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
The paper optimizes portfolios using clustering and Sharpe ratio-based optimization.
problem Optimizing portfolio performance in financial modeling.
method Combines K-Means clustering for asset segmentation and Sharpe ratio-based optimization.
result Optimized portfolios outperform traditional equal-weighted benchmarks.
FCA improves fair clustering by optimizing utility and fairness.
problem Balancing fairness and utility in clustering.
method FCA alternates between aligning data and optimizing cluster centers in an aligned space.
result FCA achieves a superior trade-off between fairness and utility.
Graph based clustering is one of the major clustering methods. Most of it work in three separate steps: similarity graph construction, clustering label relaxing and label discretization with k-means. Such common practice has three disadvantages: 1) the predefined similarity graph is often fixed and may not be optimal f…
Extends clustering method to cost-based hierarchies.
problem Guaranteeing near-optimality in hierarchical clustering.
method Optimization-based Sublevel Set method extended to cost-based hierarchies.
result Ensures clustering is nearly optimal without distributional assumptions.
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.
A new framework for predictive clustering and optimization.
problem Finding clusters of data that yield low error on a supervised target.
method Generalized optimization framework using MILP and MM for scalability.
result Models can uncover different interpretable discrete cluster structures.
Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering algorithms, whose goals are to group points based on some similarity criterion. A c…
DCMAP optimizes clustering in Bayesian Networks with dependent costs.
problem Optimal clustering in Bayesian Networks with cost dependency.
method DCMAP algorithm that iteratively finds near-optimal cluster mappings.
result DCMAP finds all least cost cluster mappings optimally with minimal iterations.
Paper optimizes clustering for multi-layer networks and discrete mixtures.
problem Optimizing clustering in multi-layer networks and discrete mixtures.
method Two-stage method: tensor-based initialization and likelihood-based refinement.
result Achieves minimax optimal error rate for multi-layer networks and discrete mixtures.
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.
Proposes a novel approach for cluster-aware matching using Laplacian Optimal Transport.
problem Matching point clouds with intrinsic cluster structure requires robust region-to-region alignment over precise point-to-point correspondence.
method Laplacian Optimal Transport (LapOT) with regularization for cluster-aware matching and Refined Simultaneous Clustering (RSC) for consistent partitions.
result Laplacian Optimal Transport produces more consistent and meaningful alignments between point clouds.
The paper provides guarantees for clustering validity without distributional assumptions.
problem Validating clustering results without distributional assumptions.
method Generic method to obtain post-inference guarantees of near-optimality and stability for clustering.
result The guarantees do not depend on distributional assumptions but depend on the data set admitting a stable clustering.
New method speeds up k-means clustering using sketch-and-solve.
problem Efficiently solving k-means clustering for large datasets.
method Sketch-and-solve approach with Peng-Wei semidefinite relaxation.
result Provides high-confidence lower bounds on k-means optimal value.
Optimizes clustering in Gaussian mixtures with varying covariance matrices.
problem Clustering with anisotropic Gaussian mixture models where covariance matrices vary.
method Proposes a computationally feasible hard EM type algorithm.
result Achieves optimal clustering rate with few iterations.
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.
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…
Convex clustering solves a stable optimization problem for clustering.
problem Clustering with stable and scalable solutions.
method Solving a convex optimization problem with a single tuning parameter.
result The optimization problem has a unique global minimizer stable to inputs.
We present a global optimization approach for solving the maximum a-posteriori (MAP) clustering problem under the Gaussian mixture model.Our approach can accommodate side constraints and it preserves the combinatorial structure of the MAP clustering problem by formulating it asa mixed-integer nonlinear optimization pro…
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.
Network Lasso clusters sparse graph clusters efficiently.
problem Local graph clustering of sparse and chain-like clusters.
method Network Lasso minimizes total variation of cluster indicator signals.
result Network Lasso handles sparse clusters difficult for spectral clustering.
Enhances clustering performance with a novel high-order Laplacian matrix.
problem Limited representation capability and insufficient information exploitation in multi-view spectral clustering.
method Proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix.
result Improves clustering performance through enhanced representation capacity of the learned optimal Laplacian matrix.
Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point…
This paper certifies cluster assignments from sum-of-norms clustering algorithms.
problem Certifying the correct cluster assignments from approximate solutions of sum-of-norms clustering.
method Presented a clustering test that identifies and certifies the correct cluster assignment from an approximate solution.
result The correct cluster assignment is guaranteed to be certified by a primal-dual path following algorithm after sufficient iterations.
Combinatorial optimization problems for clustering are known to be NP-hard. Most optimization methods are not able to find the global optimum solution for all datasets. To solve this problem, we propose a global optimal path-based clustering (GOPC) algorithm in this paper. The GOPC algorithm is based on two facts: (1) …
BalLOT uses optimal transport for balanced k-means clustering.
problem Balanced k-means clustering of data. method BalLOT is an optimal transport approach to alternating minimization.
result BalLOT provides theoretical guarantees for exact and partial recoveries of planted clusters.
A new algorithm speeds up convex clustering.
problem Optimizing clustering with convex optimization and avoiding local minima.
method Smoothing proximal gradient algorithm (Sproga) for convex clustering.
result Sproga is faster and uses less memory than existing methods.
