Data Representation for Learning and Information Fusion in Bioinformatics

This thesis deals with the rigorous application of nonlinear dimension reduction and data organization techniques to biomedical data analysis. The Laplacian Eigenmaps algorithm is representative of these methods and has been widely applied in manifold learning and related areas. While their asymptotic manifold recovery behavior has been well-characterized, the clustering properties of Laplacian embeddings with finite data are largely motivated by heuristic arguments. We develop a precise bound, characterizing cluster structure preservation under Laplacian embeddings. From this foundation, we introduce flexible and mathematically well-founded approaches for information fusion and feature representation. These methods are applied to three substantial case studies in bioinformatics, illustrating their capacity to extract scientifically valuable information from complex data

Spatial-Spectral Manifold Embedding of Hyperspectral Data

In recent years, hyperspectral imaging, also known as imaging spectroscopy, has been paid an increasing interest in geoscience and remote sensing community. Hyperspectral imagery is characterized by very rich spectral information, which enables us to recognize the materials of interest lying on the surface of the Earth more easier. We have to admit, however, that high spectral dimension inevitably brings some drawbacks, such as expensive data storage and transmission, information redundancy, etc. Therefore, to reduce the spectral dimensionality effectively and learn more discriminative spectral low-dimensional embedding, in this paper we propose a novel hyperspectral embedding approach by simultaneously considering spatial and spectral information, called spatial-spectral manifold embedding (SSME). Beyond the pixel-wise spectral embedding approaches, SSME models the spatial and spectral information jointly in a patch-based fashion. SSME not only learns the spectral embedding by using the adjacency matrix obtained by similarity measurement between spectral signatures, but also models the spatial neighbours of a target pixel in hyperspectral scene by sharing the same weights (or edges) in the process of learning embedding. Classification is explored as a potential strategy to quantitatively evaluate the performance of learned embedding representations. Classification is explored as a potential application for quantitatively evaluating the performance of these hyperspectral embedding algorithms. Extensive experiments conducted on the widely-used hyperspectral datasets demonstrate the superiority and effectiveness of the proposed SSME as compared to several state-of-the-art embedding methods

Graph Embedding via High Dimensional Model Representation for Hyperspectral Images

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance to deal with hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the (typically low) latent space is linear. This is a particularly strong assumption, especially when dealing with hyperspectral images due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on High Dimensional Model Representation (HDMR) is proposed, which enables to present a nonlinear embedding function to project out-of-sample samples into the latent space. The proposed method is compared to manifold learning methods along with its linear counterparts and achieves promising performance in terms of classification accuracy of a representative set of hyperspectral images.Comment: This is an accepted version of work to be published in the IEEE Transactions on Geoscience and Remote Sensing. 11 page

Virtual Reality Aided Mobile C-arm Positioning for Image-Guided Surgery

Image-guided surgery (IGS) is the minimally invasive procedure based on the pre-operative volume in conjunction with intra-operative X-ray images which are commonly captured by mobile C-arms for the confirmation of surgical outcomes. Although currently some commercial navigation systems are employed, one critical issue of such systems is the neglect regarding the radiation exposure to the patient and surgeons. In practice, when one surgical stage is finished, several X-ray images have to be acquired repeatedly by the mobile C-arm to obtain the desired image. Excessive radiation exposure may increase the risk of some complications. Therefore, it is necessary to develop a positioning system for mobile C-arms, and achieve one-time imaging to avoid the additional radiation exposure. In this dissertation, a mobile C-arm positioning system is proposed with the aid of virtual reality (VR). The surface model of patient is reconstructed by a camera mounted on the mobile C-arm. A novel registration method is proposed to align this model and pre-operative volume based on a tracker, so that surgeons can visualize the hidden anatomy directly from the outside view and determine a reference pose of C-arm. Considering the congested operating room, the C-arm is modeled as manipulator with a movable base to maneuver the image intensifier to the desired pose. In the registration procedure above, intensity-based 2D/3D registration is used to transform the pre-operative volume into the coordinate system of tracker. Although it provides a high accuracy, the small capture range hinders its clinical use due to the initial guess. To address such problem, a robust and fast initialization method is proposed based on the automatic tracking based initialization and multi-resolution estimation in frequency domain. This hardware-software integrated approach provides almost optimal transformation parameters for intensity-based registration. To determine the pose of mobile C-arm, high-quality visualization is necessary to locate the pathology in the hidden anatomy. A novel dimensionality reduction method based on sparse representation is proposed for the design of multi-dimensional transfer function in direct volume rendering. It not only achieves the similar performance to the conventional methods, but also owns the capability to deal with the large data sets

Spatial-Spectral Manifold Embedding of Hyperspectral Data

In recent years, hyperspectral imaging, also known as imaging spectroscopy, has been paid an increasing interest in geoscience and remote sensing community. Hyperspectral imagery is characterized by very rich spectral information, which enables us to recognize the materials of interest lying on the surface of the Earth more easier. We have to admit, however, that high spectral dimension inevitably brings some drawbacks, such as expensive data storage and transmission, information redundancy, etc. Therefore, to reduce the spectral dimensionality effectively and learn more discriminative spectral low-dimensional embedding, in this paper we propose a novel hyperspectral embedding approach by simultaneously considering spatial and spectral information, called spatialspectral manifold embedding (SSME). Beyond the pixel-wise spectral embedding approaches, SSME models the spatial and spectral information jointly in a patch-based fashion. SSME not only learns the spectral embedding by using the adjacency matrix obtained by similarity measurement between spectral signatures, but also models the spatial neighbours of a target pixel in hyperspectral scene by sharing the same weights (or edges) in the process of learning embedding. Classification is explored as a potential strategy to quantitatively evaluate the performance of learned embedding representations. Classification is explored as a potential application for quantitatively evaluating the performance of these hyperspectral embedding algorithms. Extensive experiments conducted on the widely-used hyperspectral datasets demonstrate the superiority and effectiveness of the proposed SSME as compared to several state-of-the-art embedding methods

Graph-based Methods for Visualization and Clustering

The amount of data that we produce and consume is larger than it has been at any point in the history of mankind, and it keeps growing exponentially. All this information, gathered in overwhelming volumes, often comes with two problematic characteristics: it is complex and deprived of semantical context. A common step to address those issues is to embed raw data in lower dimensions, by finding a mapping which preserves the similarity between data points from their original space to a new one. Measuring similarity between large sets of high-dimensional objects is, however, problematic for two main reasons: first, high-dimensional points are subject to the curse of dimensionality and second, the number of pairwise distances between points is quadratic with respect to the amount of data points. Both problems can be addressed by using nearest neighbours graphs to understand the structure in data. As a matter of fact, most dimensionality reduction methods use similarity matrices that can be interpreted as graph adjacency matrices. Yet, despite recent progresses, dimensionality reduction is still very challenging when applied to very large datasets. Indeed, although recent methods specifically address the problem of scaleability, processing datasets of millions of elements remain a very lengthy process. In this thesis, we propose new contributions which address the problem of scaleability using the framework of Graph Signal Processing, which extends traditional signal processing to graphs. We do so motivated by the premise that graphs are well suited to represent the structure of the data. In the first part of this thesis, we look at quantitative measures for the evaluation of dimensionality reduction methods. Using tools from graph theory and Graph Signal Processing, we show that specific characteristics related to quality can be assessed by taking measures on the graph, which indirectly validates the hypothesis relating graph to structure. The second contribution is a new method for a fast eigenspace approximation of the graph Laplacian. Using principles of GSP and random matrices, we show that an approximated eigensubpace can be recovered very efficiently, which be used for fast spectral clustering or visualization. Next, we propose a compressive scheme to accelerate any dimensionality reduction technique. The idea is based on compressive sampling and transductive learning on graphs: after computing the embedding for a small subset of data points, we propagate the information everywhere using transductive inference. The key components of this technique are a good sampling strategy to select the subset and the application of transductive learning on graphs. Finally, we address the problem of over-discriminative feature spaces by proposing a hierarchical clustering structure combined with multi-resolution graphs. Using efficient coarsening and refinement procedures on this structure, we show that dimensionality reduction algorithms can be run on intermediate levels and up-sampled to all points leading to a very fast dimensionality reduction method. For all contributions, we provide extensive experiments on both synthetic and natural datasets, including large-scale problems. This allows us to show the pertinence of our models and the validity of our proposed algorithms. Following reproducible principles, we provide everything needed to repeat the examples and the experiments presented in this work

