Solves clustering contradictions by high-dimensional embedding with wide gaps.
problem Kleinberg's clustering axioms are contradictory.
method Embedding in high-dimensional space with wide gaps between clusters.
result Handles clustering contradictions by design.
A new measure identifies clusters without assuming data distribution.
problem Identifying the correct number of clusters in data without distribution assumptions.
method Nonparametric interpoint distance-based approach.
result Superior to existing clustering measures, validated on synthetic and real data.
A new Wasserstein K-means method for clustering probability distributions.
problem Clustering probability distributions using the Wasserstein metric.
method Distance-based K-means with SDP relaxation for Wasserstein barycenters. result Distance-based K-means outperforms centroid-based K-means for clustering probability distributions. ClusTR improves clustering-based models' robustness without adversarial training.
problem Improving clustering-based models' robustness.
method Proposes ClusTR, a clustering-based training framework for robust models without adversarial training.
result ClusTR outperforms adversarially-trained models by up to 4% under strong PGD attacks.
Paper analyzes classical multidimensional scaling for cluster recovery.
problem Cluster recovery from noisy data.
method Classical multidimensional scaling followed by distance-based clustering.
result Scaling conditions for high probability cluster recovery.
In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a distance-ba…
The paper improves uncertainty quantification for node classification using distance-based regularization.
problem Uncertainty in deep learning models, especially for node classification tasks.
method Graph posterior networks (GPNs) with UCE loss function, followed by a distance-based regularization.
result The proposed distance-based regularization outperforms state-of-the-art methods in OOD detection and misclassification detection.
Bayesian distance clustering improves robustness to kernel choice.
problem Kernel sensitivity in model-based clustering.
method Modeling pairwise distances instead of original data.
result Dramatic gains in cluster inference robustness.
Bayesian hierarchical clustering (BHC) is an agglomerative clustering method, where a probabilistic model is defined and its marginal likelihoods are evaluated to decide which clusters to merge. While BHC provides a few advantages over traditional distance-based agglomerative clustering algorithms, successive evaluatio…
For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distanc…
OSil algorithm optimizes clustering quality using ASW.
problem Optimizing clustering quality using ASW.
method Distance-based objective function optimizing ASW for clustering.
result OSil algorithm outperforms other clustering methods in clustering quality.
CAST improves spectral clustering for multi-scale data by integrating reachability similarity.
problem Applying spectral clustering to multi-scale data where clusters vary in size and density.
method CAST integrates reachability similarity with distance-based similarity to derive a coefficient matrix, then applies trace Lasso regularization.
result CAST provides excellent performance and robustness across various multi-scale data test cases.
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.
The paper compares clustering methods for improving time series forecasting accuracy.
problem Improving time series forecasting accuracy using neural networks.
method Investigates feature-based and distance-based clustering methods for time series forecasting.
result Feature-based clustering outperforms distance-based clustering in terms of speed and efficiency.
In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive Information-Theoretic Feature Clustering model in probabilistic space with Kullbac…
A new CVI called DSI evaluates clustering results without true labels.
problem No universal CVI for clustering without true labels.
method DSI based on data separability measure.
result DSI is an effective, unique, and competitive CVI.
Study compares clustering methods for mixed-type data.
problem Challenges in clustering mixed-type data.
method Distance-based (k-prototypes, PDQ, convex k-means), probabilistic (KAY-means, MBNs, LCM).
result KAMILA, LCM, and k-prototypes perform best.
In this paper we tackle the issue of clustering trajectories of geolocalized observations. Using clustering technics based on the choice of a distance between the observations, we first provide a comprehensive review of the different distances used in the literature to compare trajectories. Then based on the limitation…
In this paper we present a method for the unsupervised clustering of high-dimensional binary data, with a special focus on electronic healthcare records. We present a robust and efficient heuristic to face this problem using tensor decomposition. We present the reasons why this approach is preferable for tasks such as …
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular schemes to construct a similarity graph, i.e., pairwise distance based scheme an…
Study evaluates initialization strategies for infinite hidden Markov models.
problem Limited attention to initialization in infinite hidden Markov models.
method Systematically evaluated distance-based clustering, model-based, and uniform initializations.
result Distance-based clustering initializations consistently outperform other methods.
Outliers are ubiquitous in modern data sets. Distance-based techniques are a popular non-parametric approach to outlier detection as they require no prior assumptions on the data generating distribution and are simple to implement. Scaling these techniques to massive data sets without sacrificing accuracy is a challeng…
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.
Hierarchical clustering uses OWA operators to generalize linkage methods and avoid dendrogram inversions.
problem Avoiding unaesthetic inversions in hierarchical clustering dendrograms.
method OWA-based linkages combined with the Lance-Williams formula and conditions on weight generators.
result Conditions for weight generators to produce dendrograms without inversions.
