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In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two…
Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised,…
The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
Time series clustering is the process of grouping time series with respect to their similarity or characteristics. Previous approaches usually combine a specific distance measure for time series and a standard clustering method. However,…
In order to improve the efficiency and sustainability of electricity systems, most countries worldwide are deploying advanced metering infrastructures, and in particular household smart meters, in the residential sector. This technology is…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
Climate change is a critical issue that will be in the political agenda for the next decades. While it is important for this topic to be discussed at higher levels, it is also of paramount importance that the populations became aware of the…
The $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means…
Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…
This paper deals with a clustering algorithm for histogram data based on a Self-Organizing Map (SOM) learning. It combines a dimension reduction by SOM and the clustering of the data in a reduced space. Related to the kind of data, a…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…
Solar irradiance clustering can enhance solar power capacity planning and help improve forecasting models by identifying similar irradiance patterns influenced by seasonal and weather changes. In this study, we adopt an efficient two-level…
In data containing heterogeneous subpopulations, classification performance benefits from incorporating the knowledge of cluster structure in the classifier. Previous methods for such combined clustering and classification either 1) are…
Clustering stands as one of the most prominent challenges in unsupervised machine learning. Among centroid-based methods, the classic $k$-means algorithm, based on Lloyd's heuristic, is widely used. Nonetheless, it is a well-known fact that…
The aim of this work was to predict the probability of the spread of rock formations with hydrocarbon-collecting properties in the studied coastal area using a stack of machine learning algorithms and data augmentation and modification…
The $k$-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to…
This paper proposes a centroid-based clustering algorithm which is capable of clustering data-points with n-features, without having to specify the number of clusters to be formed. The core logic behind the algorithm is a similarity…