Aprendizado de variedades para a síntese de áudio espacial

Orientadores: Luiz César Martini, Bruno Sanches MasieroTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: O objetivo do áudio espacial gerado com a técnica binaural é simular uma fonte sonora em localizações espaciais arbitrarias através das Funções de Transferência Relativas à Cabeça (HRTFs) ou também chamadas de Funções de Transferência Anatômicas. As HRTFs modelam a interação entre uma fonte sonora e a antropometria de uma pessoa (e.g., cabeça, torso e orelhas). Se filtrarmos uma fonte de áudio através de um par de HRTFs (uma para cada orelha), o som virtual resultante parece originar-se de uma localização espacial específica. Inspirados em nossos resultados bem sucedidos construindo uma aplicação prática de reconhecimento facial voltada para pessoas com deficiência visual que usa uma interface de usuário baseada em áudio espacial, neste trabalho aprofundamos nossa pesquisa para abordar vários aspectos científicos do áudio espacial. Neste contexto, esta tese analisa como incorporar conhecimentos prévios do áudio espacial usando uma nova representação não-linear das HRTFs baseada no aprendizado de variedades para enfrentar vários desafios de amplo interesse na comunidade do áudio espacial, como a personalização de HRTFs, a interpolação de HRTFs e a melhoria da localização de fontes sonoras. O uso do aprendizado de variedades para áudio espacial baseia-se no pressuposto de que os dados (i.e., as HRTFs) situam-se em uma variedade de baixa dimensão. Esta suposição também tem sido de grande interesse entre pesquisadores em neurociência computacional, que argumentam que as variedades são cruciais para entender as relações não lineares subjacentes à percepção no cérebro. Para todas as nossas contribuições usando o aprendizado de variedades, a construção de uma única variedade entre os sujeitos através de um grafo Inter-sujeito (Inter-subject graph, ISG) revelou-se como uma poderosa representação das HRTFs capaz de incorporar conhecimento prévio destas e capturar seus fatores subjacentes. Além disso, a vantagem de construir uma única variedade usando o nosso ISG e o uso de informações de outros indivíduos para melhorar o desempenho geral das técnicas aqui propostas. Os resultados mostram que nossas técnicas baseadas no ISG superam outros métodos lineares e não-lineares nos desafios de áudio espacial abordados por esta teseAbstract: The objective of binaurally rendered spatial audio is to simulate a sound source in arbitrary spatial locations through the Head-Related Transfer Functions (HRTFs). HRTFs model the direction-dependent influence of ears, head, and torso on the incident sound field. When an audio source is filtered through a pair of HRTFs (one for each ear), a listener is capable of perceiving a sound as though it were reproduced at a specific location in space. Inspired by our successful results building a practical face recognition application aimed at visually impaired people that uses a spatial audio user interface, in this work we have deepened our research to address several scientific aspects of spatial audio. In this context, this thesis explores the incorporation of spatial audio prior knowledge using a novel nonlinear HRTF representation based on manifold learning, which tackles three major challenges of broad interest among the spatial audio community: HRTF personalization, HRTF interpolation, and human sound localization improvement. Exploring manifold learning for spatial audio is based on the assumption that the data (i.e. the HRTFs) lies on a low-dimensional manifold. This assumption has also been of interest among researchers in computational neuroscience, who argue that manifolds are crucial for understanding the underlying nonlinear relationships of perception in the brain. For all of our contributions using manifold learning, the construction of a single manifold across subjects through an Inter-subject Graph (ISG) has proven to lead to a powerful HRTF representation capable of incorporating prior knowledge of HRTFs and capturing the underlying factors of spatial hearing. Moreover, the use of our ISG to construct a single manifold offers the advantage of employing information from other individuals to improve the overall performance of the techniques herein proposed. The results show that our ISG-based techniques outperform other linear and nonlinear methods in tackling the spatial audio challenges addressed by this thesisDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétrica2014/14630-9FAPESPCAPE