This paper introduces a graph-based semi-supervised embedding method as well as its kernelized version for generic classification and recognition tasks. The aim is to combine the merits of flexible manifold embedding and nonlinear graph-based embedding for semi-supervised learning. The proposed linear method will be flexible since it estimates a nonlinear manifold that is the closest one to a linear embedding. The proposed kernelized method will also be flexible since it estimates a kernel-based embedding that is the closest to a nonlinear manifold. In both proposed methods, the nonlinear manifold and the mapping (linear transform for the linear method and the kernel multipliers for the kernelized method) are simultaneously estimated, which overcomes the shortcomings of a cascaded estimation. The dimension of the final embedding obtained by the two proposed methods is not limited to the number of classes. They can be used by any kind of classifiers once the data are embedded into the new subspaces. Unlike nonlinear dimensionality reduction approaches, which suffer from out-of-sample problem, our proposed methods have an obvious advantage that the learnt subspace has a direct out-of-sample extension to novel samples, and are thus easily generalized to the entire high-dimensional input space. We provide extensive experiments on seven public databases in order to study the performance of the proposed methods. These experiments demonstrate much improvement over the state-of-the-art algorithms that are based on label propagation or graph-based semi-supervised embedding.

The human brain is a dynamic networked system that continually reconfigures its functional connectivity patterns over time. Thus, developing approaches able to adequately detect fast brain dynamics is critical. Of particular interest are the methods that analyze the modular structure of brain networks, that is, the presence of clusters of regions that are densely interconnected. In this paper, we propose a novel framework to identify fast modular states that dynamically fluctuate over time during rest and task. We started by demonstrating the feasibility and relevance of this framework using simulated data. Compared with other methods, our algorithm was able to identify the simulated networks with high temporal and spatial accuracies. We further applied the proposed framework on MEG data recorded during a finger movement task, identifying modular states linking somatosensory and primary motor regions. The algorithm was also performed on dense-EEG data recorded during a picture naming task, revealing the subsecond transition between several modular states that relate to visual processing, semantic processing, and language. Next, we tested our method on a dataset of resting-state dense-EEG signals recorded from 124 patients with Parkinson’s disease. Results disclosed brain modular states that differentiate cognitively intact patients, patients with moderate cognitive deficits, and patients with severe cognitive deficits. Our new approach complements classical methods, offering a new way to track the brain modular states, in healthy subjects and patients, on an adequate task-specific timescale.

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