Non-Redundant Spectral Dimensionality Reduction

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known as the "repeated Eigen-directions" phenomenon. That is, many of the embedding coordinates they produce typically capture the same direction along the data manifold. This leads to redundant and inefficient representations that do not reveal the true intrinsic dimensionality of the data. In this paper, we propose a general method for avoiding redundancy in spectral algorithms. Our approach relies on replacing the orthogonality constraints underlying those methods by unpredictability constraints. Specifically, we require that each embedding coordinate be unpredictable (in the statistical sense) from all previous ones. We prove that these constraints necessarily prevent redundancy, and provide a simple technique to incorporate them into existing methods. As we illustrate on challenging high-dimensional scenarios, our approach produces significantly more informative and compact representations, which improve visualization and classification tasks

The Application of DTI to Investigate White Matter Abnormalities in Schizophrenia

Schizophrenia is a serious and disabling mental disorder that affects approximately 1% of the general population, with often devastating effects on the psychological and financial resources of the patient, family, and larger community. The etiology of schizophrenia is not known, although it likely involves several interacting biological and environmental factors that predispose an individual to schizophrenia. However, although the underlying pathology remains unknown, it has been believed that brain abnormalities would ultimately be linked to the etiology of schizophrenia. This theory was rekindled in the 1970s, when the first computer-assisted tomography (CT) study showed enlarged lateral ventricles in schizophrenia. Since that time, there have been many improvements in MR acquisition and image processing, including the introduction of positron emission tomography (PET), followed by functional MR (fMRI), and diffusion tensor imaging (DTI). These advances have led to an appreciation of the critical role that brain abnormalities play in schizophrenia. While structural MRI has proven to be useful in investigating and detecting gray matter abnormalities in schizophrenia, the investigation of white matter has proven to be more challenging as white matter appears homogeneous on conventional MRI and the fibers connecting different brain regions cannot be appreciated. With the development of DTI, we are now able to investigate white matter abnormalities in schizophrenia

Assessing the Reliability of Template-Based Clustering for Tractography in Healthy Human Adults

Tractography is a non-invasive technique to investigate the brain’s structural pathways (also referred to as tracts) that connect different brain regions. A commonly used approach for identifying tracts is with template-based clustering, where unsupervised clustering is first performed on a template in order to label corresponding tracts in unseen data. However, the reliability of this approach has not been extensively studied. Here, an investigation into template-based clustering reliability was performed, assessing the output from two datasets: Human Connectome Project (HCP) and MyConnectome project. The effect of intersubject variability on template-based clustering reliability was investigated, as well as the reliability of both deep and superficial white matter tracts. Identified tracts were evaluated by assessing Euclidean distances from a dataset-specific tract average centroid, the volumetric overlap across corresponding tracts, and along-tract agreement of quantitative values. Further, two template-based techniques were employed to evaluate the reliability of different clustering approaches. Reliability assessment can increase the confidence of a tract identifying technique in future applications to study pathways of interest. The two different template-based approaches exhibited similar reliability for identifying both deep white matter tracts and the superficial white matter

A Comparison of Some Dimension Reduction Techniques with Varied Parameters

This paper presents and explains several methods of dimensionality reduction of data sets, beginning with the well known PCA and moving onto techniques that deal with data on a nonlinear manifold. Methods for handling data whose underlying structure is a nonlinear manifold are separated by whether or not sparse matrices are involved in the computation. Additionally, the methods discussed are demonstrated and compared by running them on data sets whose underlying structure is known. Results from same methods with different values for input parameters are also examined. Finally, some results on a small set of Persyst EEG data collected as a part of the Epilepsy Bioinformatics Study for Antiepileptogenic Therapy from the Laboratory of Neuro Imaging at USC Stevens Institute of Neuroimaging and Informatics in the Keck School of Medicine of USC is analyzed using some of these methods

Spectral Clustering en IRM de diffusion pour Retrouver les Faisceaux de la Matière Blanche

White matter fiber clustering allows to get insight about anatomical structures in order to generate atlases, perform clear visualizations and compute statistics across subjects, all important and current neuroimaging problems. In this work, we present a Diffusion Maps clustering method applied to diffusion MRI in order to cluster and segment complex white matter fiber bundles. It is well-known that Diffusion Tensor Imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent High Angular Resolution Diffusion Imaging (HARDI) such has Q-Ball Imaging (QBI) have been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima agreeing with the underlying fiber populations. In this paper, we introduce the usage of the Diffusion Maps technique and show how it can be used to directly cluster set of fiber tracts, that could be obtained through a streamline tractography for instance, and how it can also help in segmenting fields of ODF images, obtained through a linear and regularized ODF estimation algorithm based on a spherical harmonics representation of the Q-Ball data. We first show the advantage of using Diffusion Maps clustering over classical methods such as N-Cuts and Laplacian Eigenmaps in both cases. In particular, our Diffusion Maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in fiber tract clustering and ODF image segmentation and automatically exhibits the number of clusters in both cases by using an adaptive scale-space parameter. We also show that our ODF Diffusion Maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our ODF-based method succeeds to separate fiber bundles and crossing regions whereas the DT-based methods generate artifacts and exhibit wrong number of clusters. Finally, we illustrate the potential of our approach on a real brain dataset where we successfully segment well-known fiber bundles

