MEG-EEG and EEG-fMRI) the proposed algorithm could be a common framework to compare dynamic FCGs estimated from two different modalities. The proposed method deals with a data-driven filtering of (chro)/(co)nnectomics.

Conception of the research: SD; Methods and design: SD; Data analysis (SD, CS); Drafting the manuscript: SD; Critical revision of the manuscript: IT, DL; Every author read and approved the final version of the manuscript.

This study was supported by the National Centre for Mental Health (NCMH) at Cardiff University. We would like to acknowledge Cardiff RCUK funding scheme.