Two proofs show the triangle inequality for Jaccard distance.
problem Triangle inequality for Jaccard distance
method Simple proofs using nonnegative, monotone, submodular functions
result Triangle inequality proven for Jaccard distance
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48 results for “Jaccard distance”
Two private algorithms estimate Jaccard similarity efficiently.
problem Estimating Jaccard similarity while preserving user privacy.
method Extends MinHash with Generalized Randomized Response and Laplace Mechanism.
result Achieves privacy-utility trade-off with theoretical bounds and experiments.
ProbMinHash improves Jaccard similarity hashing for big data applications.
problem Efficiently estimating set similarities in big data with weighted elements.
method Locality-sensitive hash algorithms that calculate signatures collectively.
result Significantly faster than the original approach, with improved estimation error.
Understanding and Improving UMAP with Geometric and Topological Priors: The JORC-UMAP Algorithmcs.LG
JORC-UMAP improves UMAP by incorporating geometric and topological priors.
problem UMAP's local Euclidean distance assumption fails to capture intrinsic manifold geometry, leading to topological tearing and structural collapse.
method JORC-UMAP introduces Ollivier-Ricci curvature as a geometric prior and Jaccard similarity as a topological prior to reinforce edges and reduce redundant links.
result JORC-UMAP reduces tearing and collapse more effectively than standard UMAP and other DR methods, as measured by SVM accuracy and triplet preservation scores.
FUJI scores similarity of ranked lists more robustly.
problem Improving similarity assessment of ranked lists.
method Integrates a membership function into Jaccard index for better rank consideration.
result More stable and accurate similarity estimates.
STRAPSim measures ETF portfolio similarity better than existing methods.
problem Measuring portfolio similarity for ETFs and portfolios.
method Semantic, two-level, residual-aware portfolio similarity computation.
result STRAPSim outperforms existing methods in predictive accuracy and ranking alignment.
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…
New STH distance finds patterns in event timeseries without resampling.
problem Lack of efficient analysis methods for event and state timeseries.
method Define STE-ts, propose STH, leveraging both time and state duration.
result Improved precision and computation time compared to resampled metrics.
Positive definite kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. In this paper we develop a set-theoretic interpretation of the Earth Mover's Distance (EMD) and propose Earth Mover's Interse…
The paper proposes methods to directly optimize complex classification metrics.
problem Handling class-imbalanced cases with non-decomposable metrics.
method Calibrated surrogate maximization of linear-fractional utility.
result Calibrated surrogate maximization can coincide with true utility maximization under certain conditions.
C-MinHash reduces the number of permutations needed for MinHash from thousands to just two.
problem Approximating Jaccard similarity in large binary datasets using many permutations.
method Initial permutation followed by circulant shifting of a second permutation to generate hashes.
result C-MinHash achieves unbiased Jaccard similarity estimation with uniformly smaller variance.
Efficient methods for sparse random projections improve classification accuracy in very high-dimensional data.
problem Handling very high-dimensional sparse data efficiently.
method Non-iterative and iterative classification methods using sparse random projections and Jaccard kernel.
result Non-iterative methods yield larger, more accurate models than iterative methods.
Reduced computational complexity for indoor positioning.
problem Efficiently positioning users in large areas with limited data.
method Segmentation, Jaccard index, LASSO feature selection, Bayesian MAP estimation.
result Positioning accuracy with a subset of features and sub-regions is equivalent to full data, but computation time is reduced.
Study uses U-Net for efficient urban planning map semantic segmentation.
problem Manual visual interpretation of urban planning maps is inefficient and time-consuming.
method Utilized U-shape fully convolutional architecture for end-to-end semantic segmentation.
result Achieved high Jaccard similarity coefficient of 93.63% and overall accuracy of 99.36%.
A probabilistic framework optimizes quantum clustering parameters.
problem Optimizing length parameters for quantum clustering sensitivity.
method Bayesian optimization of control parameters within a probabilistic framework.
result Optimized clustering yields better concordance with known data structure.
Conformal prediction fails under severe feature turnover in COVID-19 supply chain tasks.
problem Dealing with distribution shift in conformal prediction models.
method Using COVID-19 as a natural experiment across 8 supply chain tasks, analyzing SHAP explanations.
result Coverage drops vary widely (0% to 86.7%) and correlate with single-feature dependence.
