Structured sparsity for spatially coherent fibre orientation estimation in diffusion MRI.

We propose a novel formulation to solve the problem of intra-voxel reconstruction of the fibre orientation distribution function (FOD) in each voxel of the white matter of the brain from diffusion MRI data. The majority of the state-of-the-art methods in the field perform the reconstruction on a voxel-by-voxel level, promoting sparsity of the orientation distribution. Recent methods have proposed a global denoising of the diffusion data using spatial information prior to reconstruction, while others promote spatial regularisation through an additional empirical prior on the diffusion image at each q-space point. Our approach reconciles voxelwise sparsity and spatial regularisation and defines a spatially structured FOD sparsity prior, where the structure originates from the spatial coherence of the fibre orientation between neighbour voxels. The method is shown, through both simulated and real data, to enable accurate FOD reconstruction from a much lower number of q-space samples than the state of the art, typically 15 samples, even for quite adverse noise conditions.

Structured sparsity through reweighting and application to diffusion MRI

We consider the problem of multiple correlated sparse signals reconstruction and propose a new implementation of structured sparsity through a reweighting scheme. We present a particular application for diffusion Magnetic Resonance Imaging data and show how this procedure can be used for fibre orientation reconstruction in the white matter of the brain. In that framework, our structured sparsity prior can be used to exploit the fundamental coherence between fibre directions in neighbour voxels. Our method approaches the ℓ0 minimisation through a reweighted ℓ1-minimisation scheme. The weights are here defined in such a way to promote correlated sparsity between neighbour signals.

Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.

Pole placement method using the system matrix transfer function and sparsity

This paper presents a pole placement method using both the augmented Jacobian and the corresponding system transfer function matrices. From the manipulation of these matrices a straightforward approach results to get the coefficients of a non-linear system, whose solution gives the parameters of the stabilizers that can provide a pre-specified minimum damping to the system. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Regularization for sparsity in statistical analysis and machine learning

Pragmatism is the leading motivation of regularization. We can understand regularization as a modification of the maximum-likelihood estimator so that a reasonable answer could be given in an unstable or ill-posed situation. To mention some typical examples, this happens when fitting parametric or non-parametric models with more parameters than data or when estimating large covariance matrices. Regularization is usually used, in addition, to improve the bias-variance tradeoff of an estimation. Then, the definition of regularization is quite general, and, although the introduction of a penalty is probably the most popular type, it is just one out of multiple forms of regularization. In this dissertation, we focus on the applications of regularization for obtaining sparse or parsimonious representations, where only a subset of the inputs is used. A particular form of regularization, L1-regularization, plays a key role for reaching sparsity. Most of the contributions presented here revolve around L1-regularization, although other forms of regularization are explored (also pursuing sparsity in some sense). In addition to present a compact review of L1-regularization and its applications in statistical and machine learning, we devise methodology for regression, supervised classification and structure induction of graphical models. Within the regression paradigm, we focus on kernel smoothing learning, proposing techniques for kernel design that are suitable for high dimensional settings and sparse regression functions. We also present an application of regularized regression techniques for modeling the response of biological neurons. Supervised classification advances deal, on the one hand, with the application of regularization for obtaining a na¨ıve Bayes classifier and, on the other hand, with a novel algorithm for brain-computer interface design that uses group regularization in an efficient manner. Finally, we present a heuristic for inducing structures of Gaussian Bayesian networks using L1-regularization as a filter. El pragmatismo es la principal motivación de la regularización. Podemos entender la regularización como una modificación del estimador de máxima verosimilitud, de tal manera que se pueda dar una respuesta cuando la configuración del problema es inestable. A modo de ejemplo, podemos mencionar el ajuste de modelos paramétricos o no paramétricos cuando hay más parámetros que casos en el conjunto de datos, o la estimación de grandes matrices de covarianzas. Se suele recurrir a la regularización, además, para mejorar el compromiso sesgo-varianza en una estimación. Por tanto, la definición de regularización es muy general y, aunque la introducción de una función de penalización es probablemente el método más popular, éste es sólo uno de entre varias posibilidades. En esta tesis se ha trabajado en aplicaciones de regularización para obtener representaciones dispersas, donde sólo se usa un subconjunto de las entradas. En particular, la regularización L1 juega un papel clave en la búsqueda de dicha dispersión. La mayor parte de las contribuciones presentadas en la tesis giran alrededor de la regularización L1, aunque también se exploran otras formas de regularización (que igualmente persiguen un modelo disperso). Además de presentar una revisión de la regularización L1 y sus aplicaciones en estadística y aprendizaje de máquina, se ha desarrollado metodología para regresión, clasificación supervisada y aprendizaje de estructura en modelos gráficos. Dentro de la regresión, se ha trabajado principalmente en métodos de regresión local, proponiendo técnicas de diseño del kernel que sean adecuadas a configuraciones de alta dimensionalidad y funciones de regresión dispersas. También se presenta una aplicación de las técnicas de regresión regularizada para modelar la respuesta de neuronas reales. Los avances en clasificación supervisada tratan, por una parte, con el uso de regularización para obtener un clasificador naive Bayes y, por otra parte, con el desarrollo de un algoritmo que usa regularización por grupos de una manera eficiente y que se ha aplicado al diseño de interfaces cerebromáquina. Finalmente, se presenta una heurística para inducir la estructura de redes Bayesianas Gaussianas usando regularización L1 a modo de filtro.

