Related papers: A Unified Matrix Factorization Framework for Class…

K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as…

This paper presents an advanced mathematical analysis and simplification of the quadratic programming problem arising from fuzzy clustering with generalized capacity constraints. We extend previous work by incorporating broader balancing…

Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group…

Fuzzy clustering algorithms can be roughly categorized into two main groups: Fuzzy C-Means (FCM) based methods and mixture model based methods. However, for almost all existing FCM based methods, how to automatically selecting proper…

In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz generalized symmetric matrix factorization model that unifies a broad class of matrix factorization formulations arising in machine learning, image science, engineering, and…

Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper…

As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional…

Federated Learning (FL) is a setting where multiple parties with distributed data collaborate in training a joint Machine Learning (ML) model while keeping all data local at the parties. Federated clustering is an area of research within FL…

Kernel methods are applied to many problems in pattern recognition, including subspace clustering (SC). That way, nonlinear problems in the input data space become linear in mapped high-dimensional feature space. Thereby, computationally…

Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…

The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some…

Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model…

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…

Centroid-based clustering algorithms, such as hard K-means (HKM) and fuzzy K-means (FKM), have suffered from learning bias towards large clusters. Their centroids tend to be crowded in large clusters, compromising performance when the true…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

Keeping in consideration the high demand for clustering, this paper focuses on understanding and implementing K-means clustering using two different similarity measures. We have tried to cluster the documents using two different measures…

The Adjusted Rand Index (ARI) is a widely used method for comparing hard clusterings, but requires a choice of random model that is often left implicit. Several recent works have extended the Rand Index to fuzzy clusterings, but the…

This paper provides a theoretical support for clustering aspect of the nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker optimality conditions, we show that NMF objective is equivalent to graph clustering…

Performance of clustering algorithms is evaluated with the help of accuracy metrics. There is a great diversity of clustering algorithms, which are key components of many data analysis and exploration systems. However, there exist only few…

Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is…