Optimal Number of Clusters by Measuring Similarity Among Topographies for Spatio-Temporal ERP Analysis.

Averaging amplitudes over consecutive time samples (i.e., time window) is widely used to calculate the peak amplitude of event-related potentials (ERPs). Cluster analysis of the spatio-temporal ERP data is a promising tool to determine the time window of an ERP of interest. However, determining an appropriate number of clusters to optimally represent ERPs is still challenging. Here, we develop a new method to estimate the optimal number of clusters utilizing consensus clustering. Various polarity dependent clustering methods, namely, k-means, hierarchical clustering, fuzzy c-means, self-organizing map, spectral clustering, and Gaussian mixture model, are used to configure consensus clustering after assessing them individually. When a range of clusters is applied many times, the optimal number of clusters should correspond to the expectation, which is the average of the obtained mean inner-similarities of estimated time windows across all conditions and groups converge in the satisfactory thresholds. In order to assess our method, the proposed method has been applied to simulated data and prospective memory experiment ERP data aimed to qualify N2 and P3, and N300 and prospective positivity components, respectively. The results of determining the optimal number of clusters meet at six cluster maps for both ERP data. In addition, our results revealed that the proposed method could be reliably applied to ERP data to determine the appropriate time window for the ERP of interest when the measurement interval is not accurately defined.

Assessment of nonnegative matrix factorization algorithms for electroencephalography spectral analysis.

BACKGROUND: Nonnegative matrix factorization (NMF) has been successfully used for electroencephalography (EEG) spectral analysis. Since NMF was proposed in the 1990s, many adaptive algorithms have been developed. However, the performance of their use in EEG data analysis has not been fully compared. Here, we provide a comparison of four NMF algorithms in terms of accuracy of estimation, stability (repeatability of the results) and time complexity of algorithms with simulated data. In the practical application of NMF algorithms, stability plays an important role, which was an emphasis in the comparison. A Hierarchical clustering algorithm was implemented to evaluate the stability of NMF algorithms. RESULTS: In simulation-based comprehensive analysis of fit, stability, accuracy of estimation and time complexity, hierarchical alternating least squares (HALS) low-rank NMF algorithm (lraNMF_HALS) outperformed the other three NMF algorithms. In the application of lraNMF_HALS for real resting-state EEG data analysis, stable and interpretable features were extracted. CONCLUSION: Based on the results of assessment, our recommendation is to use lraNMF_HALS, providing the most accurate and robust estimation.

Determination of the Time Window of Event-Related Potential Using Multiple-Set Consensus Clustering.

Clustering is a promising tool for grouping the sequence of similar time-points aimed to identify the attention blocks in spatiotemporal event-related potentials (ERPs) analysis. It is most likely to elicit the appropriate time window for ERP of interest if a suitable clustering method is applied to spatiotemporal ERP. However, how to reliably estimate a proper time window from entire individual subjects' data is still challenging. In this study, we developed a novel multiset consensus clustering method in which several clustering results of multiple subjects were combined to retrieve the best fitted clustering for all the subjects within a group. Then, the obtained clustering was processed by a newly proposed time-window detection method to determine the most suitable time window for identifying the ERP of interest in each condition/group. Applying the proposed method to the simulated ERP data and real data indicated that the brain responses from the individual subjects can be collected to determine a reliable time window for different conditions/groups. Our results revealed more precise time windows to identify N2 and P3 components in the simulated data compared to the state-of-the-art methods. Additionally, our proposed method achieved more robust performance and outperformed statistical analysis results in the real data for N300 and prospective positivity components. To conclude, the proposed method successfully estimates the time window for ERP of interest by processing the individual data, offering new venues for spatiotemporal ERP processing.