Generative-Discriminative Low Rank Decomposition for Medical Imaging Applications

In this thesis, we propose a method that can be used to extract biomarkers from medical images toward early diagnosis of abnormalities. Surge of demand for biomarkers and availability of medical images in the recent years call for accurate, repeatable, and interpretable approaches for extracting meaningful imaging features. However, extracting such information from medical images is a challenging task because the number of pixels (voxels) in a typical image is in order of millions while even a large sample-size in medical image dataset does not usually exceed a few hundred. Nevertheless, depending on the nature of an abnormality, only a parsimonious subset of voxels is typically relevant to the disease; therefore various notions of sparsity are exploited in this thesis to improve the generalization performance of the prediction task. We propose a novel discriminative dimensionality reduction method that yields good classification performance on various datasets without compromising the clinical interpretability of the results. This is achieved by combining the modelling strength of generative learning framework and the classification performance of discriminative learning paradigm. Clinical interpretability can be viewed as an additional measure of evaluation and is also helpful in designing methods that account for the clinical prior such as association of certain areas in a brain to a particular cognitive task or connectivity of some brain regions via neural fibres. We formulate our method as a large-scale optimization problem to solve a constrained matrix factorization. Finding an optimal solution of the large-scale matrix factorization renders off-the-shelf solver computationally prohibitive; therefore, we designed an efficient algorithm based on the proximal method to address the computational bottle-neck of the optimization problem. Our formulation is readily extended for different scenarios such as cases where a large cohort of subjects has uncertain or no class labels (semi-supervised learning) or a case where each subject has a battery of imaging channels (multi-channel), \etc. We show that by using various notions of sparsity as feasible sets of the optimization problem, we can encode different forms of prior knowledge ranging from brain parcellation to brain connectivity

Greedy Algorithms for Cone Constrained Optimization with Convergence Guarantees

Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we consider the intermediate case of optimization over the convex cone, parametrized as the conic hull of a generic atom set, leading to the first principled definitions of non-negative MP algorithms for which we give explicit convergence rates and demonstrate excellent empirical performance. In particular, we derive sublinear ($\mathcal{O}(1/t)$) convergence on general smooth and convex objectives, and linear convergence ($\mathcal{O}(e^{-t})$) on strongly convex objectives, in both cases for general sets of atoms. Furthermore, we establish a clear correspondence of our algorithms to known algorithms from the MP and FW literature. Our novel algorithms and analyses target general atom sets and general objective functions, and hence are directly applicable to a large variety of learning settings.Comment: NIPS 201

A study of information-theoretic metaheuristics applied to functional neuroimaging datasets

This dissertation presents a new metaheuristic related to a two-dimensional ensemble empirical mode decomposition (2DEEMD). It is based on Green’s functions and is called Green’s Function in Tension - Bidimensional Empirical Mode Decomposition (GiT-BEMD). It is employed for decomposing and extracting hidden information of images. A natural image (face image) as well as images with artificial textures have been used to test and validate the proposed approach. Images are selected to demonstrate efficiency and performance of the GiT-BEMD algorithm in extracting textures on various spatial scales from the different images. In addition, a comparison of the performance of the new algorithm GiT-BEMD with a canonical BEEMD is discussed. Then, GiT-BEMD as well as canonical bidimensional EEMD (BEEMD) are applied to an fMRI study of a contour integration task. Thus, it explores the potential of employing GiT-BEMD to extract such textures, so-called bidimensional intrinsic mode functions (BIMFs), of functional biomedical images. Because of the enormous computational load and the artifacts accompanying the extracted textures when using a canonical BEEMD, GiT-BEMD is developed to cope with such challenges. It is seen that the computational cost is decreased dramatically, and the quality of the extracted textures is enhanced considerably. Consequently, GiT-BEMD achieves a higher quality of the estimated BIMFs as can be seen from a direct comparison of the results obtained with different variants of BEEMD and GiT-BEMD. Moreover, results generated by 2DBEEMD, especially in case of GiT-BEMD, distinctly show a superior precision in spatial localization of activity blobs when compared with a canonical general linear model (GLM) analysis employing statistical parametric mapping (SPM). Furthermore, to identify most informative textures, i.e. BIMFs, a support vector machine (SVM) as well as a random forest (RF) classifier is employed. Classification performance demonstrates the potential of the extracted BIMFs in supporting decision making of the classifier. With GiT-BEMD, the classification performance improved significantly which might also be a consequence of a clearer structure for these modes compared to the ones obtained with canonical BEEMD. Altogether, there is strong believe that the newly proposed metaheuristic GiT-BEMD offers a highly competitive alternative to existing BEMD algorithms and represents a promising technique for blindly decomposing images and extracting textures thereof which may be used for further analysis

Towards Patient-Specific Brain Networks Using Functional Magnetic Resonance Imaging

fMRI applications are rare in translational medicine and clinical practice. What can be inferred from a single fMRI scan is often unreliable due to the relative low signal-to-noise ratio compared to other neuroimaging modalities. However, the potential of fMRI is promising. It is one of the few neuroimaging modalities to obtain functional brain organisation of an individual during task engagement and rest. This work extends on current fMRI image processing approaches to obtain robust estimates of functional brain organisation in two resting-state fMRI cohorts. The first cohort comprises of young adults who were born at extremely low gestations and age-matched healthy controls. Group analysis between term- and preterm-born adults revealed differences in functional organisation, which were discovered to be predominantly caused by underlying structural and physiological differences. The second cohort comprises of elderly adults with young onset Alzheimer’s disease and age-matched controls. Their corresponding resting-state fMRI scans are short in scanning time resulting in unreliable spatial estimates with conventional dual regression analysis. This problem was addressed by the development of an ensemble averaging of matrix factorisations approach to compute single subject spatial maps characterised by improved spatial reproducibility compared to maps obtained by dual regression. The approach was extended with a haemodynamic forward model to obtain surrogate neural activations to examine the subject’s task behaviour. This approach applied to two task-fMRI cohorts showed that these surrogate neural activations matched with original task timings in most of the examined fMRI scans but also revealed subjects with task behaviour different than intended by the researcher. It is hoped that both the findings in this work and the novel matrix factorisation approach itself will benefit the fMRI community. To this end, the derived tools are made available online to aid development and validation of methods for resting-state and task fMRI experiments

Hadron models and related New Energy issues

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena. The authors explored some new approaches to describe novel phenomena in particle physics. M Pitkanen introduces his nuclear string hypothesis derived from his Topological Geometrodynamics theory, while E. Goldfain discusses a number of nonlinear dynamics methods, including bifurcation, pattern formation (complex GinzburgLandau equation) to describe elementary particle masses. Fu Yuhua discusses a plausible method for prediction of phenomena related to New Energy development. F. Smarandache discusses his unmatter hypothesis, and A. Yefremov et al. discuss Yang-Mills field from Quaternion Space Geometry. Diego Rapoport discusses theoretical link between Torsion fields and Hadronic Mechanic. A.H. Phillips discusses semiconductor nanodevices, while V. and A. Boju discuss Digital Discrete and Combinatorial methods and their likely implications in New Energy research. Pavel Pintr et al. describe planetary orbit distance from modified Schrödinger equation, and M. Pereira discusses his new Hypergeometrical description of Standard Model of elementary particles. The present volume will be suitable for researchers interested in New Energy issues, in particular their link with alternative hadron models and interpretation