Related papers: The topography of multivariate normal mixtures
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…
Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches…
In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
Stochastic modeling has become a popular approach to quantify uncertainty in flows through heterogeneous porous media. The uncertainty in heterogeneous structure properties is often parameterized by a high-dimensional random variable. This…
We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to…
Coincidences of maps between smooth manifolds are studied via a geometric approach which involves (nonstabilized) normal bordism theory and pathspaces.
This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…
Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…
We study various manifestations of structural crossover in the properties of a binary mixture of hard-spheres. For homogeneous mixtures that are sufficiently asymmetric, there is a crossover line in the phase diagram such that for…
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing…
Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While persistent homology, as a core tool of TDA, focuses on…
The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…
Characterization of transient intermediate or transition states is crucial for the description of biomolecular folding pathways, which is however difficult in both experiments and computer simulations. Such transient states are typically of…
In this contribution, we derive a gas-liquid two-scale multi-fluid model with capillarity effects to enable a novelinterface regularization approach for multi-fluid models. As this unified modelling is capable of switching from theinterface…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Raw images are in the form of triangulated surfaces and the first step is to create a standardised…