Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known problematic behaviour of Kleinberg's Consistency axiom, and the impossibility resu…
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48 results for “consistent clustering”
Paper proposes SLINK clustering for nonparametric data sequences with improved consistency.
problem Nonparametric clustering of data sequences from unknown distributions.
method Exponentially consistent nonparametric SLINK clustering algorithm.
result SLINK clustering achieves exponential consistency under less strict conditions.
Study of hill-climbing clustering methods and their consistency.
problem Consistency of hill-climbing clustering methods.
method Continuous-space and discrete-space hill-climbing approaches.
result Established consistency of the methods.
Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.
problem Multi-view clustering where views have both consistent and complementary information.
method Consistent and complementary graph-regularized multi-view subspace clustering (GRMSC).
result The proposed method outperforms state-of-the-art methods on benchmark datasets.
Convex clustering can only learn convex clusters, with significant gaps between clusters.
problem Understanding the limitations and capabilities of convex clustering.
method Analyzing convex clustering solutions, proving properties, and characterizing clusters.
result Convex clustering can only learn convex clusters with significant gaps between clusters.
The study investigates the consistency of -means clustering under finite expectation assumptions.
problem Consistency of -means clustering under finite expectation assumptions.
method Investigates the conditions under which -means clustering is consistent, considering finite expectation instead of finite variance.
result Inconsistency can arise due to extreme cluster imbalance, leading to some clusters having few points.
Asymptotics for The -meansstat.ML
A new -means method improves clustering accuracy and robustness.
problem Insufficient asymptotic properties in existing -means methods.
method Introducing clustering consistency and proposing a new -means method.
result The new -means method has lower clustering error rates and is more robust.
Enhanced spectral clustering for geometric graphs improves clustering accuracy.
problem Ineffective standard spectral clustering for geometric graphs.
method Higher-order spectral clustering using higher-order eigenvectors.
result Established weak and strong consistency for Soft Geometric Block Model.
Clustering processescs.LG
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist, under most general non-parametric assumptions. The notion of consistency is as f…
Clustering processescs.LG
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist, under most general non-parametric assumptions. The notion of consistency is as f…
MAS scores cluster size consistency from points, robust to label changes.
problem Desired uniformity in cluster sizes, stability under label perturbations.
method Mass Agreement Score (MAS) measures point-centric cluster size consistency, robust to label changes.
result MAS yields similar scores for partitions with similar bulk structure, sensitive to genuine redistribution of cluster mass.
Study on Dirichlet process mixtures for clustering consistency.
problem Consistency of clustering with Dirichlet process mixtures.
method Analysis of posterior distribution as sample size increases, focusing on consistency for the number of clusters.
result Consistency for the number of clusters can be achieved with a properly adapted concentration parameter in a Bayesian setting.
Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.
problem Achieving strong consistency in spectral clustering for the stochastic block model.
method Entrywise analysis of the Fielder eigenvector of graph Laplacians.
result Spectral clustering achieves exact recovery of hidden communities under matching information-theoretic limits.
New theory for clustering in geometric and adaptive settings.
problem Clustering in non-Euclidean spaces and adaptive parameters.
method Asymptotic theory for -means and related methods.
result Strong consistency and asymptotic limit theorems for various clustering procedures.
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…
Paper improves short text clustering by integrating semantic relationships into Optimal Transport.
problem Erroneous pseudo-labels caused by neglecting semantic consistency in existing OT methods.
method Designs an instance-level attention mechanism to capture semantic relationships and integrates them into the OT formulation.
result Generates reliable pseudo-labels that improve clustering accuracy.
Decoding Financial Health in Kenyas' Medical Insurance Sector: A Data-Driven Cluster Analysisq-fin.CP
Study clusters Kenyan medical insurance companies based on financial performance and reporting consistency.
problem Identifying financial health and reporting consistency in Kenyan medical insurance companies.
method Advanced clustering techniques (KMeans, DTW) on financial ratios and time series data.
result Four distinct clusters identified, each representing different financial performance and reporting consistency combinations.
Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to construct a consistent modal regression algorithm.
Study provides guarantees for kernel clustering under non-parametric mixtures.
problem Statistical guarantees for kernel-based clustering without strong assumptions.
method Non-parametric mixture models, kernel-based clustering, consistency guarantees.
result Necessary and sufficient separability conditions for consistent clustering recovery.
Cluster Analysis on Locally Asymptotically Self-similar Processes with Known Number of Clustersstat.ML
We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new covariance-based dissimilarity measure is introduced, from which we obtain the approxima…
Consistent spectral clustering with fairness constraints on representation graphs.
problem Finding balanced clusters in similarity graphs with fairness constraints.
method Developed variants of unnormalized and normalized spectral clustering for fair planted partitions.
result Consistency results for constrained spectral clustering under fair planted partitions.
Efficient clustering in high dimensions with Quick Shift and LSH.
problem Density-based clustering in high-dimensional data.
method Combines Quick Shift and LSH for efficient density estimation.
result Achieves almost linear time complexity for consistency.
Proposes a neural network method to improve consistencies in high dimensional data analysis.
problem Inconsistencies among dimensionality reduction, clustering, and visualization tasks in high dimensional data analysis.
method Consistent Representation Learning (CRL) neural network that performs NLDR transformations to satisfy LGP constraints.
result Improves consistencies in data interpretation through end-to-end task execution.
Proposes CI-GMVC to improve graph-based multi-view clustering performance.
problem Inconsistency in multi-view data affects clustering performance.
method Integrates consistent and inconsistent parts of multiple views using a unified matrix.
result Demonstrates improved clustering performance on real-world datasets.
