Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means and Gaussian mixture models to massive data sets. However, until now,…
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48 results for “hard clustering”
Many graph clustering quality functions suffer from a resolution limit, the inability to find small clusters in large graphs. So called resolution-limit-free quality functions do not have this limit. This property was previously introduced for hard clustering, that is, graph partitioning. We investigate the resolution-…
Paper explores limits of high-order clustering with planted structures.
problem Statistical and computational limits of high-order clustering with planted structures.
method Developed methods for detection and recovery of clusters, identified signal-to-noise ratio boundaries.
result Sharp boundaries of signal-to-noise ratio for statistical and computational feasibility.
A new model for graph clustering using curvature spaces.
problem Graph clustering from a geometric perspective.
method Introducing a heterogeneous curvature space and a contrastive learning approach.
result CONGREGATE model outperforms state-of-the-art competitors.
This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM, and provides a h…
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.
An evolutionary algorithm (EA) is developed as an alternative to the EM algorithm for parameter estimation in model-based clustering. This EA facilitates a different search of the fitness landscape, i.e., the likelihood surface, utilizing both crossover and mutation. Furthermore, this EA represents an efficient approac…
Develops clustering methods based on likelihood and convergence proved.
problem Hard clustering based on likelihood.
method k-MLE, k-Bregman, k-VARs approaches.
result Convergence proved for clustering methods.
Proposes new random models for fuzzy clustering similarity measures.
problem Challenges in choosing a random model for fuzzy clustering similarity measures.
method Introduces three intuitive and explainable random models for fuzzy clusterings.
result Each random model has distinct behavior, emphasizing the importance of accurate model selection.
New computational methods improve clustering of objects.
problem Clustering objects based on their joint occurrence in sets.
method Genetic algorithm with renumbering, local search, and simplified model.
result Improvements enhance computational performance of genetic algorithm.
Proposes individual fairness for clustering, making data points prefer their own cluster.
problem No fair clustering for clustering data points.
method Introduces a new fairness notion for clustering and studies its feasibility and heuristics.
result Individual fairness for clustering is NP-hard in general but feasible for one-dimensional data.
Efficiently clusters noisy data with minimal queries.
problem Clustering elements with noisy oracle feedback.
method Combination of sampling strategy and correlation clustering algorithm.
result First polynomial-time algorithms for NP-hard optimization problem.
New clustering method for exponential family data.
problem Improving clustering for non-Gaussian data.
method Bregman Power k-Means algorithm.
result Outperforms existing methods in non-Gaussian data settings.
We propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where…
RECODE uses clustering and embedding to track state visitation counts in RL.
problem Efficient novelty-based exploration in nonstationary RL environments.
method Non-parametric clustering, online density estimation, inverse dynamics loss.
result RECODE achieves state-of-the-art performance in challenging RL tasks.
It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to come up with notions of clusterability that distinguish realistically interestin…
In this paper, we formulate the problem of inferring a Finite Mixture Model from discrete data as an optimal transport problem with entropic regularization of parameter . Our method unifies hard and soft clustering, the Expectation-Maximization (EM) algorithm being exactly recovered for . The family of cl…
Data de-duplication is the task of detecting multiple records that correspond to the same real-world entity in a database. In this work, we view de-duplication as a clustering problem where the goal is to put records corresponding to the same physical entity in the same cluster and putting records corresponding to diff…
We describe -MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization (EM) soft clustering technique that monotonically increases the incomplete (expec…
We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this output to a hard clustering. We provide a generic method for proving performance guar…
Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDTstat.ML
New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.
problem Resolving algorithmic hardness in asymmetric binary perceptrons.
method Fully lifted random duality theory (fl RDT) and large deviation upgrade (sfl LD RDT).
result Local entropy breaks down for constraint densities in (0.77, 0.78) interval, matching current solver limits.
Fuzzy clustering with similarity queries improves efficiency and accuracy.
problem Clustering uncertain or vague datasets.
method Semi-supervised active clustering framework with oracle similarity queries.
result Polynomial-time approximation algorithm for fuzzy clustering with few similarity queries.
We propose a simple and easy to implement neural network compression algorithm that achieves results competitive with more complicated state-of-the-art methods. The key idea is to modify the original optimization problem by adding K independent Gaussian priors (corresponding to the k-means objective) over the network p…
Assignment methods are at the heart of many algorithms for unsupervised learning and clustering - in particular, the well-known K-means and Expectation-Maximization (EM) algorithms. In this work, we study several different methods of assignment, including the "hard" assignments used by K-means and the ?soft' assignment…
New unsupervised method selects hard negative samples for contrastive learning.
problem How to select good negative examples for contrastive learning without using true similarity information.
method Developed a new family of unsupervised sampling methods for hard negative selection.
result Improves downstream performance across multiple modalities.