Grouped sparsity algorithm for multichannel intracardiac ECG synchronization

In this paper, a new method is presented to ensure automatic synchronization of intracardiac ECG data, yielding a three-stage algorithm. We first compute a robust estimate of the derivative of the data to remove low-frequency perturbations. Then we provide a grouped-sparse representation of the data, by means of the Group LASSO, to ensure that all the electrical spikes are simultaneously detected. Finally, a post-processing step, based on a variance analysis, is performed to discard false alarms. Preliminary results on real data for sinus rhythm and atrial fibrillation show the potential of this approach.

Sparsity and "something else": an approach to encrypted image folding

A property of sparse representations in relation to their capacity for information storage is discussed. It is shown that this feature can be used for an application that we term Encrypted Image Folding. The proposed procedure is realizable through any suitable transformation. In particular, in this paper we illustrate the approach by recourse to the Discrete Cosine Transform and a combination of redundant Cosine and Dirac dictionaries. The main advantage of the proposed technique is that both storage and encryption can be achieved simultaneously using simple processing steps.

On stopwords, filtering and data sparsity for sentiment analysis of Twitter

Sentiment classification over Twitter is usually affected by the noisy nature (abbreviations, irregular forms) of tweets data. A popular procedure to reduce the noise of textual data is to remove stopwords by using pre-compiled stopword lists or more sophisticated methods for dynamic stopword identification. However, the effectiveness of removing stopwords in the context of Twitter sentiment classification has been debated in the last few years. In this paper we investigate whether removing stopwords helps or hampers the effectiveness of Twitter sentiment classification methods. To this end, we apply six different stopword identification methods to Twitter data from six different datasets and observe how removing stopwords affects two well-known supervised sentiment classification methods. We assess the impact of removing stopwords by observing fluctuations on the level of data sparsity, the size of the classifier's feature space and its classification performance. Our results show that using pre-compiled lists of stopwords negatively impacts the performance of Twitter sentiment classification approaches. On the other hand, the dynamic generation of stopword lists, by removing those infrequent terms appearing only once in the corpus, appears to be the optimal method to maintaining a high classification performance while reducing the data sparsity and substantially shrinking the feature space

Sparse matrix multiplication on a reconfigurable many-core architecture

Sparse matrix-vector multiplication (SMVM) is a fundamental operation in many scientific and engineering applications. In many cases sparse matrices have thousands of rows and columns where most of the entries are zero, while non-zero data is spread over the matrix. This sparsity of data locality reduces the effectiveness of data cache in general-purpose processors quite reducing their performance efficiency when compared to what is achieved with dense matrix multiplication. In this paper, we propose a parallel processing solution for SMVM in a many-core architecture. The architecture is tested with known benchmarks using a ZYNQ-7020 FPGA. The architecture is scalable in the number of core elements and limited only by the available memory bandwidth. It achieves performance efficiencies up to almost 70% and better performances than previous FPGA designs.

