Identification of Optimal and Most Significant Event Related Brain Functional Network

Advancements in network science have facilitated the study of brain communication networks. Existing techniques for identifying event-related brain functional networks (BFNs) often result in fully connected networks. However, determining the optimal and most significant network representation for event-related BFNs is crucial for understanding complex brain networks. The presence of both false and genuine connections in the fully connected network requires network thresholding to eliminate false connections. However, a generalized framework for thresholding in network neuroscience is currently lacking. To address this, we propose four novel methods that leverage network properties, energy, and efficiency to select a generalized threshold level. This threshold serves as the basis for identifying the optimal and most significant event-related BFN. We validate our methods on an openly available emotion dataset and demonstrate their effectiveness in identifying multiple events. Our proposed approach can serve as a versatile thresholding technique to represent the fully connected network as an event-related BFN.


I. INTRODUCTION
T HE network approach provides valuable insights into the brain's complex information processing and underlying mechanisms [1], [2], [3], [4], [5].However, current analysis methods using fully connected networks are complex and lack a clear relation to underlying mechanisms.Eventrelated brain functional networks (BFNs) aid in understanding by identifying event-related neural signatures and regions.Extracting BFNs while preserving core properties is challenging due to hidden spurious connections.Precise measurement of correlated activities is crucial for conceptualizing BFNs.Synchronized activity analysis [6], [7] has been widely used, but existing methods often include both relevant and irrelevant connectivity information.
Thresholding techniques are commonly used to optimize the construction of event-related BFNs.However, there is no consensus on the selection of thresholds, leading to an open problem in neuroscience.Existing techniques include statistical significance [8], [9], arbitrary/random selection, and connected/giant component [10] methods.The impact of these techniques on backbone network properties and their generalizability across different networks remains unclear [8], [9].Fundamental network properties like connectivity and component graph formation can be utilized for thresholding.Efficiency in information exchange [11] has not been studied in the context of threshold formulation and optimal BFN formation.Eigenvalue-based thresholding and optimal BFN formulation, which relate to the network's energy [12], have not been explored to date.
To analyze event-related BFNs, synchronous brain activity is measured and represented as synchronization matrices across different EEG electrodes and frequency bands [13], [14], [15].Phase locking value (PLV) is a crucial metric used to quantify synchronization and phase coherence between signals, facilitating the examination of local and global connections [4], [16], [17], [18], [19], [20].PLV analysis is valuable in studying coordination, communication between brain regions, and analyzing rhythmic activities like neural oscillations.It helps identify abnormal synchronization patterns, aiding the understanding of underlying mechanisms and contributing to cognitive research and neurological studies.While this paper does not focus on a specific measure, PLV [21] is employed for easier generalization.
The primary objective of this study is to establish a comprehensive framework for identifying the most significant and optimal BFN.We focus on emotion-related BFNs as a case study.Existing approaches for emotion detection rely on discriminative features, regions, or frequency bands, but mapping emotion models onto the brain is challenging due to inconsistent results [22], [23], [24].We use phase synchronization as a starting point and create a synchronization measure matrix to capture changes in synchronization strength during an event.Comparing relative synchrony between task and rest activity helps distinguish true synchronization from false synchronization [25].This enables the identification of most reactive pairs (MRPs) that correspond to an event by analyzing dissimilarities between event and rest conditions.Selecting the top 'M' pairs with the largest synchronization difference as MRPs is crucial for forming the event-related BFN.Our proposed methods utilize network properties like component graph, connected graph, energy, and efficiency to form the event-related BFN and determine the optimal value of 'M'.
This paper builds upon previously published works, such as the ones mentioned in the [26], [27], [28], [29].However, the present submission introduces novel methods and presents a multitude of new results.It offers an extensive analysis that includes a comparative evaluation of the performance of different methods, statistical significance assessments, and a comparison with random networks.The journal version also showcases the application of the developed techniques for identifying significant networks related to events and presents classification results using the benchmark Emotion dataset.