In this paper, we propose a general model for plane-based clustering. The general model contains many existing plane-based clustering methods, e.g., k-plane clustering (kPC), proximal plane clustering (PPC), twin support vector clustering (TWSVC) and its extensions. Under this general model, one may obtain an appropria…
Develops a new random forest method for clustered data with improved prediction and inference.
problem Improving prediction and inference accuracy for clustered data with within-cluster dependence.
method Clustered Random Forests, using weighted least squares estimators for leaf predictions.
result Optimal prediction and inference weights vary under covariate shift, necessitating user-chosen weights.
Information-maximization clustering learns a probabilistic classifier in an unsupervised manner so that mutual information between feature vectors and cluster assignments is maximized. A notable advantage of this approach is that it only involves continuous optimization of model parameters, which is substantially easie…
New method optimizes clustering with better log-likelihood landscape.
problem Nonconvex log-likelihood optimization in model-based clustering.
method Entropic optimal transport loss for Sinkhorn-EM algorithm.
result New loss function avoids spurious local optima.
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering pr…
Competency questions help experts select best clustering for energy data.
problem Ad hoc and subjective selection of clustering structures by domain experts.
method Formalize expert knowledge and requirements with competency questions.
result Competency questions improve reproducibility and evaluation of clustering applications.
To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their result is pivotal for deriving interesting properties of consensus clustering beyond…
New algorithm optimally clusters networks with side information.
problem Improving network clustering with side information.
method Iterative clustering algorithm for Contextual Stochastic Block Model.
result Optimal performance under Contextual Symmetric Stochastic Block Model.
New method optimizes mixed integer optimization for hierarchical modeling of clustered and longitudinal data.
problem Optimizing subset selection in hierarchical models with clustered and longitudinal data.
method Distribution-free mixed-integer optimization approach for cluster-aware regression.
result The method efficiently solves problems within minutes and outperforms traditional models in generating sparse solutions with high predictive power.
Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.
problem Achieving optimal error rates in clustering sub-exponential mixture models.
method Establishes universal lower bounds and demonstrates iterative algorithms' optimality in sub-exponential mixture models.
result Iterative algorithms achieve the universal lower bound in sub-exponential mixture models.
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed by applying the Fourier transform and a Gaussian filter. The determination of th…
A new framework learns clustering and dimensionality reduction together.
problem Challenges in clustering high-dimensional data.
method Gradient-based manifold optimization for joint learning.
result Better performance compared to existing clustering algorithms.
Unified framework for efficient Frank-Wolfe optimization of Dominant Set Clustering.
problem Optimizing Dominant Set Clustering with various Frank-Wolfe algorithms.
method Unified framework for pairwise, standard, and away-steps Frank-Wolfe algorithms, with explicit convergence rates.
result Explicit convergence rates for Frank-Wolfe methods in Dominant Set Clustering.
New algorithm clusters trajectories from multiple Markov chains with near-optimal error.
problem Clustering trajectories from multiple unknown Markov chains.
method Two-stage algorithm: spectral clustering followed by likelihood-based refinement.
result Achieves near-optimal clustering error with high probability.
GCAO improves clustering of high-dimensional data by grouping low-density boundary points.
problem Stability and accuracy of clustering in high-dimensional, non-uniform data.
method Group-level optimization with gravitational attraction and optimization.
result GCAO outperforms 11 clustering methods on multiple datasets.
Paper characterizes optimal graph clustering limits under a new model.
problem Graph clustering under varying edge density signals.
method Introduced Popularity-Adjusted Block Model (PABM) to address SBM and DCBM limitations.
result Cluster recovery possible even when edge density signals vanish, highlighting local connectivity differences.
The study compares clustering risk in Hidden Markov and i.i.d. models, showing the Bayes classifier is nearly optimal.
problem Comparing clustering risk in Hidden Markov and i.i.d. models.
method Analysis of Bayes risk, theoretical bounds, and simulations.
result The Bayes classifier is nearly optimal for clustering in both Hidden Markov and i.i.d. models.
Paper tackles clustering with ordinal comparisons, achieving near-optimal results.
problem Clustering with ordinal comparisons when similarity measures are not available.
method Two-step procedure: estimate similarity matrix from comparisons, then apply SDP clustering.
result Near-optimal recovery of planted clustering using near-optimal number of comparisons.
The clustering methods have recently absorbed even-increasing attention in learning and vision. Deep clustering combines embedding and clustering together to obtain optimal embedding subspace for clustering, which can be more effective compared with conventional clustering methods. In this paper, we propose a joint lea…
Model for optimal cybersecurity investment considering clustered cyberattacks.
problem Optimal investment in cybersecurity to reduce system vulnerability under clustered cyberattacks.
method Developed a continuous-time stochastic model using a Hawkes process, extended Gordon-Loeb model, solved as a Markovian stochastic optimal control problem.
result Investment policies that account for attack clustering lead to more effective and responsive strategies, improving upon static and Poisson-based approaches.
Plain vanilla K-means clustering has proven to be successful in practice, yet it suffers from outlier sensitivity and may produce highly unbalanced clusters. To mitigate both shortcomings, we formulate a joint outlier detection and clustering problem, which assigns a prescribed number of datapoints to an auxiliary outl…