Tuning metadata for better movie content-based recommendation systems

The increasing number of television channels, on-demand services and online content, is expected to contribute to a better quality of experience for a costumer of such a service. However, the lack of efficient methods for finding the right content, adapted to personal interests, may lead to a progressive loss of clients. In such a scenario, recommendation systems are seen as a tool that can fill this gap and contribute to the loyalty of users. Multimedia content, namely films and television programmes are usually described using a set of metadata elements that include the title, a genre, the date of production, and the list of directors and actors. This paper provides a deep study on how the use of different metadata elements can contribute to increase the quality of the recommendations suggested. The analysis is conducted using Netflix and Movielens datasets and aspects such as the granularity of the descriptions, the accuracy metric used and the sparsity of the data are taken into account. Comparisons with collaborative approaches are also presented.

Portuguese plain architecture: history opening a closed sequence

The paper will address George Kubler’s Portuguese Plain Architecture [PPA] (1972) and its effect in Portuguese architectural practice. Kubler’s philosophy of art history implied that closed sequences of objects could be opened by several reasons. Thus, it will be argued that there is an effect upon Portuguese architecture post 1974, that is apparent by the reemergence of some of the form classes treated by Kubler. This was mostly achieved through the popularity of Kubler’s book within architectural practice, scholarship and moreover by the establishment of the term “Plain Architecture” in portuguese architectural vocabulary. Plain Architecture of the seventeenth and eighteenth centuries shared some qualities with the architecture to be built in post‑revolutionary Portugal, most importantly the effect that could be achieved with low budget buildings that were responding to a situation of crisis, and simultaneously exhaled aristocratic sparsity. The connection of PPA with the ideological attributes of early modernism and the political context of the time catalysed the reemergence of a new order of Portuguese Plain that resonates still in contemporary architecture.

Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

Characterization of chromosomal instability in murine colitis-associated colorectal cancer.

AbstractBACKGROUND: Patients suffering from ulcerative colitis (UC) bear an increased risk for colorectal cancer. Due to the sparsity of colitis-associated cancer (CAC) and the long duration between UC initiation and overt carcinoma, elucidating mechanisms of inflammation-associated carcinogenesis in the gut is particularly challenging. Adequate murine models are thus highly desirable. For human CACs a high frequency of chromosomal instability (CIN) reflected by aneuploidy could be shown, exceeding that of sporadic carcinomas. The aim of this study was to analyze mouse models of CAC with regard to CIN. Additionally, protein expression of p53, beta-catenin and Ki67 was measured to further characterize murine tumor development in comparison to UC-associated carcinogenesis in men.METHODS: The AOM/DSS model (n = 23) and IL-10(-/-) mice (n = 8) were applied to monitor malignancy development via endoscopy and to analyze premalignant and malignant stages of CACs. CIN was assessed using DNA-image cytometry. Protein expression of p53, beta-catenin and Ki67 was evaluated by immunohistochemistry. The degree of inflammation was analyzed by histology and paralleled to local interferon-γ release.RESULTS: CIN was detected in 81.25% of all murine CACs induced by AOM/DSS, while all carcinomas that arose in IL-10(-/-) mice were chromosomally stable. Beta-catenin expression was strongly membranous in IL-10(-/-) mice, while 87.50% of AOM/DSS-induced tumors showed cytoplasmatic and/or nuclear translocation of beta-catenin. p53 expression was high in both models and Ki67 staining revealed higher proliferation of IL-10(-/-)-induced CACs.CONCLUSIONS: AOM/DSS-colitis, but not IL-10(-/-) mice, could provide a powerful murine model to mechanistically investigate CIN in colitis-associated carcinogenesis.PMID: 21799775 [PubMed - in process] PMCID: PMC3142131Free PMC Article

Accelerated MR imaging with spread spectrum encoding

We advocate the use of a novel compressed sensing technique for accelerating the magnetic resonance image acquisition process, coined spread spectrum MR imaging or simply s2MRI. The method resides in pre-modulating the signal of interest by a linear chirp, resulting from the application of quadratic phase profiles, before random k-space under-sampling with uniform average density. The effectiveness of the procedure is theoretically underpinned by the optimization of the coherence between the sparsity and sensing bases. The application of the technique for single coil acquisitions is thoroughly studied by means of numerical simulations as well as phantom and in vivo experiments on a 7T scanner. The corresponding results suggest a favorable comparison with state-of-the-art variable density k-space under-sampling approaches.