Alp Ozdemir

Hierarchical Spectral Consensus Clustering for Group Analysis of Functional Brain Networks

A central question in cognitive neuroscience is how cognitive functions depend on the integration of specialized widely distributed brain regions. In recent years, graph theoretical methods have been used to characterize the structure of the brain functional connectivity. In order to understand the organization of functional connectivity networks, it is important to determine the community structure underlying these complex networks. Moreover, the study of brain functional networks is confounded by the fact that most neurophysiological studies consists of data collected from multiple subjects; thus, it is important to identify communities representative of all subjects. Typically, this problem is addressed by averaging the data across subjects which omits the variability across subjects or using voting methods, which requires a priori knowledge of cluster labels. In this paper, we propose a hierarchical consensus spectral clustering approach to address these problems. Furthermore, new information-theoretic criteria are introduced for selecting the optimal community structure. The proposed framework is applied to electroencephalogram data collected during a study of error-related negativity to better understand the community structure of functional networks involved in the cognitive control.

Recursive Tensor Subspace Tracking for Dynamic Brain Network Analysis

Recent years have seen a rapid growth in computational methods for a better understanding of functional connectivity brain networks constructed from neuroimaging data. Most of the current work has been limited to static functional connectivity networks (FCNs), where the relationships between different brain regions is assumed to be stationary. Recent work indicates that functional connectivity is a dynamic process over multiple time scales and the dynamic formation and dissolution of connections plays a key role in cognition, memory, and learning. In the proposed work, we introduce a tensor-based approach for tracking dynamic functional connectivity networks. The proposed framework introduces a robust low-rank+sparse structure learning algorithm for tensors to separate the low-rank community structure of connectivity networks from sparse outliers. The proposed framework is used to both identify change points, where the low-rank community structure of the FCN changes significantly, and summarize this community structure within each time interval. The proposed framework is applied to the study of cognitive control from electroencephalogram data during a Flanker task.

Locally linear low-rank tensor approximation

Recently, collecting and storing higher order data has become more feasible with the use of methods from multilinear algebra. High order data usually lies in a low dimensional subspace or manifold along each mode and its intrinsic structure can be revealed by linear methods such as higher order SVD. However, these linear approaches may not capture the local nonlinearities in the data that may occur due to moving sensors or other nonlinearities in the measurements. In this paper, we propose to use a piecewise linear model to better identify the non-linearities in higher order data. The proposed approach decomposes the higher-order data into subtensors and fits a low rank model to each subtensor. The proposed approach is applied to simulated datasets and a video sequence captured across different angles to show its robustness to non-linear structures.

Multiscale tensor decomposition

Large datasets usually contain redundant information and summarizing these datasets is important for better data interpretation. Higher-order data reduction is usually achieved through low-rank tensor approximation which assumes that the data lies near a linear subspace across each mode. However, non-linearities in the data cannot be captured well by linear methods. In this paper, we propose a multiscale tensor decomposition to better approximate local nonlinearities in tensors. The proposed multiscale approach constructs hierarchical low-rank structure by dividing the tensor into subtensors sequentially and fitting a low-rank model to each subtensor.

Multi-scale higher order singular value decomposition (MS-HoSVD) for resting-state FMRI compression and analysis

Advances in information technology are making it possible to collect increasingly massive amounts of multidimensional, multi-modal neuroimaging data such as functional magnetic resonance imaging (fMRI). Current fMRI datasets involve multiple variables including multiple subjects, as well as both temporal and spatial data. These high dimensional datasets pose a challenge to the signal processing community to develop data reduction methods that can exploit their rich structure and extract meaningful summarizations. In this paper, we propose a tensor-based framework for data reduction and low-dimensional structure learning with a particular focus on reducing high dimensional fMRI data sets into physiologically meaningful network components. We develop a multiscale tensor factorization method for higher order data inspired by hybrid linear modeling and subspace clustering techniques. In particular, we develop a multi-scale HoSVD approach where a given tensor is first permuted and then partitioned into several sub-tensors each of which can be represented more efficiently. This multi-scale framework is applied to resting state fMRI data to identify the default mode network from compressed data.

A multiscale approach for tensor denoising

As higher-order datasets become more common, researchers are primarily focused on how to analyze and compress them. However, the most common challenge encountered in any type of data, including tensor data, is noise. Furthermore, the methods developed for denoising vector or matrix type datasets cannot be applied directly to higherorder datasets. This motivates the development of denoising methods for tensors. In this paper, we propose the use of a multiscale approach for denoising general higher-order datasets. The proposed approach works by decomposing the higher-order data into subtensors, and then denoises the subtensors by recursively exploiting filtered residuals. The method is validated on both hyperspectral image and brain functional connectivity network data.

Multiple subject analysis of functional brain network communities through co-regularized spectral clustering

In recent years, the human brain has been characterized as a complex network composed of segregated modules linked by short path lengths. In order to understand the organization of the network, it is important to determine these modules underlying the functional brain networks. However, the study of these modules is confounded by the fact that most neurophysiological studies consist of data collected from multiple subjects. Typically, this problem is addressed by either averaging the data across subjects which omits the variability across subjects or using consensus clustering methods which treats all subjects equally irrespective of outliers in the data. In this paper, we adapt a recently introduced co-regularized multiview spectral clustering approach to address these problems. The proposed framework is applied to EEG data collected during a study of error-related negativity (ERN) to better understand the functional networks involved in cognitive control and to compare between the network structure between error and correct responses.

Graph wavelet transform: Application to image segmentation

Recently, there has been a lot of work on extending traditional signal processing methods to irregular domains such as graphs. Graph wavelet transform offers a multiscale analysis of graphs similar to traditional wavelets. Similar to wavelets which are effective at detecting transients in a signal, graph wavelets can be used to detect discontinuities of functions defined on graphs. In this paper, we use this realization to propose a graph wavelet based approach to image segmentation. The images are first transformed to the graph domain and the graph wavelet transform is used to detect the discontinuities in the pixel domain.