Parametric Sparse Coding of Brain Connectivity Graph Signals for Schizophrenic EEG data

Graph Signal (GS) representations of multi-variable brain recordings offer a synergistic integration between regional brain activity and global communications inside the human brain. The recent advent of Graph Signal Processing tools provides novel mathematical structures to analyze the brain GSs, thus offering a unique opportunity to trace the information flow inside the brain and identify essential biomarkers. However, brain recording’s intrinsically noisy and high-dimensional nature often leads to the misidentification of critical biomarkers and increased computational requirements. Sparsity-based approaches provide data compression and noise reduction by capturing the most significant information using a limited number of non-zero coefficients from an overcomplete basis dictionary. But their application is limited only to regular data structures. This study proposes a framework for sparse representation of the brain GSs that are defined on the irregular connectivity graph structure. The proposed framework incorporates the connectivity information into the basis dictionary in the form of the normalized Laplacian of the underlying weighted network. Specifically, the proposed parametric dictionary consists of multiple concatenated sub-dictionaries, each being a polynomial of the graph Laplacian matrix. This graph-structure-aware sparse representation framework serves the conflicting requirements of both sparsity and discriminability of the resulting sparse codes. The proposed framework is implemented on open-source Schizophrenic Electroencephalogram data, where a 0.0296 sparse reconstruction RMS error is achieved for only 5 non-zero coefficients. Further, utilizing the sparse codes for normal and Schizophrenic detection using the XGBoost model, 10 -fold cross-validated detection accuracies of $88.43 \%$ and $\mathbf{9 5 . 5 9 \%}$ are achieved for 5 and 8 non-zero coefficients, respectively.