II. METHODS
Fig. 1 presents an overview of the proposed framework for identifying and analyzing event-related BFNs.The main goal is to identify the most reactive electrode pairs associated with an event, known as event-related BFNs (highlighted in blocks C and D).The framework involves computing the synchronization measure, PLV, between all electrode pair combinations using 'n' channel EEG data trials.Based on the PLV difference between a reference and an event, the reactive band, highly synchronized regions, and the reactive pairs are identified.The paper discusses four new methods (depicted in Fig. 1) to identify event-related BFNs.The stages depicted as blocks A-E in Fig. 1 are sequentially organized as subsections.

A. Phase Locking Value
The analysis of EEG synchrony involves decomposing the signal's phase using time-frequency decomposition techniques.Wavelet transform is commonly employed to estimate the instantaneous phase of the signal.Compared to the Hilbert transform, wavelet-based methods have been demonstrated to be better suited for analyzing event-related EEG data [30].To enhance the temporal resolution at lower frequencies and improve the frequency resolution at higher frequencies within the desired frequency range, the number of cycles of wavelets (NCW) is increased gradually, as suggested in the study conducted by [31].In this study, we utilize PLV as a measure to examine the degree of phase synchronization between electrode pairs [21].
For a single trial data, phase synchronization measure PLV at a time-frequency instant PLV(t, f ) can be defined as [21], where N denotes the number of samples presented in the time period of analysis.The quantity △ n (t, f ) = i (t, f ) − j (t, f ) represents the instantaneous phase difference between a pair of nodes for the n th trial with i (t, f ) and j (t, f ) correspond to instantaneous phases of the signals in channels 'i' and 'j', respectively.A PLV value of zero indicates no coupling between the two signals, while a PLV value of one signifies complete coupling.

B. Reactive Band
In this study, the term 'reactive band' is used to describe the specific frequency band in the EEG signal that exhibits noteworthy distinctions between the event being analyzed and a reference task.To identify the reactive band, the researchers calculate the difference in Phase Locking Value (dPLV) between the event state and the reference state for each pair of electrodes within the desired frequency range.The dPLV for each event, denoted as dPLV event , is defined as [32]: where PLV event is the PLV during the event period and PLV r e f is the PLV during reference task.We compute dPLV event for all possible combinations of electrode pairs across all tasks using (2).To identify the reactive band, we plot dPLV event Vs frequency.The frequency range exhibiting significant variation in PLV can be determined by examining the average dPLV event .To accomplish this, a search algorithm similar to the approach employed in [32] or a frequency band with high average dPLV event can be utilized.The identified band is specific to the subject and event.By identifying the frequency band with the most significant variations in dPLV event , referred to as the reactive band (RB), we can focus on analyzing dPLV R B (dPLV event in reactive band) specifically within this band.Subsequently, the subsequent analysis in this paper will primarily concentrate on dPLV R B .