Cross-manifold clustering is a hard topic and many traditional clustering methods fail because of the cross-manifold structures. In this paper, we propose a Multiple Flat Projections Clustering (MFPC) to deal with cross-manifold clustering problems. In our MFPC, the given samples are projected into multiple subspaces t…
Lossy compression and clustering fundamentally involve a decision about what features are relevant and which are not. The information bottleneck method (IB) by Tishby, Pereira, and Bialek formalized this notion as an information-theoretic optimization problem and proposed an optimal tradeoff between throwing away as ma…
Clustering is an extensive research area in data science. The aim of clustering is to discover groups and to identify interesting patterns in datasets. Crisp (hard) clustering considers that each data point belongs to one and only one cluster. However, it is inadequate as some data points may belong to several clusters…
New methods interpret clustering outcomes without altering data structure.
problem Post-processing methods destroy data integrity and obscure interpretations.
method Algorithm-agnostic interpretation methods using permutation feature importance, individual conditional expectation, and partial dependence.
result Preserves original feature structure and explains clustering outcomes.
We study the problem of clustering a set of items from binary user feedback. Such a problem arises in crowdsourcing platforms solving large-scale labeling tasks with minimal effort put on the users. For example, in some of the recent reCAPTCHA systems, users clicks (binary answers) can be used to efficiently label imag…
We study the question of fair clustering under the {\em disparate impact} doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the -center and the -median objectives, and show that even with two protected classes th…
In this paper we present deterministic conditions for success of sparse subspace clustering (SSC) under missing data, when data is assumed to come from a Union of Subspaces (UoS) model. We consider two algorithms, which are variants of SSC with entry-wise zero-filling that differ in terms of the optimization problems u…
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…
A new measure DCSI quantifies separability for density-based clustering.
problem Quantifying meaningful clusters in data sets.
method Developed a new separability measure DCSI based on separation and connectedness.
result Correctly identifies touching or overlapping classes that do not correspond to meaningful density-based clusters.
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For the most part, such flexibility is lacking in classical clustering methods such a…
Sparse GEMINI selects relevant features for clustering without assumptions.
problem Feature selection in clustering with relevant clusters and variables.
method Discriminative clustering model maximizing GEMINI with l1 penalty.
result Sparse GEMINI selects relevant subsets of variables without prior hypotheses.
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) …
Adapts DR objectives for both sample and feature size reduction.
problem Simultaneously reduce sample and feature sizes.
method Semi-relaxed Gromov-Wasserstein optimal transport.
result OT plan delivers competitive hard clustering.
K-ARMA models cluster time series data robustly.
problem Clustering time series data effectively.
method Model-based K-ARMA clustering algorithm with robust outlier detection.
result K-ARMA models outperform existing methods for time series clustering.
In Bipartite Correlation Clustering (BCC) we are given a complete bipartite graph 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…
K-means clustering improved for robustness to outliers and distribution shifts.
problem K-means is brittle to outliers, distribution shifts, and limited samples.
method Developed a distributionally robust variant using Wasserstein-2 ball around the empirical distribution.
result Substantial gains in outlier detection and robustness to noise demonstrated.
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global optimum. In order to algorithmically solve this optimization problem, we propose tw…
Proposes a weighted conformal approach for cluster label uncertainty.
problem Cluster label uncertainty in unlabeled data.
method Develops a conformal inference algorithm to correct label mismatch.
result Improves confidence set size in nonlinear and high-dimensional clustering.
Mixture models and topic models generate each observation from a single cluster, but standard variational posteriors for each observation assign positive probability to all possible clusters. This requires dense storage and runtime costs that scale with the total number of clusters, even though typically only a few clu…
New approach for fair graph clustering using semidefinite relaxation.
problem Ensuring equitable representation in network analysis.
method Semidefinite relaxation approach for NP-hard optimization problem.
result Optimal accuracy-fairness trade-off achieved.
Paper provides a performance guarantee for spectral clustering.
problem Finding the global solution to the minimum ratio cut problem.
method Two-step spectral clustering method with a rounding step, analyzed using two-to-infinity norm perturbation bounds.
result Spectral clustering is guaranteed to output the global solution under certain conditions.
Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive data sets. While existing approaches generally only allow for multiplicative appro…
New Ising models improve consensus clustering on specialized hardware.
problem Consensus clustering optimization problems.
method Formulated consensus clustering as Ising models and evaluated on specialized hardware.
result Our Ising models outperform existing techniques on consensus clustering.