Related papers: Fuzzy c-Means Clustering for Persistence Diagrams

Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has recently gained much popularity from its myriad successful…

Deep learning has been successfully applied to many classification problems including underwater challenges. However, a long-standing issue with deep learning is the need for large and consistently labeled datasets. Although current…

In semi-supervised fuzzy clustering, this paper extends the traditional pairwise constraint (i.e., must-link or cannot-link) to fuzzy pairwise constraint. The fuzzy pairwise constraint allows a supervisor to provide the grade of similarity…

Statistical jump models have been recently introduced to detect persistent regimes by clustering temporal features and discouraging frequent regime changes. However, they are limited to hard clustering and thereby do not account for…

One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…

In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will analyze the output of ensemble simulations by considering…

This paper addresses the ambitious goal of merging two different approaches to group detection in complex domains: one based on fuzzy clustering and the other on community detection theory. To achieve this, two clustering algorithms are…

Topic detection is a process for determining topics from a collection of textual data. One of the topic detection methods is a clustering-based method, which assumes that the centroids are topics. The clustering method has the advantage…

A framework of M-estimation based fuzzy C-means clustering (MFCM) algorithm is proposed with iterative reweighted least squares (IRLS) algorithm, and penalty constraint and kernelization extensions of MFCM algorithms are also developed.…

The purpose of this paper is to study the algorithm FCM and some of its famous innovations, analyse and discover the method of applying hedge algebra theory that uses algebra to represent linguistic-valued variables, to FCM. Then, this…

Many state-of-the-art technologies developed in recent years have been influenced by machine learning to some extent. Most popular at the time of this writing are artificial intelligence methodologies that fall under the umbrella of deep…

With the membership function being strictly positive, the conventional fuzzy c-means clustering method sometimes causes imbalanced influence when clusters of vastly different sizes exist. That is, an outstandingly large cluster drags to its…

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…

Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption…

Cluster assignment of large and complex images is a crucial but challenging task in pattern recognition and computer vision. In this study, we explore the possibility of employing fuzzy clustering in a deep neural network framework. Thus,…

Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the…

We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence…

Both FCM and PCM clustering methods have been widely applied to pattern recognition and data clustering. Nevertheless, FCM is sensitive to noise and PCM occasionally generates coincident clusters. PFCM is an extension of the PCM model by…

In a data matrix, we may distinguish between cases, each represented by a row vector for a statistical unit, and cells, which correspond to single entries of the data matrix. Recent developments in Robust Statistics have introduced the…

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,…