Proposes a method to predict cluster number and cluster representatives using cluster stability analysis.
problem Determining the number of clusters in a dataset.
method Analyzes cluster stability using Monte-Carlo simulation to predict cluster number and find cluster representatives.
result Significant improvement in predicting cluster numbers and cluster composition in large datasets.
Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the clustering solutions with different number of clusters. This article quantifies a …
Study examines how cluster number affects short-text clustering, introducing a stability metric.
problem Challenges in finding meaningful clusters in short-text data.
method Introduces a stability metric to determine cluster robustness and visualizes cluster subdivisions.
result Choosing a cluster number involves balancing informativeness and complexity, not seeking a single 'optimal' solution.
Solves K-Means clustering's need for known cluster count.
problem Determining the number of clusters for K-Means without prior knowledge.
method Uses hypersphere density to estimate clusters, visualizing density vs. number of clusters.
result Identifies the optimal number of clusters in datasets.
New indices for determining cluster compactness and separability.
problem Challenges in identifying true clusters in data sets.
method Developed absolute cluster indices to measure compactness and separability.
result Demonstrated improved performance compared to existing indices.
Cluster analysis is widely used in the areas of machine learning and data mining. Fuzzy clustering is a particular method that considers that a data point can belong to more than one cluster. Fuzzy clustering helps obtain flexible clusters, as needed in such applications as text categorization. The performance of a clu…
New criterion selects optimal number of clusters based on stability.
problem Challenges in selecting optimal number of clusters in non-parametric clustering.
method Proposes a stability-based validation criterion combining between-cluster and within-cluster stability.
result Empirically demonstrates effectiveness in selecting optimal number of clusters.
Develops a new cluster validity index to find multiple optimal cluster numbers.
problem Finding the optimal number of clusters in real-world data with varying densities, sizes, and shapes.
method A new correlation-based cluster validity index that yields multiple local peaks.
result The new index finds multiple optimal cluster numbers in various scenarios.
Paper finds methods to accurately determine the number of clusters in data.
problem Finding the correct number of clusters in a dataset.
method Penalized k-means algorithms with ideal clusters and multiplicative penalties.
result K-means with multiplicative penalties provides a clearer indication of the correct number of clusters.
Graph clustering uses multiscale community detection for improved performance.
problem Improving data clustering accuracy and robustness.
method Graph-theoretical approach combining multiscale community detection.
result Multiscale graph-based clustering achieves better performance than traditional methods.
CAF-HFCM automatically forms a cluster hierarchy and optimizes the number of clusters without trial-and-validation.
problem Challenges in determining the optimal number of clusters in fuzzy c-means.
method CAF-HFCM, an auto-fused hierarchical fuzzy c-means method.
result Automatic agglomeration and optimal number of clusters without validity indices.
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.
Recently, deep clustering, which is able to perform feature learning that favors clustering tasks via deep neural networks, has achieved remarkable performance in image clustering applications. However, the existing deep clustering algorithms generally need the number of clusters in advance, which is usually unknown in…
Study on posterior distribution for cluster number in DPMM models.
problem Understanding the posterior distribution of the number of clusters in Dirichlet process mixture models.
method Rigorous study of posterior distribution under different prior distributions and constraints on data distributions.
result Provide novel lower bounds on the ratios of probabilities between s+1 clusters and s clusters. One of the longstanding problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. In this paper, we propose AMOS…
A new medoid-based Silhouette method selects optimal cluster numbers efficiently.
problem Difficulty in evaluating clustering results and choosing the right number of clusters.
method Developed a medoid-based Silhouette variant, analyzed its properties, and provided fast optimization methods.
result A 10464x speedup in choosing optimal cluster numbers compared to original PAMMEDSIL.
BCV method helps estimate clusters and hyper-parameters in large data sets.
problem Determining the number of clusters in large-scale data.
method Bi-cross validation (BCV) for spectral clustering.
result BCV directly applies to spectral clustering for estimating clusters and hyper-parameters.
Parameter-free clustering method using cluster catch digraphs (CCDs).
problem Finding the correct number of clusters in data without specifying a parameter.
method Hybrid of density-based and graph-based clustering methods using Ripley's K function.
result Minimum dominating sets of RK-CCDs estimate and distinguish clusters from noise.
New algorithm IAC recovers hidden communities in labeled SBM with optimal performance.
problem Recovering hidden communities in Labeled Stochastic Block Model with varying cluster sizes.
method IAC (Instance-Adaptive Clustering) algorithm, consisting of spectral clustering and iterative likelihood-based improvements.
result IAC achieves optimal performance matching instance-specific lower bounds in expectation and with high probability.
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.
FBC clusters data fairly without needing cluster count.
problem Fairness in clustering groups of different sensitive groups.
method Developed a Bayesian model-based clustering method with a fair prior and efficient MCMC algorithm.
result Reasonably infers the number of clusters and achieves a fair utility trade-off.
Method estimates number of clusters in Block Markov Chain trajectories.
problem Challenges in choosing number of clusters for sequential data.
method Spectral embedding and density-based clustering.
result Asymptotically consistent method for estimating clusters.
There has been a surge in the number of large and flat data sets - data sets containing a large number of features and a relatively small number of observations - due to the growing ability to collect and store information in medical research and other fields. Hierarchical clustering is a widely used clustering tool. I…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …
A new method estimates the number of clusters on spherical data.
problem Estimating the number of clusters in spherical data.
method Spherical X-means (SX-means) method assuming von Mises-Fisher distributions.
result Shows the performance of SX-means in estimating the number of clusters.