DADApy analyzes high-dimensional data manifolds in Python.
problem Analyzing complex, high-dimensional data.
method Estimating intrinsic dimension, density, clustering, comparing distance metrics.
result Effective analysis of data manifolds in Python.
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. As such, the study of clusterability, which evaluates whether data possesses such structure, is an integral part of cluster analysis. Yet, despite their central role in the theory and application of clustering, current…
Gradient-based clustering method for various cost functions.
problem Distance-based clustering for various cost functions.
method Iterative alternating update procedure for cluster assignments and centers.
result Converges to fixed points under mild assumptions.
New unsupervised feature selection method for imbalanced datasets.
problem Feature selection challenges in imbalanced multi-class datasets.
method Distance Rank Score using Spearman's Rank Correlation.
result Outperforms existing methods on clustering problems.
A new clustering algorithm considers data smoothness for better performance.
problem Clustering multi-scale data with varying cluster densities.
method Divide objects into tiny clusters, cluster centers form smooth graphs.
result Significantly outperforms state-of-the-art clustering algorithms.
We investigate properties that intuitively ought to be satisfied by graph clustering quality functions, that is, functions that assign a score to a clustering of a graph. Graph clustering, also known as network community detection, is often performed by optimizing such a function. Two axioms tailored for graph clusteri…
Paper proposes a novel approach to improve temporal clustering of time series data.
problem Challenges in clustering temporal data with varying sampling rates and high dimensionality.
method Transform time series into Euclidean space using similarity measures, then use CNN-GRU autoencoder for latent representation.
result Approach outperforms existing methods by up to 32% on various time series datasets.
The paper confirms two groups of gamma-ray bursts using a new nonparametric metric.
problem Determining the number of inherent groups in gamma-ray bursts.
method A new nonparametric interpoint distance-based measure, combined with clustering methods.
result Confirms two groups of short and long gamma-ray bursts.
CDF transform-and-shift homogenizes cluster densities for better clustering.
problem Inhomogeneous cluster densities bias algorithms towards dense clusters.
method Apply a Cumulative Distribution Function (CDF) transform-and-shift method to homogenize cluster densities.
result The method outperforms existing solutions in clustering and anomaly detection.
Hybrid clustering combines partitional and hierarchical clustering for computational effectiveness and versatility in cluster shape. In such clustering, a dissimilarity measure plays a crucial role in the hierarchical merging. The dissimilarity measure has great impact on the final clustering, and data-independent prop…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets to estimate the subspaces. As the geometric structure of the clusters …
Extracting significant places or places of interest (POIs) using individuals' spatio-temporal data is of fundamental importance for human mobility analysis. Classical clustering methods have been used in prior work for detecting POIs, but without considering temporal constraints. Usually, the involved parameters for cl…
Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or noise in the pairwise distances and investigate the problem of estimating the HC…
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.
SDCOR clusters massive datasets efficiently, detecting outliers with low memory usage.
problem Local outlier detection in large-scale datasets.
method Chunk-based density clustering with incremental updates.
result SDCOR achieves lower linear time complexity and better efficiency than traditional methods.
Paper explains distance-based classifiers using neural network structures.
problem Making distance-based classifiers explainable.
method Uncovering latent neural network structures in distance-based classifiers.
result Novel explanation approach outperforms baselines.
Proposes a robust similarity measure for sparse time series data.
problem Sparse time course data in biological settings.
method Gaussian processes (GP) similarity measure based on log-likelihood ratio.
result Enhanced robustness to noise compared to Euclidean distance.
New methods cluster and test graphs without vertex correspondence.
problem Clustering and testing of networks without vertex correspondence.
method Inspired by graphon estimation, propose a novel graph distance and clustering algorithms.
result Prove statistical consistency of clustering algorithms under Lipschitz assumptions on graph degrees.
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.
New ensemble methods improve time series forecasting accuracy.
problem Global Forecasting Models (GFM) lack localisation for heterogeneous datasets.
method Ensemble techniques with clustering and varied GFM models.
result Significantly higher accuracy achieved compared to baseline models.
Meta-BO method clusters and learns from prior tasks to optimize heterogeneous functions.
problem Optimizing multiple functions with historical data and scalability issues.
method Clustering-based meta-learning, surrogate prototypes, adaptive weighting policies.
result Scalable and robust meta-BO method improves convergence to global optimum.
Neural networks learn distance-based representations, not just intensity.
problem Understanding how neural networks interpret and learn from internal activations.
method Manipulated ReLU and Absolute Value activations to observe sensitivity to distance and intensity perturbations.
result Neural networks are highly sensitive to small distance-based perturbations, challenging the intensity-based interpretation.
We consider classifiers for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We first show that high-dimensional data often have the SSE model. We consider a distance-based classifier using eigenstructures for the SSE model. We apply the noise reduction methodology to estimation of the eigenvalue…
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.