Decoding the Encoding of Functional Brain Networks: an fMRI Classification Comparison of Non-negative Matrix Factorization (NMF), Independent Component Analysis (ICA), and Sparse Coding Algorithms

Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet mathematical constraints such as sparse coding and positivity both provide alternate biologically-plausible frameworks for generating brain networks. Non-negative Matrix Factorization (NMF) would suppress negative BOLD signal by enforcing positivity. Spatial sparse coding algorithms ($L1$ Regularized Learning and K-SVD) would impose local specialization and a discouragement of multitasking, where the total observed activity in a single voxel originates from a restricted number of possible brain networks. The assumptions of independence, positivity, and sparsity to encode task-related brain networks are compared; the resulting brain networks for different constraints are used as basis functions to encode the observed functional activity at a given time point. These encodings are decoded using machine learning to compare both the algorithms and their assumptions, using the time series weights to predict whether a subject is viewing a video, listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects. For classifying cognitive activity, the sparse coding algorithm of $L1$ Regularized Learning consistently outperformed 4 variations of ICA across different numbers of networks and noise levels (p$<$0.001). The NMF algorithms, which suppressed negative BOLD signal, had the poorest accuracy. Within each algorithm, encodings using sparser spatial networks (containing more zero-valued voxels) had higher classification accuracy (p$<$0.001). The success of sparse coding algorithms may suggest that algorithms which enforce sparse coding, discourage multitasking, and promote local specialization may capture better the underlying source processes than those which allow inexhaustible local processes such as ICA

Automatic Localization of Epileptic Spikes in EEGs of Children with Infantile Spasms

Infantile Spasms (ISS) characterized by electroencephalogram (EEG) recordings exhibiting hypsarrythmia (HYPS) are a severe form of epilepsy. Many clinicians have been trying to improve ISS outcomes; however, quantification of discharges from hypsarrythmic EEG readings remains challenging. This thesis describes the development of a novel method that assists clinicians to successfully localize the epileptic discharges associated with ISS in HYPS. The approach includes: construct the time-frequency domain (TFD) of the EEG recording using matching pursuit TFD (MP-TFD), decompose the TFD matrix into two submatrices using nonnegative matrix factorizations (NMF), and employ the decomposed vectors to locate the spikes. The proposed method was employed to an EEG dataset of five ISS individuals, and identification of spikes was compared with those which were identified by the epileptologists and those obtained using clinical software (Persyst). Performance evaluations showed results based on classification techniques: thresholdings, and support vector machine (SVM). Using the thresholdings, average true positive (TP) and false negative (FN) percentages of 86% and 14% were achieved, which represented a significant improvement over the use of Persyst, which only achieved average TP and FN percentages of 4% and 96%, respectively. Using SVM, the percentage of area under curve (AUC) of receiver operating characteristic (ROC) was significantly improved up to 98.56%. In summary, the proposed novel algorithm based on MP-TFD and NMF was able to successfully detect the epileptic discharges from the dataset. The development of the proposed automated method can potentially assist clinicians to successfully localize the epileptic discharges associated with ISS in HYPS. The quantitative assessment of spike detection, as well as other features of HYPS, is expected to allow a more accurate assessment of the relevance of EEG to clinical outcomes, which is significant in therapy management of ISS

Decorrelation of Neutral Vector Variables: Theory and Applications

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations