We present a novel nonparametric approach for identification of nonlinear systems. Exploiting the framework Gaussian regression, unknown system is seen as realization from random field. Its covariance encodes idea “fading” memory in predictor and consists mixture kernels parametrized by few hyperparameters describing interactions among past inputs outputs. The kernel structure are estimated maximizing their marginal likelihood so that user not required to define any part algorithmic...

Person re-identification is probably the open challenge for low-level video surveillance in presence of a camera network with non-overlapped fields view. A large number direct approaches has emerged last five years, often proposing novel visual features specifically designed to highlight most discriminant aspects people, which are invariant pose, scale and illumination. On other hand, learning-based methods usually based on simpler features, trained pairs cameras discriminate between...

An important task in connectomics studies is the classification of connectivity graphs coming from healthy and pathological subjects. In this paper, we propose a mathematical framework based on Riemannian geometry kernel methods that can be applied to matrices for task. We tested our approach using different real datasets functional structural connectivity, evaluating metrics describe similarity between graphs. The empirical results obtained clearly show superior performance compared with...

This paper presents a general vector-valued reproducing kernel Hilbert spaces (RKHS) framework for the problem of learning an unknown functional dependency between structured input space and output space. Our formulation encompasses both Vector-valued Manifold Regularization Co-regularized Multi-view Learning, providing in particular unifying linking these two important approaches. In case least square loss function, we provide closed form solution, which is obtained by solving system linear...

Abstract Gaussian distributions are plentiful in applications dealing uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries probability measures, the resulting geometry on Gaussians is often expressible closed-form under frameworks. In this work, we study entropy-regularized 2-Wasserstein distance, by solutions distance interpolations between elements. Furthermore, provide a fixed-point characterization of population...

This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features, in the paradigm kernel methods on Riemannian manifolds. Our formulation provides rich representation image features by exploiting their non-linear correlations, power and geometry. Theoretically, we provide an approximate Log-Hilbert-Schmidt distance between that is efficient to compute scalable large datasets. Empirically, apply our task classification eight...

Covariance matrices play important roles in many areas of mathematics, statistics, and machine learning, as well their applications. In computer vision image processing, they give rise to a pow

We generalize the method of Slow Feature Analysis (SFA) for vector-valued functions several variables and apply it to problem blind source separation, in particular image separation. It is generally necessary use multivariate SFA instead univariate separating multi-dimensional signals. For linear case, an exact mathematical analysis given, which shows that sources are perfectly separated by if only they their first-order derivatives uncorrelated. When correlated, we following technique...

We formulate the problem of determining volume set Gaussian physical states in framework information geometry. This is done by considering phase space probability distributions parametrized their covariances and endowing resulting statistical manifold with Fisher-Rao metric. then evaluate classical, quantum, quantum entangled for two-mode systems, showing chains strict inclusions.

Identity safekeeping on chats has recently become an important problem social networks. One of the most issues is identity theft, where impostors steal a person, substituting her in chats, order to have access private information. In literature, been addressed by designing sets features which capture way person interacts through chats. However, such approaches perform well only long term, after conversation performed, this problem, since early turns conversation, much information can be...