New algorithms optimize metrics for binary classification with class imbalance.
problem Optimizing metrics like Fβ, AM, Jaccard for imbalanced classes.
method Reformulates metric optimization as cost-sensitive learning, using surrogate loss functions.
result METRO algorithms provide strong theoretical guarantees and outperform baselines.
Generative models' evaluation scores can be misleading, leading to inflated grades.
problem Misleading evaluation scores for generative models.
method Analyzed and compared various scores for evaluating synthetic vs. ground-truth data.
result The Eden score avoids grade inflation and better aligns with human perception.
This study examined how the correlation and network structure of 30 global indices and 145 local Korean indices belonging to the KOSPI 200 have changed during the 13-year period, 2000-2012. The correlations among the indices were calculated. The results showed that although the average correlations of the global indice…
IoU is not submodular, impacting machine learning applications.
problem IoU's submodularity assumption in machine learning is incorrect.
method Demonstrated through counterexamples and analysis of function properties.
result IoU is not a submodular function, invalidating its use in certain applications.
IVUS-Net automatically segments IVUS images for quicker diagnosis of cardiovascular diseases.
problem Automatically delineating lumen and media-adventitia borders in IVUS images.
method Proposes IVUS-Net, a fully convolutional network followed by post-processing.
result IVUS-Net outperforms state-of-the-art methods by 4% to 20% in HD distance.
Framework for consistent binary classification with complex metrics.
problem Consistent binary classification for non-decomposable metrics like F-measure and Jaccard.
method General framework for batch and online learning, applies to linear and non-linear models. Uses thresholding and normalized gradient ascent for threshold estimation.
result Simple normalized gradient ascent updates for threshold estimation, with finite-sample regret analysis.
TS-NMF improves topic models by incorporating user-provided labels.
problem Lack of interpretability in unsupervised topic models.
method Semi-supervised non-negative matrix factorization (TS-NMF) with user-provided labeled examples.
result TS-NMF achieves higher Jaccard similarity scores than unsupervised methods at low supervision rates.
Faster k-Medoids Clustering improves PAM, CLARA, CLARANS algorithms.
problem Efficiently clustering non-Euclidean data with high k.
method Modifications to PAM, CLARA, CLARANS algorithms to achieve O(k)-fold speedup.
result 200-fold speedup observed on real data with k=100.
C-OPH improves One Permutation Hashing by using a shorter circulant permutation.
problem Improving the accuracy of One Permutation Hashing (OPH) for Jaccard similarity estimation.
method Develops a new densification method using a shorter circulant permutation.
result Achieves the smallest estimation variance for Jaccard similarity.
Machine learning predicts movie genres from summaries with high accuracy.
problem Predicting movie genres from plot summaries.
method Used Naive Bayes, Word2Vec+XGBoost, Recurrent Neural Networks, and Gated Recurrent Units (GRU) for text classification and multi-label problem.
result GRU neural networks achieve the best result with a Jaccard Index of 50.0%, F-score of 0.56, and hit rate of 80.5%.
Proposes a new network to improve nuclei segmentation in histopathology images.
problem Challenges in separating overlapped nuclei in histopathology images.
method Introduces a bending loss regularized network to minimize contour points with large curvatures.
result Outperforms six state-of-the-art approaches on five quantitative metrics.
Extends Tanimoto kernel to real-valued functions.
problem Measuring similarity between real-valued functions.
method Unified representation of real-valued functions via sets, derived general form of the kernel, explicit feature representation, and smooth approximation.
result General Tanimoto kernel for real-valued functions.
Paper proposes a method to minimize non-differentiable loss functions.
problem Minimizing non-differentiable and non-decomposable loss functions.
method Learn smooth relaxations of true losses through surrogate neural networks, then optimize jointly with the prediction model.
result Empirical results show the efficiency of learning surrogate losses.
Stability in clinical prediction models is crucial for transferability between studies, yet has received little attention. The problem is paramount in high dimensional data which invites sparse models with feature selection capability. We introduce an effective method to stabilize sparse Cox model of time-to-events usi…
Estimates set overlap and similarity using random samples.
problem Estimating set overlap and similarity with limited data.
method Binomial model for predicting set overlap, comparing to previous methods.
result Binomial model provides better estimates with small sample sizes.
