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

Manifold Learning for Natural Image Sets, Doctoral Dissertation August 2006

The field of manifold learning provides powerful tools for parameterizing high-dimensional data points with a small number of parameters when this data lies on or near some manifold. Images can be thought of as points in some high-dimensional image space where each coordinate represents the intensity value of a single pixel. These manifold learning techniques have been successfully applied to simple image sets, such as handwriting data and a statue in a tightly controlled environment. However, they fail in the case of natural image sets, even those that only vary due to a single degree of freedom, such as a person walking or a heart beating. Parameterizing data sets such as these will allow for additional constraints on traditional computer vision problems such as segmentation and tracking. This dissertation explores the reasons why classical manifold learning algorithms fail on natural image sets and proposes new algorithms for parameterizing this type of data

Comparative study of unsupervised dimension reduction techniques for the visualization of microarray gene expression data

<p>Abstract</p> <p>Background</p> <p>Visualization of DNA microarray data in two or three dimensional spaces is an important exploratory analysis step in order to detect quality issues or to generate new hypotheses. Principal Component Analysis (PCA) is a widely used linear method to define the mapping between the high-dimensional data and its low-dimensional representation. During the last decade, many new nonlinear methods for dimension reduction have been proposed, but it is still unclear how well these methods capture the underlying structure of microarray gene expression data. In this study, we assessed the performance of the PCA approach and of six nonlinear dimension reduction methods, namely Kernel PCA, Locally Linear Embedding, Isomap, Diffusion Maps, Laplacian Eigenmaps and Maximum Variance Unfolding, in terms of visualization of microarray data.</p> <p>Results</p> <p>A systematic benchmark, consisting of Support Vector Machine classification, cluster validation and noise evaluations was applied to ten microarray and several simulated datasets. Significant differences between PCA and most of the nonlinear methods were observed in two and three dimensional target spaces. With an increasing number of dimensions and an increasing number of differentially expressed genes, all methods showed similar performance. PCA and Diffusion Maps responded less sensitive to noise than the other nonlinear methods.</p> <p>Conclusions</p> <p>Locally Linear Embedding and Isomap showed a superior performance on all datasets. In very low-dimensional representations and with few differentially expressed genes, these two methods preserve more of the underlying structure of the data than PCA, and thus are favorable alternatives for the visualization of microarray data.</p

Ensembles of Random Projections for Nonlinear Dimensionality Reduction

Dimensionality reduction methods are widely used in informationprocessing systems to better understand the underlying structuresof datasets, and to improve the efficiency of algorithms for bigdata applications. Methods such as linear random projections haveproven to be simple and highly efficient in this regard, however,there is limited theoretical and experimental analysis for nonlinearrandom projections. In this study, we review the theoretical frameworkfor random projections and nonlinear rectified random projections,and introduce ensemble of nonlinear maximum random projections.We empirically evaluate the embedding performance on 3commonly used natural datasets and compare with linear randomprojections and traditional techniques such as PCA, highlightingthe superior generalization performance and stable embedding ofthe proposed method

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. Projection to tangent spaces truly preserves topology along radial geodesics. In this paper, we propose a method for extrinsic inference on Riemannian manifold using kernel approach while topology of the entire dataset is preserved. We show that computing the Gramian matrix using geodesic distances, on a complete Riemannian manifold with unique minimizing geodesic between each pair of points, provides a feature mapping which preserves the topology of data points in the feature space. The proposed approach is evaluated on real datasets composed of EEG signals of patients with two different mental disorders, texture, visual object classes, and tracking datasets. To assess the effectiveness of our scheme, the extracted features are examined by other state-of-the-art techniques for extrinsic inference over symmetric positive definite (SPD) Riemannian manifold. Experimental results show the superior accuracy of the proposed approach over approaches which use kernel trick to compute similarity on SPD manifolds without considering the topology of dataset or partially preserving topology

