Graph neural network learns graph distances effectively.
problem Maintaining graph distance metric properties.
method GRAPH-BERT based semi-supervised distance metric learning.
result GB-DISTANCE outperforms existing methods.
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48 results for “Distance metric”
An older paper by Edwards introduced the Gromov-Hausdorff distance.
problem Determining the first inventor of the Gromov-Hausdorff distance.
method Comparing metric spaces through isometric embeddings and measuring Hausdorff distance.
result David Edwards published the Gromov-Hausdorff distance 6 years before M. Gromov.
CADM proposes a cluster-specific distance metric for categorical data clustering.
problem Inadequate distance metrics for categorical data, especially varying within clusters.
method Cluster-customized adaptive distance metric for categorical data.
result Achieved competitive performance in categorical data clustering.
Extends manifold learning to non-Euclidean metrics.
problem Applying manifold learning to data in non-Euclidean spaces.
method Generalizes manifold learning to metric spaces and studies conditions for convergence.
result Conditions for the convergence of graph Laplacian in metric spaces.
Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two major problems. First, most algorithms only offer point estimation of the distanc…
New metric learning approach for tree data reduces computation cost.
problem Efficiently computing distances between ordered labeled trees.
method Introduced pq-grams and a differentiable weighted pq-gram distance, combined with LMNN for optimization.
result Significantly reduces computation time for tree classification problems.
A new robust time series distance metric for k-NN classification.
problem Robustness against arbitrary data contamination in time series classification.
method Proposes a novel distance metric with worst-case complexity.
result Demonstrates competitive classification accuracy in k-NN time series classification.
Improved image ranking model using ordinal distance metric learning and multidimensional scaling.
problem Ranking images based on known ranked images.
method Proposes an improved linear ordinal distance metric learning approach using multidimensional scaling.
result Demonstrates improved ranking performance and speed over the linear distance metric learning model.
Bounds on geodesic distances on Stiefel manifold derived from new metrics.
problem Improving geodesic computation algorithms and understanding Stiefel manifold.
method New geometric insights and Lipschitz constants for geodesic distances.
result Explicit bounds on geodesic distances and conditions for attaining bounds.
Metrics converge under certain conditions, leading to a coinciding limit distance function.
problem Convergence of metrics with bounded scalar curvature.
method Convergence in and subconvergence of distance functions.
result Limit distance function coincides with the induced distance function.
The -metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type in a Riemannian manifold induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that its geodesic distance is a good topological metric. The vanishing phenomenon for…
A new supervised tree-Wasserstein distance improves document classification.
problem Measuring document similarity efficiently and accurately.
method Rewriting Wasserstein distance on tree metric, using contrastive loss for optimization.
result The Supervised Tree-Wasserstein (STW) distance improves document classification accuracy.
This paper proposes a new method for embedding sequences using Wasserstein distances.
problem Embedding sequences in a metric space for better pattern recognition.
method Develops a deep learning model that embeds sequences as distributions and uses Wasserstein distances for comparison.
result Distributional embeddings using Wasserstein distances outperform traditional vector embeddings.
Assigns compact set distance-like functions to non-compact geodesic spaces.
problem Assigning distance-like functions to compact sets in non-compact geodesic spaces.
method Assigns each compact set a distance-like function and studies the pseudo-metric on the space of compact subsets.
result Obtains a pseudo-metric on the space of compact subsets that is less than the Hausdorff distance.
Metric learning improves tree edit distance for better classification.
problem Improving tree edit distance for better classification accuracy.
method Adaptive symbol embeddings to learn tree edit distance indirectly.
result Embedding edit distance learning (BEDL) improves upon state-of-the-art on multiple tree data sets.
Sparse metric repair minimizes changes to data to make distances metric.
problem Repairing noisy metric distances with minimal changes.
method Three combinatorial algorithms to minimize sparsity of changes.
result Guaranteed sparsest solution in one setting, metric repair in others.
Pearson distance fails to be a metric, but can be fixed.
problem The Pearson distance is not a metric, leading to issues in applications.
method Showed that Pearson distance is not a metric and provided alternative metrics.
result Pearson distance can be repaired by using alternative metrics derived from the correlation coefficient.