C. Synchronized Regions
To detect synchronized regions associated with an event, the total synchrony (TS) strength is used, which measures the level of synchronization across all electrode locations.The strength of a node is determined by summing the weights of all the connections linked to that node, as formally defined by [5].For an EEG system with 'n' channels, the average synchrony strength at the i th node is defined as follows: where, (dPLV R B ) (i, j) is dPLV R B between the electrode pair (i, j).TS i represents the average synchrony strength of node i.
Node strength reflects the level of connectivity of a node with other nodes in the network.Nodes with high TS values indicate highly synchronized nodes associated with the event.These highly synchronized nodes form the active regions related to the event.By visualizing the synchrony image activity using the average node strengths obtained from eqn. (3), the synchronized regions and important locations associated with each event can be depicted [33].To identify highly active regions during single or multiple events, this paper proposes performing an element-wise product of the synchrony strength matrices as follows: • As described in Section II-B, we identify the matrix [dPLV RB ] e i t j for all events and trials (where e i is the event, t j is the trial and the matrix size is n × n).
• Then, we identify the matrix [dPLV e i ] of each event as where, the matrix [dPLV RB ] e i t r corresponds to an event 'i' of the trial 'r ' and .* denotes element wise product operation.
• Finally, we identify the effective matrix [dPLV e (i,j) ] between all event pairs combination using the following dot product operation: • To visualize the regions corresponding to an event, we identify TS of [dPLV e i ] using eqn.(3) and plot its synchrony image activity.
• To visualize the regions responsible for combinations of events, we identify TS of [dPLV e (i,j) ] using eqn.( 3) and plot the synchrony image activity.Eqn.(4) provides the element wise product of all the trials in a single event.High values in the resulting matrix [dPLV e i ] reflects the electrode pairs that are highly active during an event e i .TS of [dPLV e i ] only corresponds to a specific event whereas, ( 5)) performs the element-wise product operation between any two events.High values in the resulting matrix [dPLV e (i,j) ] provides electrode pair combinations that are highly active during both events e i and e j .The TS calculated from [dPLV e (i,j) ] identifies the common locations or regions involved in both events.Furthermore, the element-wise product operation, [dPLV e (i,j) ], can be extended to any number of events, enabling the identification of shared active regions across multiple events.

D. Brain Functional Networks
The identification of the most reactive network within the event-related BFN is crucial for network analysis and understanding the underlying brain mechanisms evoked by the event [34], [35].In this work, we propose the use of MRPs to identify the optimal representation of the event-related network.MRPs are electrode pairs that exhibit significant differences in PLV, pairs with high dPLV R B , between the event and reference task.Selecting the appropriate number of MRPs (M) is essential for forming the event-related BFN.This paper introduces four methods as subsections to address the open problem of determining the optimal number of MRPs for representing an event-related BFN.

1) Connected Graph-BFN (CNT-BFN)::
A connected graph is one where all vertices are interconnected, allowing for a pathway between any pair of vertices.It serves as the fundamental network representation for an event, enabling the assessment of the significance of each node in the network [36], [37].To determine the appropriate number of MRPs for an event utilizing connected graph approach, the procedure involves initializing 'M = n-1' for an EEG system with 'n' channels and checking if the graph is connected.If the graph is connected, 'M' is chosen as the number of MRPs.If not, 'M' is incremented and the process is repeated until a connected graph is formed.The value of 'M' at which the connected graph is achieved is selected as the number of MRPs.

2) Component Graph-BFN (CMP-BFN):
The component graph represents a connected subgraph in an undirected graph, and removing a component can impact the structural integrity of the graph [36].In this method, MRPs are selected based on the event-related component graph.The procedure involves determining 'M' by incrementally increasing it until a connected graph is formed.The number of MRPs is chosen when the resulting network consistently remains as a single component.
3) Eigen Value-BFN (EIG-BFN):: The MRPs selection in this method is based on the Eigenvalue Similarity Index (ESI), which compares the eigenvalues of the event-related BFNs with the complete graph (squared difference).The ESI quantifies the similarity between the matrices [38], with a value Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
of 0 indicating the highest degree of similarity.To determine the optimal number of MRPs, the Eigenvalue Cost Similarity Index (ECSI) is calculated as ECSI = (1 − ESI nor m ) − cost, incorporating the normalized ESI and the cost, where cost is the ratio of selected edges' weight to the total weight in the fully connected network and ESI nor m is the normalized ESI.The optimal number of MRPs is chosen as the one that maximizes the ECSI by evaluating it for different values of M.
4) Global Efficiency-BFN (GLE-BFN):: In this method, the optimal selection of MRPs is based on the global efficiency (GE) of the network.The global efficiency measures the average of the inverse shortest path lengths and represents the information dissemination across the entire network [4], [5], [39].The global cost efficiency (GCE) is calculated as GCE = GE − cost, where cost is the ratio of the total weight of the selected edges to the total weight of the edges in the fully connected network.The optimal number of MRPs 'M' is determined by evaluating the GCE for different values of M and selecting the value that maximizes the GCE.