The Murine Accessory Olfactory Bulb as a Model Chemosensory System: Experimental and Computational Analysis of Chemosensory Representations

A common challenge across sensory processing modalities is forming meaningful associations between the neural responses and the outside world. These neural representations of the world must then be integrated across different sensory systems contributing to each individuals perceptual experience. While there has been considerable study of sensory representations in the visual system of humans and multiple model organisms, other sensory domains, including olfaction, are less well understood. In this thesis, I set out to better understand the sensory representations of the mouse accessory olfactory system (AOS), a part of the olfactory system. The mouse AOS, our model chemosensory system, comprises peripheral vomeronasal sensory neurons (VSNs), the accessory olfactory bulb (AOB), and downstream effectors. Our work describes the neural representations of multiple sensory inputs in the AOS, specifically the representations of odorants in high dimensional chemical sensory space in the AOB, and how these representations are shaped by interactions within the circuit. Given the complex nature of olfactory chemosensory representations, the features of our model system may give new perspectives on the neural representation of the outside world. In a neural representation of olfactory information, both the interactions between each receptor and odor compounds as well as the circuit mediated interactions could potentially affect the neural representations of the outside world. The initial neural response comprises component interactions between each receptor and the odor; chemical signals must interact with physical receptors. However, chemosensory processing, such as olfaction, requires interpreting a large variety of potentially overlapping chemical cues from the environment with only a finite number of receptor types. This means that each chemical cue does not necessarily activate only one receptor type or region of the circuit, but rather the cue is likely to be represented by multiple receptor and odor component interactions. Also, the component parts of odors may be processed differently when presented in isolation versus in a more complex mixture, thus allowing the response to a particular odor to vary with chemical context. Moreover, once these component representations exist, interactions within the neural circuit may further shape these responses. For example, one might expect component parts of a complex odor to specifically inhibit other component parts. In the case of the accessory olfactory system this inhibition could be at the receptor level or at the level of the sensory representation in the accessory olfactory bulb (AOB). In Chapter 3, I describe the overall organization of chemosensory representations in the accessory olfactory bulb (AOB), which is found to be a modular map in which the primary associations of functional sensory responses are spatially organized relative to one another. I find these primary associations are condensations of the first order sensory neuron axon terminals, which form population response pooling structures called glomeruli. In these glomeruli, similar response types from those sensory neurons expressing one of the approximately 300 receptor types in the vomeronasal organ (VNO) co-converge. One purpose of converging inputs of neurons expressing the same receptor is likely to minimize noise, and I demonstrate that pooling of like receptor responses into glomeruli does increase neural signal relative to noise. However, I also observed a modular organization among and between glomeruli in which certain types or patterns of chemosensory responses are always spatially adjacent to one another, while others are much farther apart than would be expected by chance. I found this spatial modularity for both ethological stimuli (urine collected from conspecifics with widely divergent physiological endocrine status) and individual sulfated steroids. In Chapter 4, I explore the consequences of changing sensory context, specifically the presentation of multiple compounds, and the role that inhibition plays in the neural representation of the sensory stimuli. First, I tested whether the circuit responds differently to demands to represent a single odor than to demands to represent multiple odors by using odors that activate glomeruli both inside and outside of modules. I found that responses to mixtures rapidly diverge from the responses of individual component parts. Moreover, there was an effect of inhibition in modulating the response to preferred stimuli in all glomeruli. However, initial analysis of one type of pregnanolone responsive glomeruli demonstrated that the divergent response to mixtures in this type of glomerulus was not mediated by inhibition at the glomerular level, but was rather attributable to bottom-up effects from the interactions of multiple ligands with chemosensory receptors in the VNO. Nonetheless, I also demonstrated that in the AOB, the axon terminals of the same sensory neurons (glomeruli) are organized into modules that allow for feedback inhibition. Significant ionotropic glutamate receptor signal modulation was observed within modules, demonstrating that there are inhibition mediated effects in the representation of complex mixtures when glomeruli are co-locally arranged. Specifically, at both the level of the VSNs and also in AOB glomeruli, the response to allopregnanolone sulfate is inhibited by co-presentation with estradiol sulfate. This both significantly increases the relative representation of estradiol sulfate and shifts representation of allopregnanolone primarily within modules. These types of context dependent interactions depend on the spatial organization described in Chapter 3 as well as mixture context, and have the potential to optimize the representation of some chemical cues in a context specific manner