New metrics improve performance in imbalanced classification problems.
problem Established metrics favor classifiers ignoring minority classes.
method Introduce robust modifications of F-score and MCC.
result TPR is bounded away from 0 in imbalanced settings.
Study uses multimodal machine learning to predict ICD-10 codes.
problem Improving accuracy and interpretability of ICD-10 code predictions.
method Developed separate models for text and tabular data, integrated using an ensemble method.
result Best-performing model achieved micro-F1 of 0.7633 and micro-AUC of 0.9541.
CNN automates vitiligo lesion segmentation quickly and accurately.
problem Manual segmentation of vitiligo lesions is time-consuming and inconsistent.
method U-Net architecture with modified contracting path, followed by watershed algorithm refinement.
result CNN achieves 73.6% Jaccard Index, significantly outperforming state-of-the-art methods.
We provide a general theoretical analysis of expected out-of-sample utility, also referred to as decision-theoretic classification, for non-decomposable binary classification metrics such as F-measure and Jaccard coefficient. Our key result is that the expected out-of-sample utility for many performance metrics is prov…
Confidence intervals improve evaluation of binary prediction rules in data mining.
problem Uncertainty in performance measures estimation from finite datasets.
method Asymptotic normal approximations for confidence intervals, with a blurring correction.
result Improved finite sample coverage probabilities and general performance measures inference.
ReliefE ranks features faster and better in high-dimensional data.
problem Feature ranking in high-dimensional spaces.
method Adapting Relief algorithms to manifold embeddings.
result ReliefE outperforms traditional Relief algorithms in feature ranking.
Higher-Order Ranking and Link Prediction: From Closing Triangles to Closing Higher-Order Motifscs.LG
New methods for faster ranking and link prediction using higher-order motifs.
problem Real-time ranking and link prediction in applications like web search.
method Higher-order ranking and link prediction methods based on closing higher-order network motifs.
result The methods are faster and more efficient than existing methods based on closing triangles.
We propose using five data-driven community detection approaches from social networks to partition the label space for the task of multi-label classification as an alternative to random partitioning into equal subsets as performed by RAkELd: modularity-maximizing fastgreedy and leading eigenvector, infomap, walktrap an…
Develops algorithms for optimizing multi-label metrics with provable guarantees.
problem Optimizing complex multi-label metrics like F-measure and Jaccard index.
method Principled learning algorithms based on H-consistency for generalized metrics.
result Provable -consistency bounds for multi-label metric optimization.
It has been noticed that some external CVIs exhibit a preferential bias towards a larger or smaller number of clusters which is monotonic (directly or inversely) in the number of clusters in candidate partitions. This type of bias is caused by the functional form of the CVI model. For example, the popular Rand index (R…
New model improves histopathology classification across magnifications.
problem Robust histopathology classification is difficult due to magnification shift.
method Domain-general model using stable sparse embedding signatures.
result Domain-general model outperformed baseline and GAN augmentation.
The paper tightens bounds on distances between Reeb graphs.
problem Certifying quasi-universality of distances between Reeb graphs.
method Establishes tight bi-Lipschitz bounds for various distances.
result Proves strict universality of the functional contortion distance for contour trees and coincides with interleaving distance for merge trees.
Paper defines new GSW distances for probability measures.
problem Computational simplicity and similarity to Wasserstein distance.
method Generalized Radon transform to define GSW distances.
result GSW and max-GSW distances are distances under certain conditions.
Paper calculates Gromov-Hausdorff distance between simplexes and 2-distance spaces.
problem Calculating Gromov-Hausdorff distance between simplexes and 2-distance spaces.
method Formulas derived for clique covering number and chromatic number of graphs.
result Complete solution to generalized Borsuk problem for 2-distance spaces.
Extends Teichmüller distance concept to non-distance maps.
problem Defining distance metrics for non-distance functions.
method Generalizes horofunction compactification to non-distance maps.
result Defines horofunction counterpart to Teichmüller distance.
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.
New network distance based on Laplacian flow captures structure.
problem Measuring similarity between network objects.
method Introducing Laplacian flow to define a new diffusion distance.
result Demonstrated utility and advantage over existing distances.