E. Application
Dimension reduction plays a crucial role in analyzing brain functional networks.While traditional methods like Principal Component Analysis (PCA) provide linear combinations of variables that are difficult to interpret, the proposed event-related BFNs offer a more direct interpretation of the connections.In this paper, we compared the classification performance of multiple events using the proposed event-related BFN features and PCA-reduced dimensions of BFNs.The results highlight the improved interpretability and potential benefits of the proposed approach.

III. DATA AND RESULTS
The framework for identifying event-related BFNs was demonstrated using the DEAP EEG dataset [40].The dataset consists of EEG recordings of 32 participants from 32 electrode locations covering the entire brain, while participants watched 40 music videos designed to elicit specific emotions.The videos were categorized according to the valence-arousal scale into four groups: high valence-high arousal (HVHA), high valence-low arousal (HVLA), low valence-low arousal (LVLA), and low valence-high arousal (LVHA).The EEG data was analyzed within the frequency range of 4-45 Hz using the complex-valued Morlet wavelet transform for time-frequency decomposition.Phase synchrony was computed for all possible pairs of electrodes, resulting in a maximum of 496 edges in the network.The connectivity graph was analyzed for each video using 2-second time epochs with a 0.5-second overlap.
The existing clinical human electrophysiology literature is deficient in providing sufficient details on sample size calculations, as highlighted by [41].To determine the required sample size with 95% confidence, and a margin of error of 5%, assuming a standard deviation of 0.5, we proceed as follows.
Where, SS is Sample size, Z is Z-score, SD is standard deviation and ME is margin of error.In this context, Z = 1.96 (95% confidence), SD = 0.5 (to ensure an adequately large sample size as S D×(1−S D) is maximized when S D = 0.5), and ME = 0.05.Consequently, the calculated sample size is 384.16.Therefore, a minimum sample size of 385 would be necessary.For this study, 390 samples per class were extracted for each subject.With 32 participants, a total of 12,480 samples per class were collected, justifying the chosen sample size.

A. EEG Phase Synchrony Analysis
In this section, we examined the PLV between all possible pairs of brain regions to identify the specific pairs contributing to different emotions.We observed a significant increase in PLV for certain electrode pairs after the stimulus, indicating enhanced neural synchronization, known as event-related synchronization (ERS).This effect was prominent in the upper beta and lower gamma frequency band, referred to as the 'reactive band'.We depicted the intensified synchronization within the reactive band for each emotion using time-frequency plots of PLV for a single electrode pair in Fig. 2a.The electrode pairs showing a significant increase in synchrony were considered responsible for the corresponding emotion.Subsequently, we focused on identifying the reactive band, brain regions with high synchrony, and the specific electrode pairs associated with each emotion.

