Alpha-divergence two-dimensional nonnegative matrix factorization for biomedical blind source separation

An alpha-divergence two-dimensional nonnegative matrix factorization (NMF2D) for biomedical signal separation is presented. NMF2D is a popular approach for retrieving low-rank approximations of nonnegative data such as image pixel, audio signal, data mining, pattern recognition and so on. In this paper, we concentrate on biomedical signal separation by using NMF2D with alpha-divergence family which decomposes a mixture into two-dimensional convolution factor matrices that represent temporal code and the spectral basis. The proposed iterative estimation algorithm (alpha-divergence algorithm) is initialized with random values, and it updated using multiplicative update rules until the values converge. Simulation experiments were carried out by comparing the original and estimated signal in term of signal-to-distortion ratio (SDR). The performances have been evaluated by including and excluding the sparseness constraint which sparseness is favored by penalizing nonzero gains. As a result, the proposed algorithm improved the iteration speed and sparseness constraints produce slight improvement of SDR

Sparse feature learning for image analysis in segmentation, classification, and disease diagnosis.

The success of machine learning algorithms generally depends on intermediate data representation, called features that disentangle the hidden factors of variation in data. Moreover, machine learning models are required to be generalized, in order to reduce the specificity or bias toward the training dataset. Unsupervised feature learning is useful in taking advantage of large amount of unlabeled data, which is available to capture these variations. However, learned features are required to capture variational patterns in data space. In this dissertation, unsupervised feature learning with sparsity is investigated for sparse and local feature extraction with application to lung segmentation, interpretable deep models, and Alzheimer\u27s disease classification. Nonnegative Matrix Factorization, Autoencoder and 3D Convolutional Autoencoder are used as architectures or models for unsupervised feature learning. They are investigated along with nonnegativity, sparsity and part-based representation constraints for generalized and transferable feature extraction

Brain connectivity mapping with diffusion MRI across individuals and species

The human brain is a highly complex organ that integrates functionally specialised subunits. Underpinning this complexity and functional specialisation is a network of structural connections, which may be probed using diffusion tractography, a unique, powerful and non-invasive MRI technique. Estimates of brain connectivity derived through diffusion tractography allow for explorations of how the brain’s functional subunits are inter-linked to subsequently produce experiences and behaviour. This thesis develops new diffusion tractography methodology for mapping brain connectivity, both across individuals and also across species; and explores frameworks for discovering associations of such brain connectivity features with behavioural traits. We build upon the hypothesis that connectional patterns can probe regions of functional equivalence across brains. To test this hypothesis we develop standardised and automated frameworks for mapping these patterns in very diverse brains, such as from human and non-human primates. We develop protocols to extract homologous fibre bundles across two species (human and macaque monkeys). We demonstrate robustness and generalisability of these protocols, but also their ability to capture individual variability. We also present investigations into how structural connectivity profiles may be used to inform us of how functionally-related features can be linked across different brains. Further, we explore how fully data-driven tractography techniques may be utilised for similar purposes, opening the door for future work on data-driven connectivity mapping. Subsequently, we explore how such individual variability in features that probe brain organisation are associated with differences in human behaviour. One approach to performing such explorations is the use of powerful multivariate statisitical techniques, such as canonical correlation analysis (CCA). After identifying issues in out-of-sample replication using multi-modal connectivity information, we perform comprehensive explorations into the robustness of such techniques and devise a generative model for forward predictions, demonstrating significant challlenges and limitations in their current applications. Specifically, we predict that the stability and generalisability of these techniques requires an order of magnitude more subjects than typically used to avoid overfitting and mis-interpretation of results. Using population-level data from the UK Biobank and confirmations from independent imaging modalities from the Human Connectome Project, we validate this prediction and demonstrate the direct link of CCA stability and generalisability with the number of subjects used per considered feature

Machine Learning Methods with Noisy, Incomplete or Small Datasets

In many machine learning applications, available datasets are sometimes incomplete, noisy or affected by artifacts. In supervised scenarios, it could happen that label information has low quality, which might include unbalanced training sets, noisy labels and other problems. Moreover, in practice, it is very common that available data samples are not enough to derive useful supervised or unsupervised classifiers. All these issues are commonly referred to as the low-quality data problem. This book collects novel contributions on machine learning methods for low-quality datasets, to contribute to the dissemination of new ideas to solve this challenging problem, and to provide clear examples of application in real scenarios

Brain connectivity mapping with diffusion MRI across individuals and species

The human brain is a highly complex organ that integrates functionally specialised subunits. Underpinning this complexity and functional specialisation is a network of structural connections, which may be probed using diffusion tractography, a unique, powerful and non-invasive MRI technique. Estimates of brain connectivity derived through diffusion tractography allow for explorations of how the brain’s functional subunits are inter-linked to subsequently produce experiences and behaviour. This thesis develops new diffusion tractography methodology for mapping brain connectivity, both across individuals and also across species; and explores frameworks for discovering associations of such brain connectivity features with behavioural traits. We build upon the hypothesis that connectional patterns can probe regions of functional equivalence across brains. To test this hypothesis we develop standardised and automated frameworks for mapping these patterns in very diverse brains, such as from human and non-human primates. We develop protocols to extract homologous fibre bundles across two species (human and macaque monkeys). We demonstrate robustness and generalisability of these protocols, but also their ability to capture individual variability. We also present investigations into how structural connectivity profiles may be used to inform us of how functionally-related features can be linked across different brains. Further, we explore how fully data-driven tractography techniques may be utilised for similar purposes, opening the door for future work on data-driven connectivity mapping. Subsequently, we explore how such individual variability in features that probe brain organisation are associated with differences in human behaviour. One approach to performing such explorations is the use of powerful multivariate statisitical techniques, such as canonical correlation analysis (CCA). After identifying issues in out-of-sample replication using multi-modal connectivity information, we perform comprehensive explorations into the robustness of such techniques and devise a generative model for forward predictions, demonstrating significant challlenges and limitations in their current applications. Specifically, we predict that the stability and generalisability of these techniques requires an order of magnitude more subjects than typically used to avoid overfitting and mis-interpretation of results. Using population-level data from the UK Biobank and confirmations from independent imaging modalities from the Human Connectome Project, we validate this prediction and demonstrate the direct link of CCA stability and generalisability with the number of subjects used per considered feature

