Multivariate texture discrimination based on geodesics to class centroids on a generalized Gaussian Manifold

A texture discrimination scheme is proposed wherein probability distributions are deployed on a probabilistic manifold for modeling the wavelet statistics of images. We consider the Rao geodesic distance (GD) to the class centroid for texture discrimination in various classification experiments. We compare the performance of GD to class centroid with the Euclidean distance in a similar context, both in terms of accuracy and computational complexity. Also, we compare our proposed classification scheme with the k-nearest neighbor algorithm. Univariate and multivariate Gaussian and Laplace distributions, as well as generalized Gaussian distributions with variable shape parameter are each evaluated as a statistical model for the wavelet coefficients. The GD to the centroid outperforms the Euclidean distance and yields superior discrimination compared to the k-nearest neighbor approach

Detection of brain functional-connectivity difference in post-stroke patients using group-level covariance modeling

Functional brain connectivity, as revealed through distant correlations in the signals measured by functional Magnetic Resonance Imaging (fMRI), is a promising source of biomarkers of brain pathologies. However, establishing and using diagnostic markers requires probabilistic inter-subject comparisons. Principled comparison of functional-connectivity structures is still a challenging issue. We give a new matrix-variate probabilistic model suitable for inter-subject comparison of functional connectivity matrices on the manifold of Symmetric Positive Definite (SPD) matrices. We show that this model leads to a new algorithm for principled comparison of connectivity coefficients between pairs of regions. We apply this model to comparing separately post-stroke patients to a group of healthy controls. We find neurologically-relevant connection differences and show that our model is more sensitive that the standard procedure. To the best of our knowledge, these results are the first report of functional connectivity differences between a single-patient and a group and thus establish an important step toward using functional connectivity as a diagnostic tool

Characterizing Distances of Networks on the Tensor Manifold

At the core of understanding dynamical systems is the ability to maintain and control the systems behavior that includes notions of robustness, heterogeneity, or regime-shift detection. Recently, to explore such functional properties, a convenient representation has been to model such dynamical systems as a weighted graph consisting of a finite, but very large number of interacting agents. This said, there exists very limited relevant statistical theory that is able cope with real-life data, i.e., how does perform analysis and/or statistics over a family of networks as opposed to a specific network or network-to-network variation. Here, we are interested in the analysis of network families whereby each network represents a point on an underlying statistical manifold. To do so, we explore the Riemannian structure of the tensor manifold developed by Pennec previously applied to Diffusion Tensor Imaging (DTI) towards the problem of network analysis. In particular, while this note focuses on Pennec definition of geodesics amongst a family of networks, we show how it lays the foundation for future work for developing measures of network robustness for regime-shift detection. We conclude with experiments highlighting the proposed distance on synthetic networks and an application towards biological (stem-cell) systems.Comment: This paper is accepted at 8th International Conference on Complex Networks 201

Second-order networks in PyTorch

International audienceClassification of Symmetric Positive Definite (SPD) matrices is gaining momentum in a variety machine learning application fields. In this work we propose a Python library which implements neural networks on SPD matrices, based on the popular deep learning framework Pytorch

Color texture discrimination using the principal geodesic distance on a multivariate generalized Gaussian manifold

We present a new texture discrimination method for textured color images in the wavelet domain. In each wavelet subband, the correlation between the color bands is modeled by a multivariate generalized Gaussian distribution with fixed shape parameter (Gaussian, Laplacian). On the corresponding Riemannian manifold, the shape of texture clusters is characterized by means of principal geodesic analysis, specifically by the principal geodesic along which the cluster exhibits its largest variance. Then, the similarity of a texture to a class is defined in terms of the Rao geodesic distance on the manifold from the texture's distribution to its projection on the principal geodesic of that class. This similarity measure is used in a classification scheme, referred to as principal geodesic classification (PGC). It is shown to perform significantly better than several other classifiers

Stochastic Development Regression on Non-Linear Manifolds

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes

Statistically Motivated Second Order Pooling

Second-order pooling, a.k.a.~bilinear pooling, has proven effective for deep learning based visual recognition. However, the resulting second-order networks yield a final representation that is orders of magnitude larger than that of standard, first-order ones, making them memory-intensive and cumbersome to deploy. Here, we introduce a general, parametric compression strategy that can produce more compact representations than existing compression techniques, yet outperform both compressed and uncompressed second-order models. Our approach is motivated by a statistical analysis of the network's activations, relying on operations that lead to a Gaussian-distributed final representation, as inherently used by first-order deep networks. As evidenced by our experiments, this lets us outperform the state-of-the-art first-order and second-order models on several benchmark recognition datasets.Comment: Accepted to ECCV 2018. Camera ready version. 14 page, 5 figures, 3 table

Observations of the post shock break-out emission of SN 2011dh with XMM-Newton

After the occurrence of the type cIIb SN 2011dh in the nearby spiral galaxy M 51 numerous observations were performed with different telescopes in various bands ranging from radio to gamma-rays. We analysed the XMM-Newton and Swift observations taken 3 to 30 days after the SN explosion to study the X-ray spectrum of SN 2011dh. We extracted spectra from the XMM-Newton observations, which took place ~7 and 11 days after the SN. In addition, we created integrated Swift/XRT spectra of 3 to 10 days and 11 to 30 days. The spectra are well fitted with a power-law spectrum absorbed with Galactic foreground absorption. In addition, we find a harder spectral component in the first XMM-Newton spectrum taken at t ~ 7 d. This component is also detected in the first Swift spectrum of t = 3 - 10 d. While the persistent power-law component can be explained as inverse Compton emission from radio synchrotron emitting electrons, the harder component is most likely bremsstrahlung emission from the shocked stellar wind. Therefore, the harder X-ray emission that fades away after t ~ 10 d can be interpreted as emission from the shocked circumstellar wind of SN 2011dh.Comment: Accepted for publication as a Research Note in Astronomy and Astrophysic