B. Reactive Band and Synchronized Regions
To identify the narrow frequency range referred to as the reactive band in this paper, the authors computed the difference in PLVs between emotional video events and rest periods.Specifically, for the HVHA, HVLA, LVLA, and LVHA emotion events, we calculated the difference in PLVs at each time epoch compared to the PLV during the rest period.This difference, denoted as dPLV, quantifies the relative change in PLV for each emotion compared to the reference/rest task.For all the emotion events, we computed the (dPLV t ) at any given time epoch using the formula similar to (2) as follows: where, the subscripts e 1 , e 2 , e 3 and e 4 corresponds to emotion task average PLV of their respective emotion epochs (i.e., PLV t H V H A , PLV t H V L A , PLV t L V L A and PLV t L V H A ) and PLV r est is the average PLV during the rest.This equation calculates the difference between the PLV of the emotion event (PLV te i ) and the average PLV during the resting state (PLV r est ).By comparing these dPLV values, one can identify the specific changes in PLV that are unique to each emotion when compared to the resting state.
The average of dPLV t for all electrode pairs for all emotions is computed and one video per emotion class is illustrated in Fig. 2b.Most pair combinations of upper beta and gamma band show high dPLV, and similar dPLV variation is observed in the rest of the video trials.The total dPLV of all pairs and emotions is analyzed to identify the reactive band that corresponds to high dPLV, which is observed in the upper beta and gamma frequency band, as shown in Fig. 2c.In order to determine the reactive band associated with the emotion analysis, a plot of total dPLV against frequency was generated and depicted in Fig. 2d.The analysis revealed that the most prominent variations in PLV were concentrated within the frequency range of 25-35Hz.Consequently, this frequency band was identified as the reactive band for the emotion analysis, forming the basis for further investigations in the study.This reactive band is used for subsequent analysis in the study.
Within the identified reactive band, we computed the PLV difference (dPLV R B ) for all emotions using eqn.(3).We further calculated the total synchrony (TS) across all nodes corresponding to each emotion event.The resulting TS values were used to visualize the active regions associated with each emotion through synchrony image activity, as described in [33].Fig. 3 presents the total synchrony and its corresponding synchrony image activity plots for all four emotions.In Fig. 3 (a), the strength of each electrode pair during each emotion is displayed, with pink-colored regions indicating active regions specific to each emotion.The nodes exhibiting higher TS values are considered the most reactive nodes, as they demonstrate stronger synchrony.Notably, Fig. 3 (d) showcases the important locations identified for all emotion events based on the TS values.
To identify the regions that are active during the processing of multiple emotions, we utilized eqns.( 4) and ( 5).The resulting synchrony image activity plots, displayed in Fig. 3 (b), illustrate the common regions that were identified for various combinations of emotions.These plots are presented using a normalized scale to enhance comprehension.Additionally, the head maps in Fig. 3 (b) provide a visual representation of the shared regions that were identified across different combinations of emotions.
The identified regions shown in Fig. 3 (b) and the important locations depicted in Fig. 3 (c) offer the potential to differentiate certain emotions.However, distinguishing between a large number of emotions becomes challenging when multiple emotions correspond to the same region.For instance, in Fig. 3 (b) and (c), it can be observed that the locations F7 and F8 (frontal homologous sites) play a crucial role in expressing both HVHA and HVLA emotions.Furthermore, the F7 location is also significant in expressing LVLA emotions.Similar similarities and differences among emotions can be observed based on the identified locations and regions.To address this challenge of discriminating between multiple emotions and gain deeper insights, the following section focuses on identifying the MRPs associated with each emotion.

C. Event Related BFN Formulation
1) Most Reactive Pairs: MRPs are electrode pairs and are used to represent specific events and show significant variations in PLV between an event and a reference task.The selection of the top 'M' number of significant pairs with high dPLV R B (difference in PLV between an event and reference task) is crucial for forming an event-related BFN.These selected MRPs represent the most reactive network related to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the event.However, determining the appropriate number of MRPs ('M') to represent an event-related BFN is currently an unresolved issue.
To identify emotion-related BFNs, PLV values in the identified reactive band are analyzed.These values indicate the strength of synchrony between all pairs of nodes during the emotion.By applying eqn.(2), pairs with significant dPLV during each emotion are identified as emotion-specific MRPs.The figures shown in Figure 4 (first three rows) illustrate the top 2.5%, 5%, 7.5%, and 10% MRPs identified for all emotions.The last row in the figure represents the connected graph of each emotion.
2) Threshold Selection: The methods developed in this paper for the identification of BFN lead to the automatic identification of threshold and optimization of the network.These 'M' pairs, as detailed in the section II-D, correspond to each emotion form the emotion-related MRPs.The emotion-related BFN identified using these methods is also presented in Fig. 5.The 'M' value (also, threshold / number of MRPs selected) identified with the proposed four methods for all emotion classes is as follows: In the CNT-BFN, the event-related BFNs are constructed as strongly connected graphs, where high-synchrony electrode pairs form the selected edges.This connected graph allows for a straightforward analysis of events and enables the application of graph network measures.The selection of MRPs depends on the complexity and application of the event analysis.The CMP-BFN method uses the minimum number of MRPs, resulting in fewer but significant connections compared to CNT-BFN.
EIG-BFN and GLE-BFN methods provide optimal choices by identifying the optimal number of MRPs based on selected metrics.They also provide additional information about the similarity and efficiency of event-related BFNs compared to their fully connected networks.These methods serve as generalizing threshold techniques for identifying event-related BFNs.The proposed thresholding techniques, based on network properties, energy, and efficiency, preserve the core network properties while identifying the backbone structure.The event-related BFNs obtained through these methods can be considered signature patterns for the corresponding events.The significance of these identified event-related BFNs is further analyzed in the following subsection.5.The identified emotion-related BFNs for all emotion classes using the proposed methods (the number of connections to form the BFNs were also shown in the figure as 'M'): a) using the connected graph (CNT) approach.b) using the component graph (CMP) approach.c) using the eigen value (EIG) approach.d) using the global efficiency (GLE) approach.