Spreadsheet Framework for Visual Exploration of Biomedical Datasets

In this paper, we present our spreadsheet framework, which uses a spreadsheet-likeinterface for exploring biomedical datasets. The principles and advantages of this classof visualization systems are illustrated, and a case study for the analysis of hip jointcongruity is presented. Throughout this use case, we see how end users can comparedifferent datasets, apply parallel operations on data, create analysis templates, andhow this helps them in the exploration process

Visual Systems for Interactive Exploration and Mining of Large-Scale Neuroimaging Data Archives

While technological advancements in neuroimaging scanner engineering have improved the efficiency of data acquisition, electronic data capture methods will likewise significantly expedite the populating of large-scale neuroimaging databases. As they do and these archives grow in size, a particular challenge lies in examining and interacting with the information that these resources contain through the development of compelling, user-driven approaches for data exploration and mining. In this article, we introduce the informatics visualization for neuroimaging (INVIZIAN) framework for the graphical rendering of, and dynamic interaction with the contents of large-scale neuroimaging data sets. We describe the rationale behind INVIZIAN, detail its development, and demonstrate its usage in examining a collection of over 900 T1-anatomical magnetic resonance imaging (MRI) image volumes from across a diverse set of clinical neuroimaging studies drawn from a leading neuroimaging database. Using a collection of cortical surface metrics and means for examining brain similarity, INVIZIAN graphically displays brain surfaces as points in a coordinate space and enables classification of clusters of neuroanatomically similar MRI images and data mining. As an initial step toward addressing the need for such user-friendly tools, INVIZIAN provides a highly unique means to interact with large quantities of electronic brain imaging archives in ways suitable for hypothesis generation and data mining

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

Local Deformation Modelling for Non-Rigid Structure from Motion

PhDReconstructing the 3D geometry of scenes based on monocular image sequences is a long-standing problem in computer vision. Structure from motion (SfM) aims at a data-driven approach without requiring a priori models of the scene. When the scene is rigid, SfM is a well understood problem with solutions widely used in industry. However, if the scene is non-rigid, monocular reconstruction without additional information is an ill-posed problem and no satisfactory solution has yet been found. Current non-rigid SfM (NRSfM) methods typically aim at modelling deformable motion globally. Additionally, most of these methods focus on cases where deformable motion is seen as small variations from a mean shape. In turn, these methods fail at reconstructing highly deformable objects such as a flag waving in the wind. Additionally, reconstructions typically consist of low detail, sparse point-cloud representation of objects. In this thesis we aim at reconstructing highly deformable surfaces by modelling them locally. In line with a recent trend in NRSfM, we propose a piecewise approach which reconstructs local overlapping regions independently. These reconstructions are merged into a global object by imposing 3D consistency of the overlapping regions. We propose our own local model – the Quadratic Deformation model – and show how patch division and reconstruction can be formulated in a principled approach by alternating at minimizing a single geometric cost – the image re-projection error of the reconstruction. Moreover, we extend our approach to dense NRSfM, where reconstructions are preformed at the pixel level, improving the detail of state of the art reconstructions. Finally we show how our principled approach can be used to perform simultaneous segmentation and reconstruction of articulated motion, recovering meaningful segments which provide a coarse 3D skeleton of the object.Fundacao para a Ciencia e a Tecnologia (FCT) under Doctoral Grant SFRH/BD/70312/2010; European Research Council under ERC Starting Grant agreement 204871-HUMANI