In this paper, a similarity-driven cluster merging method is proposed for unsuper-vised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in the data, pairs of similar clusters are merged based on the proposed similarity-…
In this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of classes assigned to the patterns by manual means or some other means in whose v…
We propose an algorithm for clustering high dimensional data. If P features for N objects are represented in an N×P matrix X, where N≪P, the method is based on exploiting the cluster-dependent structure of the N×N matrix XXT. Computational burden thus depends primarily on N, …
In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between sensors in order to reduce sensor energy consumption. In this respect, we propose one…
Bayesian models overestimate clusters, but practical summaries can correct this.
problem Bayesian mixture models overestimate the number of clusters.
method Simulations and gene expression data analysis using MCMC summarisation.
result Overestimation is limited in finite samples and can be corrected, but misspecification leads to significant overestimation.
Introduces BCVI, a Bayesian cluster validity index for better cluster selection.
problem Selecting the optimal number of clusters in clustering algorithms.
method Develops BCVI using Dirichlet or generalized Dirichlet priors, evaluated against existing indices.
result BCVI offers clear advantages in scenarios where user expertise is valuable.
Clustering is a central approach for unsupervised learning. After clustering is applied, the most fundamental analysis is to quantitatively compare clusterings. Such comparisons are crucial for the evaluation of clustering methods as well as other tasks such as consensus clustering. It is often argued that, in order to…
The paper tackles fair correlation clustering with fairness constraints.
problem Minimizing disagreements while adhering to fairness constraints for clustering.
method Two variants of fairness constraints are considered: equal distribution and relative bounds. Approximation algorithms are developed for these constraints.
result Approximation algorithms for fair correlation clustering with theoretical guarantees and empirical validation.
Improved clustering speed for 20 clusters on CIFAR-100 dataset.
problem Training time complexity for VAEs with discrete latent variables is linear in the number of clusters.
method Applied a continuous relaxation to discrete variables in Gaussian Mixture VAE, reducing training time complexity to constant.
result Reduced training time from 47 hours to 6 hours for 20 clusters on CIFAR-100.
Recently, a number of works have studied clustering strategies that combine classical clustering algorithms and deep learning methods. These approaches follow either a sequential way, where a deep representation is learned using a deep autoencoder before obtaining clusters with k-means, or a simultaneous way, where dee…
The goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a point pattern or a set of points. Moreover, many existing clustering methods requir…
A new clustering method estimates non-linear boundaries and automatically selects the number of clusters.
problem Discriminative clustering with non-linear boundaries and data abnormalities.
method Regularized mutual information objective function with a mixture of Gaussian and uniform distributions.
result Automatic selection of the number of components and estimation of non-linear boundaries.
The paper tackles the problem of identifying same-cluster elements in overlapping clusters with minimum queries.
problem Identifying same-cluster elements in overlapping clusters with minimum queries.
method The paper provides algorithms for identifying same-cluster elements in overlapping clusters with minimum queries, under both arbitrary and statistical modeling assumptions.
result The algorithms are order optimal, parameter free, efficient, and work in the presence of random noise.
This study evaluates cluster search algorithms using Gaussian mixture models.
problem Determining the optimal number of clusters in data sets generated by Gaussian mixture models.
method Examined centroid- and model-based cluster search algorithms in various cases.
result Model-based algorithms are more robust to cluster overlap and covariance type than centroid-based methods.
FOSC-X: An extended framework for extracting multiple optimal flat clusterings from hierarchical cluster trees
problem Extracting multiple optimal flat clusterings from hierarchical cluster trees
method Dynamic programming with lower and upper feasibility bounds
result Guaranteed optimal rankings of top-M solutions with linear-time complexity
In Bipartite Correlation Clustering (BCC) we are given a complete bipartite graph G with `+' and `-' edges, and we seek a vertex clustering that maximizes the number of agreements: the number of all `+' edges within clusters plus all `-' edges cut across clusters. BCC is known to be NP-hard. We present a novel approx…
We improve current instability-based methods for the selection of the number of clusters k in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously unaccounted driver of cluster instability. We show that our normalized instability mea…
New cluster validity index detects optimal number of clusters and secondary options.
problem Determining the optimal number of clusters in fuzzy clustering.
method Correlation-based fuzzy cluster validity index (WP index) using fuzzy c-means algorithm.
result WP index outperforms existing indexes in detecting optimal number of clusters and secondary options.
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…
New clustering algorithms optimize Average Silhouette Width for better cluster quality.
problem Optimizing clustering using Average Silhouette Width (ASW).
method Proposed two algorithms: OSil and FOSil, compared with existing methods.
result New methods prove useful and sensible in many cases, but with some weaknesses.
CCMM efficiently solves large-scale convex clustering problems.
problem Scalability and hierarchical structure in convex clustering.
method Majorization-minimization algorithm with cluster fusions and efficient updating.
result CCMM achieves efficient solutions for large datasets.
This paper presents a neural network-based end-to-end clustering framework. We design a novel strategy to utilize the contrastive criteria for pushing data-forming clusters directly from raw data, in addition to learning a feature embedding suitable for such clustering. The network is trained with weak labels, specific…
The paper proposes a method to automatically determine the number of clusters in data.
problem Determining the number of clusters in data without making strong assumptions.
method Using nonparametric concentration inequalities to infer the number of clusters.
result The method can automatically determine the appropriate value for k, without assumptions on the data distribution.