New metrics unify and generalize popular distances for data mining.
problem Unified and generalized distances for data mining.
method Introducing new metrics on sets, vectors, and functions.
result New metrics outperform traditional ones in real-valued and structured data.
Modified cosine distance improves similarity performance in data with variance and correlation.
problem Limitations of traditional cosine similarity in random variable spaces with variance and correlation.
method Proposed a variance-adjusted cosine distance metric to overcome limitations of traditional cosine similarity.
result Modified cosine distance shows 100% test accuracy in KNN model on the Wisconsin Breast Cancer Dataset.
Study uses equivariant topology to measure distances between G metric spaces.
problem Measuring distances between G metric spaces.
method Equivariant topology methods to derive lower bounds.
result Sharp bounds on Gromov Hausdorff distance between spheres.
New method learns local metrics for k-NN classification using sample similarity.
problem Improving k-NN classification accuracy through better distance metrics.
method Local distance metric learning based on sample similarity, using conical combinations of metric weight matrices.
result New metrics yield smaller distances for similar samples and larger distances for dissimilar ones.
Compactness theorem for timed-metric spaces established.
problem Compactness of timed-metric spaces and causality.
method Timed-Gromov--Hausdorff distance and intrinsic timed-Hausdorff distance.
result Induces same notion of convergence as intrinsic timed-Hausdorff distance.
Tree Edit Distance Learning via Adaptive Symbol Embeddings: Supplementary Materials and Resultscs.LG
A new method embeds tree nodes to vectors for better tree edit distance learning.
problem Learning tree edit distances directly often violates metric axioms and is hard to interpret.
method Adaptive symbol embeddings to learn tree edit distances indirectly.
result Improves tree edit distance learning on multiple datasets.
Sharp estimates for Finsler metrics in convex domains.
problem Estimating distances in Finsler metrics near convex points.
method Sharp estimates for intrinsic distances of Finsler metrics.
result Characterization of -quasi hyperbolic metric in convex geometry.
A new method learns meaningful distances between samples using optimal transport.
problem Learning meaningful distances between samples in datasets without labeled data.
method Computes OT distances between samples and features using singular vectors of a function mapping ground metrics to OT distances.
result Wasserstein Singular Vectors provide a scalable solution for unsupervised ground metric learning.
Limit curve theorems for incomplete metric spaces and the null distance on Lorentzian manifoldsmath.DG
Proves limit curve theorem for incomplete metric spaces, applies to null distance in Lorentzian manifolds.
problem Control of Lorentzian lengths of limit curves in incomplete metric spaces.
method Proves limit curve theorem for incomplete metric spaces and applies to null distance.
result Strong control on Lorentzian lengths of limit curves in Sormani and Vegas' null distance.
A new method clusters categorical data by learning their optimal order and distance.
problem Clustering categorical data lacks a well-defined metric space.
method Order distance metric learning for categorical data.
result Superior clustering accuracy on categorical and mixed datasets.
Vanishing geodesic distances in infinite dimensions can be created.
problem Vanishing geodesic distances in infinite-dimensional spaces.
method Constructing a weak Riemannian metric in a Hilbert manifold.
result Vanishing geodesic distances can be engineered.
Boundary distances determine conformal metrics
problem Determining conformal metrics from boundary distances
method Comparing renormalized boundary distances
result Metrics are equal if distances match
Study on Frechet distance properties for paths and graphs.
problem Understanding topological properties of Frechet distance spaces.
method Proving path-connectedness of Frechet distance spaces and metric balls.
result Spaces of paths and graphs under Frechet distance are path-connected.
A new metric mav offers a practical alternative to costly Riemannian distance.
problem Efficiently compute Riemannian distance on SE(3) invariant metrics.
method Propose mav distance, defined as Riemannian length of a curve.
result Mav distance offers a trainable invariant for geometric deep learning.
Self-supervised metric learning boosts downstream tasks in multi-view data.
problem Improving distance-based downstream tasks without labeled data.
method Developed a statistical framework to study self-supervised metric learning in multi-view data.
result Self-supervised metric learning improves target distances for various downstream tasks.
This tutorial explains distance metric learning, its algorithms, and evaluates their performance.
problem Improving similarity-based algorithms by learning distances from data.
method Describes the problem, mathematical foundations, and evaluates popular algorithms.
result Outstanding algorithms identified for distance metric learning.
