A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Finite mapping class groups for Heegaard splittings with distance ≥ 3, but not for distance 2.
New distances defined on Legendrian spaces without positive loops.
This paper refines MMD for domain adaptation by balancing intra-class and inter-class distances.
In this paper, we focus on the separability of classes with the cross-entropy loss function for classification problems by theoretically analyzing the intra-class distance and inter-class distance (i.e. the distance between any two points belonging to the same class and different classes, respectively) in the feature s…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
Defines Lorentzian distance on contactomorphisms, proving continuity and finite conditions.
Study shows intrinsic timed Hausdorff convergence leads to Gromov-Hausdorff and big bang convergence.
A new data augmentation method selects mixed classes based on class distances for better performance.
We show that if the Hempel distance of a Heegaard splitting is larger than three then the mapping class group of the Heegaard splitting is isomorphic to a subgroup of the mapping class group of the ambient 3-manifold. This implies that given two handlebody sets in the curve complex for a surface that are distance at le…
Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of testing one by one the entries of an ever-expanding dictionary of {\em ad hoc} dis…
Physics: Similar long-distance properties can mask vastly different short-distance metrics.
Study geodesic distances and convexity in contact sets.
Person re-identification (Re-ID) aims at matching images of the same person across disjoint camera views, which is a challenging problem in multimedia analysis, multimedia editing and content-based media retrieval communities. The major challenge lies in how to preserve similarity of the same person across video footag…
New distances measure mixtures of Gaussians, useful in machine learning.
SWRLDA improves LDA for multi-class classification with edge classes.
Despite numerous attempts to defend deep learning based image classifiers, they remain susceptible to the adversarial attacks. This paper proposes a technique to identify susceptible classes, those classes that are more easily subverted. To identify the susceptible classes we use distance-based measures and apply them …
This thesis uses Kantorovich-Rubinstein distance for classifying points based on their measures.
We show that on a certain class of bounded, complete Reinhardt domains in that enjoy a lot of symmetries, the Carathéodory pseudo-distance and the geodesic distance of the complete Kähler-Einstein metric with Ricci curvature are different.
SQFA learns features maximizing Fisher-Rao distance for better classification.
We show that if is a closed three manifold with a Heegaard splitting with sufficiently big "handlebody distance" then the subgroup of the mapping class group of the Heegaard surface, which extend to both handlebodies is finite. As a corollary, this implies that under the same hypothesis, the mapping class group of …
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproduc…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as establ…
We introduce an asymmetric distance function, which we call the `left Hausdorff distance function', on the space of geodesic laminations on a closed hyperbolic surface of genus at least 2. This distance is an asymmetric version of the Hausdorff distance between compact subsets of a metric space. We prove a rigidity res…
A slice distance for the class of weak abelian Lp-bundles in 3 dimensions was introduced in a previous article in collaboration with Tristan Rivière, where it was used to prove the closure of such class of bundles for the weak Lp-convergence. We further investigate this distance here, and we prove more properties of it…
New bounds on curve distances on surfaces of arbitrary genus.
Flexible classifier using Mahalanobis distances for non-elliptical distributions.
Unsupervised clustering can reproduce categorization systems if features and metrics are correctly selected.
A new kNN imputation method improves classification performance on datasets with missing data.
End-to-end approach learns pseudo-distance for verifying example sets.
New method estimates SW distance using CDFs for scalable data parallelism.
Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing deep metric learning techniques, the embedding of an instance is given by a featur…
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize some of the popular metrics, such as the Jaccard and bag distances on sets, Man…
We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow …
New measures assess differences in causal graphs' separations.
New formula and algorithm for computing distances on complex Riemann surfaces.
Tomova, along with results of Bachman and Schleimer, showed that any high distance knot has a stair-step bridge spectrum. In this paper, we compute the bridge spectra and distance of generalized Montesinos knots. In particular, we produce the first example of a class of knots which attain the stair-step bridge spectra …
Study convexity of Mabuchi functional in big cohomology classes.
Boundary distances determine conformal metrics
We calculate Euclidean distance degrees for common manifold optimization types.
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative coefficient matrix, and the coefficient matrix is used as the new representation. …
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics whenever the ground distance between the marginals is a metric, generalize both…
We develop the distance dependent Chinese restaurant process (CRP), a flexible class of distributions over partitions that allows for non-exchangeability. This class can be used to model many kinds of dependencies between data in infinite clustering models, including dependencies across time or space. We examine the pr…
Random forest can be adapted for open-set recognition with improved performance.
Example shows learnable distributions not privately learnable.
A new method estimates uncertainty without explicit prediction models.
A Discriminative Deep Forest (DisDF) as a metric learning algorithm is proposed in the paper. It is based on the Deep Forest or gcForest proposed by Zhou and Feng and can be viewed as a gcForest modification. The case of the fully supervised learning is studied when the class labels of individual training examples are …
Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance. Specifically, we construct confidence intervals for the Sliced Wasserstein distanc…