Hyekyoung Lee

Noninvasive BCIs: Multiway Signal-Processing Array Decompositions

In addition to helping better understand how the human brain works, the brain-computer interface neuroscience paradigm allows researchers to develop a new class of bioengineering control devices and robots, offering promise for rehabilitation and other medical applications as well as exploring possibilities for advanced human-computer interfaces.

Semi-Supervised Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a popular method for low-rank approximation of nonnegative matrix, providing a useful tool for representation learning that is valuable for clustering and classification. When a portion of data are labeled, the performance of clustering or classification is improved if the information on class labels is incorporated into NMF. To this end, we present semi-supervised NMF (SSNMF), where we jointly incorporate the data matrix and the (partial) class label matrix into NMF. We develop multiplicative updates for SSNMF to minimize a sum of weighted residuals, each of which involves the nonnegative 2-factor decomposition of the data matrix or the label matrix, sharing a common factor matrix. Experiments on document datasets and EEG datasets in BCI competition confirm that our method improves clustering as well as classification performance, compared to the standard NMF, stressing that semi-supervised NMF yields semi-supervised feature extraction.

Non-negative matrix factorization with α-divergence

Non-negative matrix factorization (NMF) is a popular technique for pattern recognition, data analysis, and dimensionality reduction, the goal of which is to decompose non-negative data matrix X into a product of basis matrix A and encoding variable matrix S with both A and S allowed to have only non-negative elements. In this paper, we consider Amaris @a-divergence as a discrepancy measure and rigorously derive a multiplicative updating algorithm (proposed in our recent work) which iteratively minimizes the @a-divergence between X and AS. We analyze and prove the monotonic convergence of the algorithm using auxiliary functions. In addition, we show that the same algorithm can be also derived using Karush-Kuhn-Tucker (KKT) conditions as well as the projected gradient. We provide two empirical study for image denoising and EEG classification, showing the interesting and useful behavior of the algorithm in cases where different values of @a (@a=0.5,1,2) are used.

NONNEGATIVE TENSOR FACTORIZATION FOR CONTINUOUS EEG CLASSIFICATION

In this paper we present a method for continuous EEG classification, where we employ nonnegative tensor factorization (NTF) to determine discriminative spectral features and use the Viterbi algorithm to continuously classify multiple mental tasks. This is an extension of our previous work on the use of nonnegative matrix factorization (NMF) for EEG classification. Numerical experiments with two data sets in BCI competition, confirm the useful behavior of the method for continuous EEG classification.

PCA+HMM+SVM for EEG pattern classification

Electroencephalogram (EEG) pattern classification plays an important role in the domain of brain computer interface (BCI). Hidden Markov model (HMM) might be a useful tool in EEG pattern classification since EEG data is a multivariate time series data which contains noise and artifacts. In this paper we present methods for EEG pattern classification which jointly employ principal component analysis (PCA) and HMM. Along this line, two methods are introduced: (1) PCA+HMM; (2) PCA+HMM+SVM. Usefulness of principal component features and our hybrid method is confirmed through the classification of EEG that is recorded during the imagination of a left or right hand movement.

Persistent Brain Network Homology From the Perspective of Dendrogram

The brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level. The problem with this standard method is that we do not have any generally accepted criteria for determining a proper threshold. Thus, we propose a novel multiscale framework that models all brain networks generated over every possible threshold. Our approach is based on persistent homology and its various representations such as the Rips filtration, barcodes, and dendrograms. This new persistent homological framework enables us to quantify various persistent topological features at different scales in a coherent manner. The barcode is used to quantify and visualize the evolutionary changes of topological features such as the Betti numbers over different scales. By incorporating additional geometric information to the barcode, we obtain a single linkage dendrogram that shows the overall evolution of the network. The difference between the two networks is then measured by the Gromov-Hausdorff distance over the dendrograms. As an illustration, we modeled and differentiated the FDG-PET based functional brain networks of 24 attention-deficit hyperactivity disorder children, 26 autism spectrum disorder children, and 11 pediatric control subjects.

Sparse Brain Network Recovery Under Compressed Sensing

Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the small-n large-p situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l1-norm penalty, also known as the least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity. LASSO is a well-known decoding algorithm in the compressed sensing (CS). The CS theory states that LASSO can reconstruct the exact sparse signal even from a small set of noisy measurements. We briefly show that the penalized linear regression for partial correlation estimation is related to CS. It opens a new possibility that the proposed framework can be used for a sparse brain network recovery. As an illustration, we construct sparse brain networks of 97 regions of interest (ROIs) obtained from FDG-PET imaging data for the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. As validation, we check the network reproducibilities by leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.

Nonnegative matrix factorization for motor imagery EEG classification

In this paper, we present a method of feature extraction for motor imagery single trial EEG classification, where we exploit nonnegative matrix factorization (NMF) to select discriminative features in the time-frequency representation of EEG. Experimental results with motor imagery EEG data in BCl competition 2003, show that the method indeed finds meaningful EEG features automatically, while some existing methods should undergo cross-validation to find them.

Kernel nonnegative matrix factorization for spectral EEG feature extraction

Nonnegative matrix factorization (NMF) seeks a decomposition of a nonnegative matrix X>=0 into a product of two nonnegative factor matrices U>=0 and V>=0, such that a discrepancy between X and UV^@? is minimized. Assuming U=XW in the decomposition (for W>=0), kernel NMF (KNMF) is easily derived in the framework of least squares optimization. In this paper we make use of KNMF to extract discriminative spectral features from the time-frequency representation of electroencephalogram (EEG) data, which is an important task in EEG classification. Especially when KNMF with linear kernel is used, spectral features are easily computed by a matrix multiplication, while in the standard NMF multiplicative update should be performed repeatedly with the other factor matrix fixed, or the pseudo-inverse of a matrix is required. Moreover in KNMF with linear kernel, one can easily perform feature selection or data selection, because of its sparsity nature. Experiments on two EEG datasets in brain computer interface (BCI) competition indicate the useful behavior of our proposed methods.

Discriminative persistent homology of brain networks

It is known that the brain network has small-world and scale-free topology, but the network structures drastically change depending on how to threshold a connectivity matrix. The exact threshold criterion is difficult to determine. In this paper, instead of trying to determine one fixed optimal threshold, we propose to look at the topological changes of brain network while increasing the threshold continuously. This process of continuously changing threshold level and looking at the resulting topological feature is related to the Rips filtration in persistent homology. The sequence of topological features obtained during the Rips filtration can be visualized and interpreted using barcode. As an illustration, we apply the Rips filtration to construct the FDG-PET based functional brain networks out of 24 attention deficit hyperactivity disorder (ADHD) children, 26 autism spectrum disorder (ASD) children and 11 pediatric control subjects. We visually show the topological evolution of the brain networks using the barcode and perform statistical inference on the group differences. This is the first paper that deals with the persistence homology of the brain networks.