Coloring of DT-MRI fiber Traces using Laplacian Eigenmaps

We propose a novel post processing method for visualization of fiber traces from DT-MRI data. Using a recently proposed non-linear dimensionality reduction technique, Laplacian eigenmaps [3], we create a mapping from a set of fiber traces to a low dimensional Euclidean space. Laplacian eigenmaps constructs this mapping so that similar traces are mapped to similar points, given a custom made pairwise similarity measure for fiber traces. We demonstrate that when the low-dimensional space is the RGB color space, this can be used to visualize fiber traces in a way which enhances the perception of fiber bundles and connectivity in the human brain.ope

Visualización bidimensional de problemas de clasificación en alta dimensión

El objetivo de este proyecto es obtener buenas representaciones en dos dimensiones de problemas N dimensionales. Para ello se propone una función de coste que mida la similitud entre una representación en N dimensiones y la misma en 2 dimensiones. Esto permite que se pueda realizar una comparación de la eficacia y una clasificación de diferentes técnicas de reducción de dimensionalidad para descubrir en distintos conjuntos cuales de estas son las que mantienen un mayor grado de similitud entre ambos espacios dimensionales.The main objective of this Project is to get proper good-quality representations in two dimensions of N dimensional problems. In order to do that, a cost function is proposed to measure the similarity between a representation in N dimensions and the same in two dimensions. ; that allows us to be able to carry out an effectiveness comparison and a classification of different techniques to reduce ‘dimensionality’ so as to find out, in different data sets, which of those are the ones that keep an upper similarity level between both dimensional spaces.Ingeniería Técnica en Sonido e Image

Segmentation of diffusion weighted MRI using the level set framework

Medical imaging is a rapidly growing field in which diffusion imaging is a recently developed modality. This novel imaging contrast permits in-vivo measurement of the diffusion of water molecules. This is particularly interesting in brain imaging where the diffusion reveals an amazing insight into the neuronal organization and cerebral cytoarchitecture. Diffusion images contain from six up to hundreds of values in each voxel and are represented as tensor fields (Diffusion Tensor Imaging (DTI)) or as fields of functions (High Angular Resolution Diffusion (HARD) imaging). To fully extract the large amount of data contained within these images new processing and analysis tools are needed. The aim of this thesis is the development of such tools. The method we have been mainly focusing on for this purpose is the level set method. The level set method is a numerical and theoretical tool for propagating interfaces. In image processing it is used for propagating curves in 2D or surfaces in 3D for delineation of objects or for regularization purposes. In this thesis we have explored some of the numerous aspects of the level set frame work to see how the diffusion properties can be used for segmentation. For segmentation of tensor fields we have considered similarity measures for comparison of tensors. From these similarity measures several applications of the level set method have been developed for the segmentation of different structures. Different measures of similarity have been used dependent on the application. When segmenting white matter regions in DTI, the similarity measure emphasizes anisotropic regions. The segmentation algorithm itself has a very local dependence since white matter, in general fiber tracts, experiences different diffusion in different parts of the structure. The presented results show segmentations of the major fiber tracts in the brain. Other structures, such as the deep cerebral nuclei, that are mainly composed of gray matter, have more homogenous diffusion properties than white matter structures. Therefore, in these structures we maximize the internal coherence within the entire structure by using a region based approach to the segmentation problem. Segmentations of the thalamus and its nuclei as well as on tensor fields from fluid mechanics are presented. For High Angular Resolution Diffusion (HARD) images, two methods for fiber tract segmentation are presented based on different types of coherence. The coherence is either measured as the similarity between fibers obtained from a tractography algorithm, or the similarity of scalar values in a five-dimensional non-Euclidean space. The similarity between two fibers is determined by a counting strategy and is equal to the number of voxels they have in common. A spectral clustering algorithm is then used for grouping fibers with a high inter-resemblance. When segmenting white matter with the level set method, we propose to expand the space we are working in from a three-dimensional space of Orientation Distribution Functions (ODF) to a five-dimensional space of position and orientation. By a careful definition of this space and an adaptation of the level set to five dimensions the fibers tracts can be segmented as separated structures. We show some preliminary results from segmentations in this 5D space. The approaches proposed in this thesis permit a consideration of the fiber tracts and gray matter structures as an entity, allowing quantitative measures of the diffusion without losing information by simplifying the images to scalar representations

Cerebral white matter analysis using diffusion imaging

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2006.Includes bibliographical references (p. 183-198).In this thesis we address the whole-brain tractography segmentation problem. Diffusion magnetic resonance imaging can be used to create a representation of white matter tracts in the brain via a process called tractography. Whole brain tractography outputs thousands of trajectories that each approximate a white matter fiber pathway. Our method performs automatic organization, or segmention, of these trajectories into anatomical regions and gives automatic region correspondence across subjects. Our method enables both the automatic group comparison of white matter anatomy and of its regional diffusion properties, and the creation of consistent white matter visualizations across subjects. We learn a model of common white matter structures by analyzing many registered tractography datasets simultaneously. Each trajectory is represented as a point in a high-dimensional spectral embedding space, and common structures are found by clustering in this space. By annotating the clusters with anatomical labels, we create a model that we call a high-dimensional white matter atlas.(cont.) Our atlas creation method discovers structures corresponding to expected white matter anatomy, such as the corpus callosum, uncinate fasciculus, cingulum bundles, arcuate fasciculus, etc. We show how to extend the spectral clustering solution, stored in the atlas, using the Nystrom method to perform automatic segmentation of tractography from novel subjects. This automatic tractography segmentation gives an automatic region correspondence across subjects when all subjects are labeled using the atlas. We show the resulting automatic region correspondences, demonstrate that our clustering method is reproducible, and show that the automatically segmented regions can be used for robust measurement of fractional anisotropy.by Lauren Jean O'Donnell.Ph.D