A novel criterion selects optimal distance metrics for cell profile analysis.
problem Determining the most accurate distance metric for high-dimensional cell profiles.
method Generalized proposition and corollaries to evaluate and select distance metrics.
result Wasserstein and cosine similarity metrics are optimal for general cases.
Geodesic distance vanishes for certain Sobolev metrics on diffeomorphisms.
problem Analyzing geodesic distance in diffeomorphism groups for various Sobolev norms.
method Study of right-invariant Sobolev metrics on compactly supported diffeomorphisms.
result Geodesic distance vanishes identically for , and is positive otherwise.
Automatically tunes distance threshold in metric learning.
problem Manual tuning of distance threshold in ITML-based methods is sensitive and time-consuming.
method Optimized metric learning algorithm using Dykstra algorithm to solve nonlinear equation efficiently.
result The proposed metric learning algorithm automatically tunes the distance threshold and achieves comparable accuracy.
Novel distances between distributions using conditional ground distances.
problem Quantifying distances between statistical multivariate distributions.
method Optimal transport with entropic regularization and ground distance on conditionals.
result Upper bounds for jointly convex distances and improved GMM learning.
Enhances nearest neighbor classifier performance with local distance metric learning.
problem Inconsistent data distribution across feature space.
method Local Mahalanobis Distance Learning (LMDL) considers neighborhood influence and learns multiple distance metrics for prototypes.
result LMDL improves nearest neighbor classifier performance on various datasets.
Paper proves rigidity of inversive distance circle packings.
problem Proving rigidity of inversive distance circle packings.
method Variational principles and combinatorial curvature study.
result Global rigidity of inversive distance circle packings proved.
Different distances on symmetrical domains in complex space.
problem Comparing distances on specific complex domains.
method Examined Carathéodory pseudo-distance and Kähler-Einstein metric distances.
result Found the distances differ on certain complex domains.
Proves compactness for timed-metric spaces using new distance and maps.
problem Weak convergence of space-times using timed-Hausdorff distance.
method Uses Gromov's original compactness theorem and introduces addresses.
result Establishes compactness theorem for intrinsic timed-Hausdorff convergence.
Study sequences of static spacetimes using null distance convergence.
problem How to define convergence for sequences of spacetimes.
method Define null distance metric space structure compatible with Lorentzian structure.
result Prove VADB theorem for sequences of static spacetimes with null distance.
New neural nets respect triangle inequality, improving graph and reinforcement learning performance.
problem Neural nets lack inductive bias for certain subadditive distances.
method Introduced novel architectures that universally approximate norm-induced metrics.
result Neural nets with triangle inequality inductive bias outperform existing approaches.
Neural networks can learn distance metrics affecting model performance.
problem Understanding how neural networks learn and represent data.
method Experiments with six MNIST architectures, constrained to learn either distance or intensity representations.
result Distance-based learning affects model performance, validating the geometric framework.
The paper establishes Sobolev inequalities between Riemannian metrics and their distance functions.
problem Establishing a theory of Sobolev inequalities for Riemannian metrics and distance functions.
method Analyzing the sub-critical case $p < rac{m}{2}$, proving a Sobolev inequality linking $L^{ rac{p}{2}}$ bounds on metrics to bounds on distance functions.
result A Sobolev inequality exists between Riemannian metrics and their distance functions, leading to a convergence theorem.
Physics: Similar long-distance properties can mask vastly different short-distance metrics.
problem Classifying homogeneous metrics on group manifolds by long-distance properties.
method Apply universality concept to geometry, focusing on metrics on Lie groups.
result Many metrics on low-dimensional Lie groups have similar long-distance properties despite differing short-distance properties.
Geodesic rays and chordal distances link algebraic and geometric properties of positive metrics.
problem Understanding the geometry of the space of positive metrics at infinity.
method Using Monge-Ampère equations and test configurations, algebraic descriptions of geodesic rays and chordal distances are derived.
result The Mabuchi chordal distance between geodesic rays associated with ample test configurations equals the spectral distance between their filtrations.
This paper converts dtw-distance to a semi-metric for data mining.
problem dtw-distance lacks warping-invariance and triangle inequality.
method Semi-metrification of dtw-distance.
result The canonical extension of the semi-metric is warping-invariant.