Related papers: Second-order difference subspace
This paper proposes a new method for anomaly detection in time-series data by incorporating the concept of difference subspace into the singular spectrum analysis (SSA). The key idea is to monitor slight temporal variations of the…
This paper presents a novel method for introducing time into discrete and continuous spatial representations used in mobile robotics, by modelling long-term, pseudo-periodic variations caused by human activities. Unlike previous approaches,…
Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…
The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory.…
The goal of subspace learning is to find a $k$-dimensional subspace of $\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a…
This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of…
Many machine learning methods look for low-dimensional representations of the data. The underlying subspace can be estimated by first choosing a dimension $q$ and then optimizing a certain objective function over the space of…
The increasing use of multiple sensors, which produce a large amount of multi-dimensional data, requires efficient representation and classification methods. In this paper, we present a new method for multi-dimensional data classification…
We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example we give the gauge-invariant definition of the second-order curvature perturbation on uniform density…
The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability. However,…
Symmetry detection and morphological classification of anatomical structures play pivotal roles in medical image analysis. The application of kinematic surface fitting, a method for characterizing shapes through parametric stationary…
We propose a conjugate gradient type optimization technique for the computation of the Karcher mean on the set of complex linear subspaces of fixed dimension, modeled by the so-called Grassmannian. The identification of the Grassmannian…
The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by…
Dynamic subspace estimation, or subspace tracking, is a fundamental problem in statistical signal processing and machine learning. This paper considers a geodesic model for time-varying subspaces. The natural objective function for this…
This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is…
The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that…
Imaging with the second-order correlation of two light fields is a method to image an object by two-photon interference involving a joint detection of two photons at distant space-time points. We demonstrate for the first time that an image…
We continue to study the 2nd-order cosmological perturbations in synchronous coordinates in the framework of the general relativity (GR) during the radiation dominated (RD) stage, and to focus on the scalar-tensor and tensor-tensor…