D. Significance and Validation of MRPs
To assess the distinctiveness of the identified event-related BFNs, we conducted statistical significance tests using multiple comparisons for a two-way ANOVA.This test aimed to determine if there were any significant differences in the means across all groups.Following a two-way ANOVA, we have used Tukey-Kramer as a post-hoc test to assess all potential pairwise mean differences, ensuring a balance between Type I and Type II errors.The null hypothesis (H 0 ) stated that the mean of group 1 is equal to the mean of group 2, which is also equal to the mean of group 3, and so on up to group k.In the case of multiple comparisons, we specifically tested the means of each pair of groups.The null hypothesis (H 0 ) for each comparison stated that the mean of group i is equal to the mean of group j, where i and j range from 1 to k and are not equal to each other.
In this paper, multiple events (k in number), the event-related BFNs discrimination significance test is performed as follows: 1) select the dPLV R B values for all the identified event-related BFNs as multiple groups i.e, dPLV R B values of e 1 related MRPs -Group 01, dPLV R B values of e 2 related MRPs -Group 02, . . ., dPLV R B values of e i related MRPs -Group i, . . ., dPLV R B values of e k related MRPs -Group k; where, e i is the event.
2) for each event i (where i = 1, 2, . . ., k), test for the statistical significance of Group i with all other groups.
If, during a specific event i, Group i shows a significant difference compared to all other groups, it indicates that the identified BFN associated with event e i is significant.By observing this pattern for all events, from i = 1 to k, we can conclude that all the event-related BFNs are both significant and distinct.
The entire dataset was used to calculate PLV for each 2-second time epoch with 0.5-second overlap, resulting in 12480 dPLV samples per emotion (a total of 49920 samples, each with 496 dimensions).The mean dPLV of four emotion-related BFNs were considered for discrimination: Group 1 (MRPs of HVHA), Group 2 (MRPs of LVLA), Group 3 (MRPs of HVLA), and Group 4 (MRPs of LVHA).The statistical test results are shown in Figure 6.The results indicate that during HVHA emotion events, Group 1 (MRPs of HVHA) have a statistically significant dPLV when compared to all other groups.Similarly, during emotion events e i , the group of MRPs related to e i is statistically significant compared to its respective groups (where i = 1, 2, 3, and 4. e 1 = HVHA, e 2 = HVLA, e 3 = LVHA, and e 4 = LVLA).Therefore, the BFNs related to specific emotions are highly active and distinctive during their corresponding emotions.
To further demonstrate the significance of the identified event-related BFNs, Eigenvector similarity index and Global Efficiency are analyzed with MRP's selection.Fig. 7, displays Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the metrics associated with the selected MRPs for analysis as well as the metrics for random networks with the same number of connections as the MRPs.To obtain the metrics for random networks, 60 different random networks were generated for each 'M' value, and the corresponding metric was averaged across these networks.Result shows the eigenvector similarity and global efficiency of the identified emotion-related BFNs is high at any 'M' and significant.This confirms that the identified event-related BFNs are not random but representing the events.The consistency of these networks are analyzed in the following by employing a threshold to the network.
Emotion-wise connectivity presence (CP) of the emotionrelated BFNs is computed by defining CP as above.Where, N C M k represents the k number of connections that are matched with emotion-related BFNs.The variables s and T N S represent the sample number and the total number of samples, respectively.The value of N C M k is '1' if there are at least k connections that match exactly with the identified emotionrelated BFN, and '0' otherwise.The eqn. ( 6) defines the CP range as [0, 1] with CP = 1 indicating that all the analyzed samples have at least k exact connection matching with the identified emotion-related BFNs.
The dynamic changes in the identified emotion-related BFNs of CNT-BFN and CMP-BFN were analyzed using all subjects and emotion-related videos as trials (320 trials per emotion).Methods EIG-BFN and GLE-BFN displayed a similar presence as compared to CNT-BFN.Results show that more than 50% of the identified event-related BFNs exists in 60% of total trials.These results indicate that emotion-related BFNs identified with the proposed methods are consistent within the emotion and distinctive across the emotions.The proposed methodology can be easily extended to dynamic analysis of the event processing in the brain.

