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.
Differentially private data structures for estimating distances between strings.
problem Estimating distances between query strings and database strings while ensuring privacy.
method Proposes differentially private data structures for Hamming and edit distances using randomized response technique.
result Efficient data structures that provide accurate distance estimates with strong privacy guarantees.
Transforms distance-based outlier scores into interpretable probabilistic estimates.
problem Difficult interpretation of distance-based outlier scores.
method Generic transformation of scores into probabilistic estimates using distance probability distributions.
result Probabilistic transformation improves interpretability without impacting detection performance.
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.
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 framework for measuring differences in categorical data.
problem Measuring differences between categorical variables.
method Introduces a general framework for efficient and flexible implementation of distances for categorical variables.
result Framework allows for incorporation of existing distances and introduces new formulations.
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.
We address noisy Euclidean distances in high dimensions, estimating noise levels and correcting distances.
problem Distorted pairwise Euclidean distances due to heteroskedastic noise.
method Developed a hyperparameter-free approach to jointly estimate noise magnitudes and correct distances.
result Our method provides accurate noise magnitude estimates and corrected distances in high-dimensional settings.
This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usu…
Paper proposes a method to estimate total variation distance for synthetic data fidelity.
problem Assessing the fidelity of synthetic data generated by AI.
method Discriminative approach to estimate total variation distance between two distributions.
result Estimation of total variation distance reduces to quantifying Bayes risk in classification.
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately calculate distances. When data points are real-valued vectors, by far the most common c…
Quantum Earth Mover's distance improves stability and efficiency in quantum learning.
problem Quantum learning's loss landscapes often lead to poor local minima and gradients.
method Introduced the quantum Earth Mover's (EM) distance and proposed a quantum Wasserstein generative adversarial network (qWGAN).
result The quantum EM distance makes quantum learning more stable and efficient.
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 O(nlogn) complexity. result Demonstrates competitive classification accuracy in k-NN time series classification.
We improve density-based distances using normalizing flows and score matching.
problem Inaccurate density estimates and poor convergence in graph-based methods for high-dimensional spaces.
method Learn densities with normalizing flows and refine geodesics with a score model.
result Improved density-based distances that scale to high dimensions and improve numerical stability.
Study infinite Euclidean distance discriminants of algebraic varieties.
problem Understanding the structure of data points with infinitely many critical points in Euclidean distance correspondence.
method Developed computer code to compute discriminants and proved properties of fibers.
result Infinite Euclidean distance discriminants contain all data points with infinitely many critical points for the nearest-point problem.
A new model encodes distances and topology in latent variables.
problem Modeling dissimilarity data with latent variables and invariances.
method Isometric Gaussian Process Latent Variable Model using Riemannian geometry and variational inference.
result The model can encode invariances in learned manifolds.
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.
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…
This paper introduces a noise-robust clustering method using distribution distances.
problem Reducing noise impact on clustering results.
method Introduces expectation distance (ED) for distribution clustering, extending K-means and K-medoids.
result Improved clustering accuracy and reduced computation time.
A new spherical Sliced-Wasserstein distance for data on spheres.
problem Defining Wasserstein distance on manifolds, especially spheres.
method Closed-form solutions of the Wasserstein distance on the circle and a new spherical Radon transform.
result A novel spherical Sliced-Wasserstein (SW) discrepancy for data on spheres.
A new metric HCP distance for comparing distributions.
problem Comparing high-dimensional probability distributions efficiently.
method Hilbert curve projection to low-dimensional coupling, followed by transport distance calculation.
result HCP distance is a proper metric for probability measures with bounded supports.
This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on the space of persistence diagrams generates relevant input features for a classifi…
New method estimates SW distance using CDFs for scalable data parallelism.
problem Estimating SW distance efficiently for large datasets.
method Estimators based on CDFs of projected measures, avoiding sorting.
result Efficient estimation for large datasets and federated learning.
kdiff measures distances for time series and structured data.
problem Estimating distances between time series and structured data.
method kdiff uses non-linear kernel distances based on matching overlapping distributions.
result kdiff is more robust to noise and partial occlusions.
Paper defines a new distance metric for comparing learning tasks.
problem Comparing difficulty of learning tasks between source and target.
method Information geometry, optimal transport, coupled transfer distance.
result Coupled transfer distance correlates with fine-tuning difficulty.
