arXiv research

The paper quantizes concatenated noisy vectors to a common cluster center, improving performance over naive methods.

The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first consider the similarity of elements in the data as the connectivity of nodes in an…

One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the distribution of the underlying data. This can be highly disadvantageous in problems wh…

The paper analyzes $k$-means clustering for missing data, proving statistical guarantees under MCAR.

We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a $K$-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the $K$-means clustering method achieves such sharp threshol…

New distributed clustering algorithms show resilience to initialization issues.

New algorithm for clustering data streams with no substitutions.

Determinantal consensus clustering improves clustering robustness.

New method for better initial centers in clustering with improved accuracy and privacy.

Proposes a new clustering method based on expectiles for non-spherical clusters.

Gradient-based clustering method for various cost functions.

A novel k-means method for MNAR data improves clustering accuracy.

Replicable clustering algorithms for k-medians, k-means, and k-centers are proposed.

New clustering method ensures fairness and community preservation.

Suppose one is faced with the challenge of tissue segmentation in MR images, without annotators at their center to provide labeled training data. One option is to go to another medical center for a trained classifier. Sadly, tissue classifiers do not generalize well across centers due to voxel intensity shifts caused b…

The paper introduces group-representative clustering to ensure fair representation of different groups in clusters.

$k$-means clustering is a fundamental problem in unsupervised learning. The problem concerns finding a partition of the data points into $k$ clusters such that the within-cluster variation is minimized. Despite its importance and wide applicability, a theoretical understanding of the $k$-means problem has not been comp…

We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering $n$ points with $k$ centers, we define fairness as proportionality to mean that any $n/k$ points are entitled to form their own cluster if there is another center that is clo…

As one type of efficient unsupervised learning methods, clustering algorithms have been widely used in data mining and knowledge discovery with noticeable advantages. However, clustering algorithms based on density peak have limited clustering effect on data with varying density distribution (VDD), equilibrium distribu…

In data summarization we want to choose $k$ prototypes in order to summarize a data set. We study a setting where the data set comprises several demographic groups and we are restricted to choose $k_i$ prototypes belonging to group $i$. A common approach to the problem without the fairness constraint is to optimize a c…

CDL index improves clustering validation for non-convex data.

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 $k$-center and the $k$-median objectives, and show that even with two protected classes th…

Develops a fair clustering algorithm for datasets with outliers.

DEMVC improves multi-view clustering with collaborative training and deep autoencoders.

We give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x…

A new hybrid fuzzy-crisp clustering algorithm addresses imbalanced cluster sizes.

Paper tackles noisy comparison oracle for robust clustering algorithms.

Offline k-means clustering was studied extensively, and algorithms with a constant approximation are available. However, online clustering is still uncharted. New factors come into play: the ordering of the dataset and whether the number of points, n, is known in advance or not. Their exact effects are unknown. In this…

Proposes a data augmentation method to improve multi-label learning performance.

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and…

Finding the optimal $k$-means clustering is NP-hard in general and many heuristics have been designed for minimizing monotonically the $k$-means objective. We first show how to extend Lloyd's batched relocation heuristic and Hartigan's single-point relocation heuristic to take into account empty-cluster and single-poin…

A new federated learning method clusters users into multiple models for better data distribution handling.

The study investigates the consistency of $k$-means clustering under finite expectation assumptions.

Traditional load analysis is facing challenges with the new electricity usage patterns due to demand response as well as increasing deployment of distributed generations, including photovoltaics (PV), electric vehicles (EV), and energy storage systems (ESS). At the transmission system, despite of irregular load behavio…

It has always been a great challenge for clustering algorithms to automatically determine the cluster numbers according to the distribution of datasets. Several approaches have been proposed to address this issue, including the recent promising work which incorporate Bayesian Nonparametrics into the $k$-means clusterin…

A new method improves graph-based learning for high-dimensional data.

The paper studies properties of stated SL(n)-skein algebras and their centers.

Cloud computing data centers are growing in size and complexity to the point where monitoring and management of the infrastructure become a challenge due to scalability issues. A possible approach to cope with the size of such data centers is to identify VMs exhibiting a similar behavior. Existing literature demonstrat…

Study reveals structure of local minima in GMMs, identifying key cluster centers.

For Machine Learning (ML) classification problem, where a vector of $\mathbf{x}$--observations (values of attributes) is mapped to a single $y$ value (class label), a generalized Radon--Nikodym type of solution is proposed. Quantum--mechanics --like probability states $ψ^2(\mathbf{x})$ are considered and "Cluster Cente…

With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering and proposes a unified clustering framework. In order to find fixed points as c…

The paper analyzes how clustering sensitive data can improve model generalization without revealing individual information.

With the rapid growth of the data volume and the fast increasing of the computational model complexity in the scenario of cloud computing, it becomes an important topic that how to handle users' requests by scheduling computational jobs and assigning the resources in data center. In order to have a better perception of…

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…

Optimizes clustering in Gaussian mixtures with varying covariance matrices.

This paper introduces individual fairness in clustering using $f$-divergence.

This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following a classic approach in clustering by \cite{har2004coresets}, we reduce the proble…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth skeleton of embedding points in a low-dimensional space from high-dimensional noisy…