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In supervised machine learning, models are typically trained using data with hard labels, i.e., definite assignments of class membership. This traditional approach, however, does not take the inherent uncertainty in these labels into…
We present a clustering method and provide a theoretical analysis and an explanation to a phenomenon encountered in the applied statistical literature since the 1990's. This phenomenon is the natural adaptability of the order when using a…
We study graph clustering in the Stochastic Block Model (SBM) in the presence of both large clusters and small, unrecoverable clusters. Previous convex relaxation approaches achieving exact recovery do not allow any small clusters of size…
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…
Soft-constraint affinity propagation (SCAP) is a new statistical-physics based clustering technique. First we give the derivation of a simplified version of the algorithm and discuss possibilities of time- and memory-efficient…
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
Performance disparities of image recognition across demographic groups are known to exist in deep learning-based models, due to imbalanced group representations or spurious correlation between group and target labels. Previous work has…
Ensuring data trustworthiness within individual edge nodes while facilitating collaborative data processing poses a critical challenge in edge computing systems (ECS), particularly in resource-constrained scenarios such as autonomous…
Proofs of convergence of adaptive finite element methods for the approximation of eigenvalues and eigenfunctions of linear elliptic problems have been given in a several recent papers. A key step in establishing such results for multiple…
Fuzzy K-Means clustering is a critical technique in unsupervised data analysis. Unlike traditional hard clustering algorithms such as K-Means, it allows data points to belong to multiple clusters with varying degrees of membership,…
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…
In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…
Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, each facility has a capacity limit and may belong to one or more demographic…
Deep neural networks (DNNs) have the capacity to fit extremely noisy labels nonetheless they tend to learn data with clean labels first and then memorize those with noisy labels. We examine this behavior in light of the Shannon entropy of…
We are concerned in clustering continuous data sets subject to non-ignorable missingness. We perform clustering with a specific semi-parametric mixture, under the assumption of conditional independence given the component. The mixture model…
Variational autoencoder (VAE) and generative adversarial networks (GAN) have found widespread applications in clustering and have achieved significant success. However, the potential of these approaches may be limited due to VAE's mediocre…
A growing specter in the rise of machine learning is whether the decisions made by machine learning models are fair. While research is already underway to formalize a machine-learning concept of fairness and to design frameworks for…
This paper presents a comparative analysis of different optimization techniques for the K-means algorithm in the context of big data. K-means is a widely used clustering algorithm, but it can suffer from scalability issues when dealing with…
Recent state-of-the-art methods in imbalanced semi-supervised learning (SSL) rely on confidence-based pseudo-labeling with consistency regularization. To obtain high-quality pseudo-labels, a high confidence threshold is typically adopted.…
We investigate the problem of segmenting unlabeled speech into word-like units and clustering these to create a lexicon. Prior work can be categorized into two frameworks. Bottom-up methods first determine boundaries and then cluster the…