E. Application
In this section, we compare the classification performance of multiple events using two different sets of features: emotionrelated BFNs and PCA-reduced dimensions of BFNs.A total of 49,920 samples were extracted, with 12,480 samples per emotion.The sample dimension in the reactive band is determined as 32 C 2 = 496.The data was divided into two parts: two-thirds for training and one-third for testing.A Support Vector Machines (SVM) based classifier was employed using the one-against-one approach.By comparing the classification results, we can evaluate the effectiveness of each approach.
For example, the reduction dimension of 196 with EIG-BFN has a classification accuracy of 83.44% against 84.2% obtained with the same PCA reduced dimension.Classification accuracies obtained with the proposed methods CMP-BFN (64), GLE -BFN (212), and CNT-BFN (305) are 72.76%,84.52%, and 86.56% respectively.For the same PCA reduced dimensions 64, 212, and 305, classification results obtained are 73.04%,84.90%, and 87.55% respectively.Findings indicate that events can be distinguished with reasonable accuracy even with a reduced MRP selection.Enhanced accuracy can be achieved by employing other MRP selection methods.Further, comparative performance with the PCA reduced the dimension of BFNs as features show the significance of the selected pairs for representation of the optimal BFN.The proposed methods also provide better insight into the brain regions and their connectivity analysis.
There are numerous studies on EEG-based emotion recognition in the literature as summarized in [2].For performance comparison, we compared our classification results with the classification accuracy reported in [42], [43], and [44] as they employed the same dataset and emotion classes in their analysis.Results stand on par with the aforementioned studies, showcasing comparable accuracy levels and aligning with state-of-the-art standards.

