Related papers: Geometric Data Analysis, From Correspondence Analy…
Structural features are important features in a geometrical graph. Although there are some correlation analysis of features based on covariance, there is no relevant research on structural feature correlation analysis with graph neural…
These lecture notes present a computation driven pathway from classical complex analysis to the theory of compact Riemann surfaces and their connections to algebraic geometry. The exposition follows a compute first then abstract philosophy,…
Data models are necessary for the birth of data and of any data-driven system. Indeed, every algorithm, every machine learning model, every statistical model, and every database has an underlying data model without which the system would…
While pre-trained large-scale vision models have shown significant promise for semantic correspondence, their features often struggle to grasp the geometry and orientation of instances. This paper identifies the importance of being…
Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of…
This is a comment on [G. Knight and R. Klages, Phys. Rev. E 84, 041135 (2011); also available at arXiv:1107.5293v2 [math-ph]].
Graph Networks (GNs) enable the fusion of prior knowledge and relational reasoning with flexible function approximations. In this work, a general GN-based model is proposed which takes full advantage of the relational modeling capabilities…
Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies. CA has found applications in fields ranging from epidemiology to social sciences. However, current methods used to perform CA…
A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.
Creating virtual models of real spaces and objects is cumbersome and time consuming. This paper focuses on the problem of geometric reconstruction from sparse data obtained from certain image-based modeling approaches. A number of elegant…
Image-text matching has received growing interest since it bridges vision and language. The key challenge lies in how to learn correspondence between image and text. Existing works learn coarse correspondence based on object co-occurrence…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
We introduce a method to learn a hierarchy of successively more abstract representations of complex data based on optimizing an information-theoretic objective. Intuitively, the optimization searches for a set of latent factors that best…
This text is based on a translation of a chapter in a handbook about network analysis (published in German) where we tried to make beginners familiar with some basic notions and recent developments of network analysis applied to…
With systems for acquiring 3D surface data being evermore commonplace, it has become important to reliably extract specific shapes from the acquired data. In the presence of noise and occlusions, this can be done through the use of…
Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…
Comment on "High Resolution Polar Effect Measurements of Sr2RuO4: Evidence for Broken Time-Reversal Symmetry in the Superconducting State" by J. Xia et al., Phys. Rev. Lett. 97, 167002 (2006).
Graphical modelling has a long history in statistics as a tool for the analysis of multivariate data, starting from Wright's path analysis and Gibbs' applications to statistical physics at the beginning of the last century. In its modern…
Discussion of "Treelets--An adaptive multi-scale basis for sparse unordered data" [arXiv:0707.0481]
Discussion of "Treelets--An adaptive multi-scale basis for sparse unordered data" [arXiv:0707.0481]