The blessing of Dimensionality: Feature Selection outperforms functional connectivity-based feature transformation to classify ADHD subjects from EEG patterns of phase synchronisation

Abstract

Functional connectivity (FC) characterizes brain activity from a multivariate set of N brain signals by means of an NxN matrix A, whose elements estimate the dependence within each possible pair of signals. Such matrix can be used as a feature vector for (un)supervised subject classification. Yet if N is large, A is highly dimensional. Little is known on the effect that different strategies to reduce its dimensionality may have on its classification ability. Here, we apply different machine learning algorithms to classify 33 children (age [6-14 years]) into two groups (healthy controls and Attention Deficit Hyperactivity Disorder patients) using EEG FC patterns obtained from two phase synchronisation indices. We found that the classification is highly successful (around 95%) if the whole matrix A is taken into account, and the relevant features are selected using machine learning methods. However, if FC algorithms are applied instead to transform A into a lower dimensionality matrix, the classification rate drops to less than 80%. We conclude that, for the purpose of pattern classification, the relevant features should be selected among the elements of A by using appropriate machine learning algorithms.

Biomagnetic biomarkers for dementia: A pilot multicentre study with a recommended methodological framework for magnetoencephalography

“…Although this may not be the optimal approach in this context (cf. [18]), it has the advantage of selecting a small set of features with a clear‐cut procedure.…”

“…Artifact-related components were removed. MEG data were segmented into 4-second epochs and filtered using a 2000th order FIR band-pass filter with a Hanning window into five bands (with 2 seconds of real data padding added either side): for source analysis: broad band (2-45 Hz), and for connectivity analysis: theta (4-8 Hz), alpha (8-12 Hz), beta (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and gamma (30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45). The data were coregistered to the T1-weighted MRI and the forward model calculated using a realistic single shell head [11].…”

High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality

“…Ideas of the blessing of dimensionality became popular in signal processing, for example in compressed sensing [22,23] or in recovering a vector of signals from corrupted measurements [24], and even in such specific problems as analysis and classification of EEG patterns for attention deficit hyperactivity disorder diagnosis [25].…”

“…It was clearly articulated as a basis of future data mining in the Donoho "Millenium manifesto" [14]. After that, the effects of the blessing of dimensionality were discovered in many applications, for example in face recognition [15], in analysis and separation of mixed data that lie on a union of multiple subspaces from their corrupted observations [16], in multidimensional cluster analysis [17], in learning large Gaussian mixtures [18], in correction of errors of multidimensonal machine learning systems [19], in evaluation of statistical parameters [20], and in the development of generalized principal component analysis that provides low-rank estimates of the natural parameters by projecting the saturated model parameters [21].Ideas of the blessing of dimensionality became popular in signal processing, for example in compressed sensing [22,23] or in recovering a vector of signals from corrupted measurements [24], and even in such specific problems as analysis and classification of EEG patterns for attention deficit hyperactivity disorder diagnosis [25].There exist exponentially large sets of pairwise almost orthogonal vectors ('quasiorthogonal' bases, [26]) in Euclidean space. It was noticed in the analysis of several n-dimensional random vectors drawn from the standard Gaussian distribution with zero mean and identity covariance matrix, that all the rays from the origin to the data points have approximately equal length, are nearly orthogonal and the distances between data points are all about √ 2 times larger [27].…”

Non-stationary Group-Level Connectivity Analysis for Enhanced Interpretability of Oddball Tasks

“…Despite the evident impact of channel-level connectivity analysis, it lacks a standard analytic framework and supplies deficient spatial resolution (Bathelt et al, 2013), resulting in several limitations: (i) a growing need for connectivity measures extracted from high-resolution EEG data to provide a tradeoff between local specialization and global integration of brain tasks, assuring caution for the interpretation of connectivity estimates at the same time (Bastos and Schoffelen, 2016); (ii) extraction/modeling of informative graph-based neuromarkers from all feasible inter-channel interactions, which may result in high dimensional connectivity matrices with redundant or worthless features, hindering a proper data analysis because of noisy links (not to mention computational cost issues) (Van Wijk et al, 2010;De Vico Fallani et al, 2014); and, lastly, (iii) EEG non-stationarity, which makes the brain networks intrinsically and dramatically change over time, degrading the assessment of pairwise interactions typically operationalized through the full or partial correlation/information between all pairs of regional time series (Pereda et al, 2018).…”