IV. DISCUSSION
In this paper, a novel framework is developed to identify optimal and significant event-related BFNs.The framework is demonstrated using EEG data from the DEAP dataset, but it can be extended to other neuroimaging modalities such as MRI.The identified signature patterns can be utilized for discriminating between disease and control subjects in various disorders.The identification of event-related BFNs has broad applications in fields like ICT, autonomous cars, clinical research, entertainment, brain mapping, BCI, computer-aided diagnosis, and more.
The time-frequency analysis of emotions using PLV reveals a notable level of synchrony in the alpha, beta, and gamma frequency bands.This finding is consistent with previous studies.Furthermore, the identified frequency bands, as depicted in Fig. 2b, align closely with those reported in previous research.However, the predominant increase of synchrony in a band for an emotion task compared to the rest task is mainly observed in the reactive band (frequency range of (25-35)Hz) and is similar to the band identified in [45].With the help of identified synchrony strength in the reactive band, it was possible to identify the event-related regions, active nodes, and also active regions that are common to multiple emotional events.The findings of this study are also consistent with previous research like [1], [15], [22], and [46] in the following aspects.The activation of prefrontal and occipital regions during emotional processing, as identified in this study, is consistent with the findings reported in [46].Moreover, the identified brain regions are similar to those reported in earlier studies that used fMRI [1], [22].The regions that are commonly identified across multiple emotional states are similar to the observations reported in [1] and [15].
The number of MRPs determines the threshold for identifying significant connections in event-related BFNs, allowing for real-time connectivity analysis.MRPs exhibit distinct network patterns for each emotion without overlaps.Accurate mapping of emotions to BFNs enables effective emotion differentiation.Dense and dynamic MRPs confirm the stability of event-related networks, making them suitable for various applications.These stable patterns were used for emotion recognition from EEG data.Single-trial studies demonstrate the consistent identification of emotion-related BFNs using the proposed methods.
The emotion-related component graph remains the same despite increasing the number of MRPs (as in Fig. 4), indicating the stability of the identified component.This finding is consistent with the emotion-related graphs obtained using CMP-BFN (as in section II-D).The component represents a significant and minimal representation of the BFNs.The network's growth as a single component suggests that specific emotion states cannot be processed independently by different functional groups.The component graph serves as the foundation for emotion state processing and can aid in identifying graphs with a perfect match.Increasing the number of MRPs results in more significant connections among important nodes, indicating increased within-network communication.The presence of fewer MRPs in the connected graph of HVLA suggests lower brain activity during relaxation compared to other emotional events.

V. CONCLUSION
Conclusively, it is evident from the results that the event-related BFNs identified using the proposed framework represent the optimal BFNs.Four new methods for threshold selection are proposed in this work.The formulation of BFN relies on network properties, eigen value or global efficiency of the networks.Our study also shows that the eigen value and global efficiency based approaches solve the problem of BFN optimization without leading to random network generation.Classification results on single trial data confirms the practical applicability of the proposed techniques.The results have huge potential in the fields of ICT and clinical diagnosis applications.

Fig. 1 .
Fig. 1.The proposed framework for identifying event-related brain functional networks.

Fig. 2 .
Fig. 2. Time-Frequency mapping of PLV and differential PLV (dPLV): a) Time-frequency mapping of PLV for a selected pair and video of all emotions -shows an increment in synchrony confined to a frequency band.b) dPLV of selected videos -shows the frequency band with high dPLV values.c) The collective dPLV of all pairs across different emotions and the identification of the emotion specific reactive band.d) Average dPLV of all pairs across different emotions and the identified reactive band.

Fig. 3 .
Fig. 3. Total synchrony and synchronized regions: a) Syncrony strength of all electrode pairs for all emotions.b) Active regions within emotions.c) Active regions across emotions.d) Identification of most important locations for all the emotions.

Fig. 4 .
Fig. 4. Changes in the connectivity patterns of all emotions with the increase of MRPs number.
168, and M L V L A = 183 CMP-BFN: M H V H A = 7, M H V L A = 29, M L V H A = 31, and M L V L A = 14 EIG-BFN: M H V H A = 113, M H V L A = 82, M L V H A = 56, and M L V L A = 95 GLE-BFN: M H V H A = 99, M H V L A = 71, M L V H A = 67, and M L V L A = 131

Fig.
Fig.5.The identified emotion-related BFNs for all emotion classes using the proposed methods (the number of connections to form the BFNs were also shown in the figure as 'M'): a) using the connected graph (CNT) approach.b) using the component graph (CMP) approach.c) using the eigen value (EIG) approach.d) using the global efficiency (GLE) approach.

Fig. 7 .
Fig. 7. Comparison of EIG-BFNs and GLE-BFNs with random networks for all emotions.a) (1 − ESI norm ) of BFNs and random networks with MRPs selection and b) GE of BFNs and random networks with MRPs selection.