Related papers: Adaptive Metrics for Adaptive Samples
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…
Mobile sensing has been recently proposed for sampling spatial fields, where mobile sensors record the field along various paths for reconstruction. Classical and contemporary sampling typically assumes that the sampling locations are…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling and reconstructing…
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…
Unsupervised anomaly detection aims to detect defective parts of a sample by having access, during training, to a set of normal, i.e. defect-free, data. It has many applications in fields, such as industrial inspection or medical imaging,…
In this paper, we introduce a method to build an adapted mesh representation of a 3D object for X-Ray tomography reconstruction. Using this representation, we provide means to reduce the computational cost of reconstruction by way of…
Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform…
Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to…
A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used…
The distance function to a compact set plays a crucial role in the paradigm of topological data analysis. In particular, the sublevel sets of the distance function are used in the computation of persistent homology -- a backbone of the…
Existing methods for unsupervised domain adaptation often rely on minimizing some statistical distance between the source and target samples in the latent space. To avoid the sampling variability, class imbalance, and data-privacy concerns…
To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…
We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…
Adaptive spectral (AS) decompositions associated with a piecewise constant function $u$ yield small subspaces where the characteristic functions comprising $u$ are well approximated. When combined with Newton-like optimization methods for…