Mapping connections in the neonatal brain with magnetic resonance imaging

The neonatal brain undergoes rapid development after birth, including the growth and maturation of the white matter fibre bundles that connect brain regions. Diffusion MRI (dMRI) is a unique tool for mapping these bundles in vivo, providing insight into factors that impact the development of white matter and how its maturation influences other developmental processes. However, most studies of neonatal white matter do not use specialised analysis tools, instead using tools that have been developed for the adult brain. However, the neonatal brain is not simply a small adult brain, as differences in geometry and tissue decomposition cause considerable differences in dMRI contrast. In this thesis, methods are developed to map white matter connections during this early stage of neurodevelopment. First, two contrasting approaches are explored: ROI-constrained protocols for mapping individual tracts, and the generation of whole-brain connectomes that capture the developing brain's full connectivity profile. The impact of the gyral bias, a methodological confound of tractography, is quantified and compared with the equivalent measurements for adult data. These connectomes form the basis for a novel, data-driven framework, in which they are decomposed into white matter bundles and their corresponding grey matter terminations. Independent component analysis and non-negative matrix factorisation are compared for the decomposition, and are evaluated against in-silico simulations. Data-driven components of dMRI tractography data are compared with manual tractography, and networks obtained from resting-state functional MRI. The framework is further developed to provide corresponding components between groups and individuals. The data-driven components are used to generate cortical parcellations, which are stable across subjects. Finally, some future applications are outlined that extend the use of these methods beyond the context of neonatal imaging, in order to bridge the gap between functional and structural analysis paradigms, and to chart the development of white matter throughout the lifespan and across species

Mapping connections in the neonatal brain with magnetic resonance imaging

The neonatal brain undergoes rapid development after birth, including the growth and maturation of the white matter fibre bundles that connect brain regions. Diffusion MRI (dMRI) is a unique tool for mapping these bundles in vivo, providing insight into factors that impact the development of white matter and how its maturation influences other developmental processes. However, most studies of neonatal white matter do not use specialised analysis tools, instead using tools that have been developed for the adult brain. However, the neonatal brain is not simply a small adult brain, as differences in geometry and tissue decomposition cause considerable differences in dMRI contrast. In this thesis, methods are developed to map white matter connections during this early stage of neurodevelopment. First, two contrasting approaches are explored: ROI-constrained protocols for mapping individual tracts, and the generation of whole-brain connectomes that capture the developing brain's full connectivity profile. The impact of the gyral bias, a methodological confound of tractography, is quantified and compared with the equivalent measurements for adult data. These connectomes form the basis for a novel, data-driven framework, in which they are decomposed into white matter bundles and their corresponding grey matter terminations. Independent component analysis and non-negative matrix factorisation are compared for the decomposition, and are evaluated against in-silico simulations. Data-driven components of dMRI tractography data are compared with manual tractography, and networks obtained from resting-state functional MRI. The framework is further developed to provide corresponding components between groups and individuals. The data-driven components are used to generate cortical parcellations, which are stable across subjects. Finally, some future applications are outlined that extend the use of these methods beyond the context of neonatal imaging, in order to bridge the gap between functional and structural analysis paradigms, and to chart the development of white matter throughout the lifespan and across species

Factor analysis of dynamic PET images

Thanks to its ability to evaluate metabolic functions in tissues from the temporal evolution of a previously injected radiotracer, dynamic positron emission tomography (PET) has become an ubiquitous analysis tool to quantify biological processes. Several quantification techniques from the PET imaging literature require a previous estimation of global time-activity curves (TACs) (herein called \textit{factors}) representing the concentration of tracer in a reference tissue or blood over time. To this end, factor analysis has often appeared as an unsupervised learning solution for the extraction of factors and their respective fractions in each voxel. Inspired by the hyperspectral unmixing literature, this manuscript addresses two main drawbacks of general factor analysis techniques applied to dynamic PET. The first one is the assumption that the elementary response of each tissue to tracer distribution is spatially homogeneous. Even though this homogeneity assumption has proven its effectiveness in several factor analysis studies, it may not always provide a sufficient description of the underlying data, in particular when abnormalities are present. To tackle this limitation, the models herein proposed introduce an additional degree of freedom to the factors related to specific binding. To this end, a spatially-variant perturbation affects a nominal and common TAC representative of the high-uptake tissue. This variation is spatially indexed and constrained with a dictionary that is either previously learned or explicitly modelled with convolutional nonlinearities affecting non-specific binding tissues. The second drawback is related to the noise distribution in PET images. Even though the positron decay process can be described by a Poisson distribution, the actual noise in reconstructed PET images is not expected to be simply described by Poisson or Gaussian distributions. Therefore, we propose to consider a popular and quite general loss function, called the $\beta$-divergence, that is able to generalize conventional loss functions such as the least-square distance, Kullback-Leibler and Itakura-Saito divergences, respectively corresponding to Gaussian, Poisson and Gamma distributions. This loss function is applied to three factor analysis models in order to evaluate its impact on dynamic PET images with different reconstruction characteristics