Related papers: Fuzzy c-Means Clustering for Persistence Diagrams
In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point…
A long-standing issue with deep learning is the need for large and consistently labeled datasets. Although the current research in semi-supervised learning can decrease the required amount of annotated data by a factor of 10 or even more,…
We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and…
Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to…
Numerous learning methods for fuzzy cognitive maps (FCMs), such as the Hebbian-based and the population-based learning methods, have been developed for modeling and simulating dynamic systems. However, these methods are faced with several…
In this paper, we propose a new fuzzy clustering algorithm based on the mode-seeking framework. Given a dataset in $\mathbb{R}^d$, we define regions of high density that we call cluster cores. We then consider a random walk on a…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…
We discuss topological aspects of cluster analysis and show that inferring the topological structure of a dataset before clustering it can considerably enhance cluster detection: theoretical arguments and empirical evidence show that…
Cluster analysis which focuses on the grouping and categorization of similar elements is widely used in various fields of research. Inspired by the phenomenon of atomic fission, a novel density-based clustering algorithm is proposed in this…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
Persistent homology has been widely used to study the topology of point clouds in $\mathbb{R}^n$. Standard approaches are very sensitive to outliers, and their computational complexity depends badly on the number of data points. In this…
Information Retrieval systems can be improved by exploiting context information such as user and document features. This article presents a model based on overlapping probabilistic or fuzzy clusters for such features. The model is applied…
Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be…
Recently, several studies have claimed that using class-specific feature subsets provides certain advantages over using a single feature subset for representing the data for a classification problem. Unlike traditional feature selection…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
In this paper, we describe an algorithm FARDiff (Fuzzy Adaptive Resonance Dif- fusion) which combines Diffusion Maps and Fuzzy Adaptive Resonance Theory to do clustering on high dimensional data. We describe some applications of this method…
The volatility features of financial data would considerably change in different periods, that is one of the main factors affecting the applications of machine learning in quantitative trading. Therefore, to effectively distinguish…
High utility itemset mining approaches discover hidden patterns from large amounts of temporal data. However, an inescapable problem of high utility itemset mining is that its discovered results hide the quantities of patterns, which causes…
Fuzzy clustering methods allow the objects to belong to several clusters simultaneously, with different degrees of membership. However, a factor that influences the performance of fuzzy algorithms is the value of fuzzifier parameter. In…