Simple Measures of Individual Cluster-Membership Certainty for Hard Partitional Clustering

We propose two probability-like measures of individual cluster-membership certainty which can be applied to a hard partition of the sample such as that obtained from the Partitioning Around Medoids (PAM) algorithm, hierarchical clustering or k-means clustering. One measure extends the individual silhouette widths and the other is obtained directly from the pairwise dissimilarities in the sample. Unlike the classic silhouette, however, the measures behave like probabilities and can be used to investigate an individual's tendency to belong to a cluster. We also suggest two possible ways to evaluate the hard partition. We evaluate the performance of both measures in individuals with ambiguous cluster membership, using simulated binary datasets that have been partitioned by the PAM algorithm or continuous datasets that have been partitioned by hierarchical clustering and k-means clustering. For comparison, we also present results from soft clustering algorithms such as soft analysis clustering (FANNY) and two model-based clustering methods. Our proposed measures perform comparably to the posterior-probability estimators from either FANNY or the model-based clustering methods. We also illustrate the proposed measures by applying them to Fisher's classic iris data set

Fuzzy clustering with spatial-temporal information

Clustering geographical units based on a set of quantitative features observed at several time occasions requires to deal with the complexity of both space and time information. In particular, one should consider (1) the spatial nature of the units to be clustered, (2) the characteristics of the space of multivariate time trajectories, and (3) the uncertainty related to the assignment of a geographical unit to a given cluster on the basis of the above com- plex features. This paper discusses a novel spatially constrained multivariate time series clustering for units characterised by different levels of spatial proximity. In particular, the Fuzzy Partitioning Around Medoids algorithm with Dynamic Time Warping dissimilarity measure and spatial penalization terms is applied to classify multivariate Spatial-Temporal series. The clustering method has been theoretically presented and discussed using both simulated and real data, highlighting its main features. In particular, the capability of embedding different levels of proximity among units, and the ability of considering time series with different length

Hard and soft clustering of categorical time series based on two novel distances with an application to biological sequences

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG.[Abstract]: Two novel distances between categorical time series are introduced. Both of them measure discrepancies between extracted features describing the underlying serial dependence patterns. One distance is based on well-known association measures, namely Cramer's v and Cohen's κ. The other one relies on the so-called binarization of a categorical process, which indicates the presence of each category by means of a canonical vector. Binarization is used to construct a set of innovative association measures which allow to identify different types of serial dependence. The metrics are used to perform crisp and fuzzy clustering of nominal series. The proposed approaches are able to group together series generated from similar stochastic processes, achieve accurate results with series coming from a broad range of models and are computationally efficient. Extensive simulation studies show that both hard and soft clustering algorithms outperform several alternative procedures proposed in the literature. Two applications involving biological sequences from different species highlight the usefulness of the introduced techniques.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; ED431C-2020-14The research of Ángel López-Oriona and José A. Vilar has been supported by the Ministerio de Economía y Competitividad (MINECO) grants MTM2017-82724-R and PID2020-113578RB-100, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14), and the Centro de Investigación del Sistema Universitario de Galicia “CITIC” grant ED431G 2019/01; all of them through the European Regional Development Fund (ERDF). This work has received funding for open access charge by Universidade da Coruña/CISUG. The author Ángel López-Oriona is very grateful to researcher Maite Freire for her lessons about DNA theory

A Machine Learning-Based Framework for Clustering Residential Electricity Load Profiles to Enhance Demand Response Programs

Load shapes derived from smart meter data are frequently employed to analyze daily energy consumption patterns, particularly in the context of applications like Demand Response (DR). Nevertheless, one of the most important challenges to this endeavor lies in identifying the most suitable consumer clusters with similar consumption behaviors. In this paper, we present a novel machine learning based framework in order to achieve optimal load profiling through a real case study, utilizing data from almost 5000 households in London. Four widely used clustering algorithms are applied specifically K-means, K-medoids, Hierarchical Agglomerative Clustering and Density-based Spatial Clustering. An empirical analysis as well as multiple evaluation metrics are leveraged to assess those algorithms. Following that, we redefine the problem as a probabilistic classification one, with the classifier emulating the behavior of a clustering algorithm,leveraging Explainable AI (xAI) to enhance the interpretability of our solution. According to the clustering algorithm analysis the optimal number of clusters for this case is seven. Despite that, our methodology shows that two of the clusters, almost 10\% of the dataset, exhibit significant internal dissimilarity and thus it splits them even further to create nine clusters in total. The scalability and versatility of our solution makes it an ideal choice for power utility companies aiming to segment their users for creating more targeted Demand Response programs.Comment: 29 pages, 19 figure

Quantile-Based Fuzzy Clustering of Multivariate Time Series in the Frequency Domain