Improves clustering performance by mixing latent representations.
problem Finding well-defined clusters in data representations.
method Mixing Consistent Deep Clustering method that encourages realistic interpolations and semantic consistency.
result Improved clustering performance across various models and datasets.
New method shows spectral clustering is consistent with theoretical guarantees.
problem Lack of theoretical support for anchor-based spectral clustering.
method Defined and analyzed a specific anchor-based algorithm.
result Theoretical consistency of the method in asymptotic settings.
New spectral clustering method handles discrete covariates for better community detection.
problem Community detection in networks with discrete covariates.
method Spectral algorithm that separates latent network structure from observed covariates.
result Achieves perfect clustering with high probability in large, sparse networks.
Stable density-based clustering via multiparameter persistence.
problem Density-based clustering stability to data perturbations.
method Degree-Rips construction, correspondence-interleaving distance, multiparameter stability analysis.
result Persistable pipeline yields stable, consistent density-based clustering.
Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given dens…
Clustering is one of the most important unsupervised problems in machine learning and statistics. Among many existing algorithms, kernel k-means has drawn much research attention due to its ability to find non-linear cluster boundaries and its inherent simplicity. There are two main approaches for kernel k-means: SVD o…
New algorithms improve community detection in network data with strong consistency.
problem Challenges in effectively adapting spectral clustering techniques and achieving strong consistency in label recovery.
method Proposed Thresholded Cosine Spectral Clustering (TCSC) and one-step Refined TCSC algorithms, with strong consistency proofs.
result One-step Refined TCSC achieves strong consistency in community detection under PABM, correctly recovering all labels with high probability.
For a density on , a {\it high-density cluster} is any connected component of , for some . The set of all high-density clusters forms a hierarchy called the {\it cluster tree} of . We present two procedures for estimating the cluster tree given samples from . The first…
New method clusters multimodal data with consistency.
problem Multimodal clustering with unaligned data.
method Conjugate mixture models and EM algorithm.
result Consistent multimodal clustering achieved.
Consistent estimator for mixtures of nonparametric elliptical distributions helps cluster analysis.
problem Consistency of maximum likelihood estimator for mixtures of nonparametric elliptical distributions.
method Maximum likelihood estimation for mixtures of elliptically-symmetric distributions under nonparametric .
result Components of the estimator correspond to well-separated components of the underlying distribution .
Although consistency is a minimum requirement of any estimator, little is known about consistency of the mean partition approach in consensus clustering. This contribution studies the asymptotic behavior of mean partitions. We show that under normal assumptions, the mean partition approach is consistent and asymptotic …
POTA improves short text clustering by generating reliable pseudo-labels.
problem Limited discriminative representations in short texts.
method POTA uses instance-level attention and optimal transport for semantic consistency and cluster structure.
result POTA outperforms state-of-the-art methods in short text clustering.
A Unified Framework for Variable Selection in Model-Based Clustering with Missing Not at Randomstat.ME
Unified framework for variable selection in model-based clustering with missing data.
problem Challenges in identifying relevant variables and handling missing data in model-based clustering.
method Unified framework incorporating a data-driven penalty matrix and a mechanism for missingness modeling.
result Achieves both asymptotic consistency and selection consistency in the presence of missing data.
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the graph Laplacian matrix to extract its leading eigenvectors, where is the desired number of clusters among objects. This is pro…
A framework clusters vehicle motion trajectories efficiently.
problem Costly manual annotation of vehicle motion data.
method Five-stage framework: align, embed, extract, embed, cluster.
result Framework achieves promising results on real-world dataset.
Contrastive regularization improves semi-supervised learning by better propagating confident pseudo-labels.
problem Consistency regularization's limitation in high performance and efficiency.
method Proposes contrastive regularization to update model features, pushing confident labels into unlabeled samples.
result Improves semi-supervised learning tasks with fewer training iterations and robust performance.
We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\l…
Mixed datasets consist of both numeric and categorical attributes. Various k-means-based clustering algorithms have been developed for these datasets. Generally, these algorithms use random partition as a starting point, which tends to produce different clustering results for different runs. In this paper, we propose, …
Cluster-aware Semi-supervised Learning: Relational Knowledge Distillation Provably Learns Clusteringstat.ML
RKD improves clustering in semi-supervised learning with limited labels.
problem Improving clustering accuracy in semi-supervised learning with few labeled examples.
method RKD as spectral clustering on a teacher model's graph, with clustering error quantification.
result RKD provably leads to low clustering error in semi-supervised classification problems.
Develops a framework for consistent clustering algorithm benchmarking.
problem Lack of consistent benchmarking and diverse datasets for clustering algorithms.
method Consistent methodology, aggregated and polished datasets, interactive explorer.
result Introduces a comprehensive framework for testing clustering algorithms.
Proposes a method to improve hierarchical clustering using set-level structural priors.
problem Lack of supervision for non-leaf structure in hierarchical clustering.
method Introduces set-level structural priors for semi-supervised hyperbolic hierarchical clustering.
result Improves label consistency and similarity-based tree quality over baselines.
Spectral clustering identifies clusters of multivariate extremes.
problem Analyzing the dependence structure of multivariate extremes.
method Spectral clustering based on a random -nearest neighbor graph.
result Spectral clustering can consistently identify clusters of multivariate extremes under certain conditions.
Spectral clustering for geometric graphs achieves strong consistency in community recovery.
problem Community recovery in dense geometric graphs.
method Spectral clustering algorithm using eigenvectors of adjacency matrix.
result Strong consistency in community recovery proved.
New algorithm improves hypergraph clustering for unbalanced communities.
problem Hypergraph clustering with unbalanced community sizes and outliers.
method CRTMLE algorithm using convex relaxation of truncated MLE.
result Achieves optimal recovery guarantees for unbalanced community sizes.