Clustering is one of the major roles in data mining that is widely application in pattern recognition and image segmentation. Fuzzy C-means (FCM) is the most used clustering algorithm that proven efficient, fast and easy to implement, however, FCM uses the Euclidean distance that often leads to clustering errors, espec…
Proposes Mutual Regression Distance for better distribution comparison.
problem Lack of effective distance measures for manifold data.
method Constrained mutual regression problem to exploit manifold properties.
result Mutual Regression Distance (MRD) is a pseudometric effective for manifold data.
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density. Leveraging on properties of pairwise differences between data points, we propose a…
We generalize Mallows model to learn distance metrics from data.
problem Learning optimal distance metrics from noisy ranking data.
method Propose Lα distances and develop FPTAS for sampling and MLE. result Strong consistency of estimators for various α and β. 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…
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if t…
New distances for comparing multivariate normal distributions.
problem Comparing multivariate normal distributions efficiently and accurately.
method Approximated Fisher-Rao distance and pullback SPD cone distances.
result Efficient computation of distances between normal distributions.
A new metric compares true and learned causal graphs considering data and graph structure.
problem Comparing true and learned causal graphs accurately.
method Continuous Structural Intervention Distance (CSID) using conditional mean embeddings and maximum mean discrepancy.
result Validated the CSID with synthetic data, showing its effectiveness in comparing causal graphs.
Optimal pre-processing reduces disparate impact by minimizing total variation distance.
problem Achieving fairness in data outputs based on protected attributes.
method Using pre-processing to enforce fairness, minimizing total variation distance between pre-processed and original data distributions.
result The problem of fairness can be formulated as a linear program, efficiently solvable.
This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set of closely located distributions (based on a certain distance metric between di…
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for computing this distance grow quadratically with the size of the data, making th…
New DR method uses Gromov-Wasserstein distance for high-dimensional data.
problem Analyzing relationships between high-dimensional objects.
method Optimal transportation theory and Gromov-Wasserstein distance.
result Robust and efficient solution for complex high-dimensional datasets.
This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein (W2) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the infinite-dimensional setup, that the W2 distance has a smoothing effect on the inversion pro…
Proposes a Coulomb-like model for international trade flows, fitting real-world data.
problem Describing and predicting international trade flows between countries.
method Formulated a coulomb force model where GDP represents charge and distance is influenced by various factors.
result Developed a trade strength distribution equation that fits real-world data well.
SHAP Distance assesses semantic fidelity of synthetic tabular data.
problem Semantic fidelity of synthetic tabular data is not well evaluated.
method SHAP Distance, defined as cosine distance between global SHAP attribution vectors.
result SHAP Distance detects semantic discrepancies overlooked by standard measures.
EDD uses entropy of distance distributions to cluster unlabeled data.
problem Challenges in clustering unlabeled high-dimensional data.
method EDD employs Shannon entropy to quantify distance distribution peaks.
result EDD detects varying degrees of clustering sensitivity.
The paper calculates expected distances on partially oriented flag manifolds.
problem Understanding distances on partially oriented flag manifolds.
method Computing expected distances on low-dimensional examples.
result Computed expected distances on partially oriented flag manifolds.
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.
A new method detects small holes in noisy data.
problem Detecting small holes in high-density regions from noise.
method Robust Density-Aware Distance (RDAD) filtration, incorporating distance-to-measure concept.
result The RDAD filtration prolongs the persistences of small holes, making them distinguishable from noise.
Many modern data-intensive computational problems either require, or benefit from distance or similarity data that adhere to a metric. The algorithms run faster or have better performance guarantees. Unfortunately, in real applications, the data are messy and values are noisy. The distances between the data points are …
Paper introduces CWDAE for better synthetic data generation.
problem Measuring discrepancy between generative and ground-truth distributions.
method Introduces mixture Cramer-Wold distance for joint and marginal distributional learning.
result CWDAE shows remarkable performance in generating synthetic data.
We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to employ Minimax distances with many machine learning methods that perform on numerica…
Unified framework for hyperbolic embeddings from mixed data types.
problem Computing hyperbolic embeddings from noisy metric and non-metric data.
method Semidefinite programming and spectral factorization methods.
result Efficient computation of hyperbolic embeddings from arbitrary data.