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] A novel procedure to perform fuzzy clustering of multivariate time series generated from different dependence models is proposed. Different amounts of dissimilarity between the generating models or changes on the dynamic behaviours over time are some arguments justifying a fuzzy approach, where each series is associated to all the clusters with specific membership levels. Our procedure considers quantile-based cross-spectral features and consists of three stages: (i) each element is characterized by a vector of proper estimates of the quantile cross-spectral densities, (ii) principal component analysis is carried out to capture the main differences reducing the effects of the noise, and (iii) the squared Euclidean distance between the first retained principal components is used to perform clustering through the standard fuzzy C-means and fuzzy C-medoids algorithms. The performance of the proposed approach is evaluated in a broad simulation study where several types of generating processes are considered, including linear, nonlinear and dynamic conditional correlation models. Assessment is done in two different ways: by directly measuring the quality of the resulting fuzzy partition and by taking into account the ability of the technique to determine the overlapping nature of series located equidistant from well-defined clusters. The procedure is compared with the few alternatives suggested in the literature, substantially outperforming all of them whatever the underlying process and the evaluation scheme. Two specific applications involving air quality and financial databases illustrate the usefulness of our approach.The authors are grateful to the anonymous referees for their comments and suggestions. The research of Ángel López-Oriona and José A. Vilar has been supported by the Ministerio de Economía y Competitividad (MINECO) grants MTM2017-82724-R and PID2020-113578RB-100, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14), and the Centro de Investigación del Sistema Universitario de Galicia “CITIC” grant ED431G 2019/01; all of them through the European Regional Development Fund (ERDF). This work has received funding for open access charge by Universidade da Coruña/CISUGXunta de Galicia; ED431C-2020-14Xunta de Galicia; ED431G 2019/0

Augmented Session Similarity Based Framework for Measuring Web User Concern from Web Server Logs

In this paper, an augmented sessions similarity based framework is proposed to measure web user concern from web server logs. This proposed framework will consider the best usage similarity between two web sessions based on accessed page relevance and URL based syntactic structure of website within the session. The proposed framework is implemented using K-medoids clustering algorithms with independent and combined similarity measures. The clusters qualities are evaluated by measuring average intra-cluster and inter-cluster distances. The experimental results show that combined augmented session dissimilarity metric outperformed the independent augmented session dissimilarity measures in terms of cluster validity measures

Review of Clustering Methods for Slow Coherency-Based Generator Grouping

Slow coherency is one of the most relevant concepts used in power systems dynamics to group generators that exhibit similar response to disturbances. Among the approaches developed for generator grouping based on slow coherency, clustering algorithms play a significant role. This paper reviews the clustering algorithms applied in model-based and data-driven approaches, highlighting the metrics used, the feature selection, the types of algorithms and the comparison among the results obtained considering simulated or measured data

Fuzzy clustering of spatial interval-valued data

In this paper, two fuzzy clustering methods for spatial intervalvalued data are proposed, i.e. the fuzzy C-Medoids clustering of spatial interval-valued data with and without entropy regularization. Both methods are based on the Partitioning Around Medoids (PAM) algorithm, inheriting the great advantage of obtaining non-fictitious representative units for each cluster. In both methods, the units are endowed with a relation of contiguity, represented by a symmetric binary matrix. This can be intended both as contiguity in a physical space and as a more abstract notion of contiguity. The performances of the methods are proved by simulation, testing the methods with different contiguity matrices associated to natural clusters of units. In order to show the effectiveness of the methods in empirical studies, three applications are presented: the clustering of municipalities based on interval-valued pollutants levels, the clustering of European fact-checkers based on interval-valued data on the average number of impressions received by their tweets and the clustering of the residential zones of the city of Rome based on the interval of price values

Fuzzy clustering of spatial interval-valued data

In this paper, two fuzzy clustering methods for spatial interval-valued data are proposed, i.e. the fuzzy C-Medoids clustering of spatial interval-valued data with and without entropy regularization. Both methods are based on the Partitioning Around Medoids (PAM) algorithm, inheriting the great advantage of obtaining non-fictitious representative units for each cluster. In both methods, the units are endowed with a relation of contiguity, represented by a symmetric binary matrix. This can be intended both as contiguity in a physical space and as a more abstract notion of contiguity. The performances of the methods are proved by simulation, testing the methods with different contiguity matrices associated to natural clusters of units. In order to show the effectiveness of the methods in empirical studies, three applications are presented: the clustering of municipalities based on interval-valued pollutants levels, the clustering of European fact-checkers based on interval-valued data on the average number of impressions received by their tweets and the clustering of the residential zones of the city of Rome based on the interval of price values

Fuzzy clustering of ordinal time series based on two novel distances with economic applications

Time series clustering is a central machine learning task with applications in many fields. While the majority of the methods focus on real-valued time series, very few works consider series with discrete response. In this paper, the problem of clustering ordinal time series is addressed. To this aim, two novel distances between ordinal time series are introduced and used to construct fuzzy clustering procedures. Both metrics are functions of the estimated cumulative probabilities, thus automatically taking advantage of the ordering inherent to the series' range. The resulting clustering algorithms are computationally efficient and able to group series generated from similar stochastic processes, reaching accurate results even though the series come from a wide variety of models. Since the dynamic of the series may vary over the time, we adopt a fuzzy approach, thus enabling the procedures to locate each series into several clusters with different membership degrees. An extensive simulation study shows that the proposed methods outperform several alternative procedures. Weighted versions of the clustering algorithms are also presented and their advantages with respect to the original methods are discussed. Two specific applications involving economic time series illustrate the usefulness of the proposed approaches