Clustering of Symbolic Data based on Affinity Coefficient: Application to a Real Data Set

Copyright © 2013 Walter de Gruyter GmbH.In this paper, we illustrate an application of Ascendant Hierarchical Cluster Analysis (AHCA) to complex data taken from the literature (interval data), based on the standardized weighted generalized affinity coefficient, by the method of Wald and Wolfowitz. The probabilistic aggregation criteria used belong to a parametric family of methods under the probabilistic approach of AHCA, named VL methodology. Finally, we compare the results achieved using our approach with those obtained by other authors

Dynamic Clustering of Histogram Data Based on Adaptive Squared Wasserstein Distances

This paper deals with clustering methods based on adaptive distances for histogram data using a dynamic clustering algorithm. Histogram data describes individuals in terms of empirical distributions. These kind of data can be considered as complex descriptions of phenomena observed on complex objects: images, groups of individuals, spatial or temporal variant data, results of queries, environmental data, and so on. The Wasserstein distance is used to compare two histograms. The Wasserstein distance between histograms is constituted by two components: the first based on the means, and the second, to internal dispersions (standard deviation, skewness, kurtosis, and so on) of the histograms. To cluster sets of histogram data, we propose to use Dynamic Clustering Algorithm, (based on adaptive squared Wasserstein distances) that is a k-means-like algorithm for clustering a set of individuals into $K$ classes that are apriori fixed. The main aim of this research is to provide a tool for clustering histograms, emphasizing the different contributions of the histogram variables, and their components, to the definition of the clusters. We demonstrate that this can be achieved using adaptive distances. Two kind of adaptive distances are considered: the first takes into account the variability of each component of each descriptor for the whole set of individuals; the second takes into account the variability of each component of each descriptor in each cluster. We furnish interpretative tools of the obtained partition based on an extension of the classical measures (indexes) to the use of adaptive distances in the clustering criterion function. Applications on synthetic and real-world data corroborate the proposed procedure

Fuzzy clustering with entropy regularization for interval-valued data with an application to scientific journal citations

In recent years, the research of statistical methods to analyze complex structures of data has increased. In particular, a lot of attention has been focused on the interval-valued data. In a classical cluster analysis framework, an interesting line of research has focused on the clustering of interval-valued data based on fuzzy approaches. Following the partitioning around medoids fuzzy approach research line, a new fuzzy clustering model for interval-valued data is suggested. In particular, we propose a new model based on the use of the entropy as a regularization function in the fuzzy clustering criterion. The model uses a robust weighted dissimilarity measure to smooth noisy data and weigh the center and radius components of the interval-valued data, respectively. To show the good performances of the proposed clustering model, we provide a simulation study and an application to the clustering of scientific journals in research evaluation

New methods for discovering local behaviour in mixed databases

Clustering techniques are widely used. There are many applications where it is desired to find automatically groups or hidden information in the data set. Finding a model of the system based in the integration of several local models is placed among other applications. Local model could have many structures; however, a linear structure is the most common one, due to its simplicity. This work aims at finding improvements in several fields, but all them will be applied to this finding of a set of local models in a database. On the one hand, a way of codifying the categorical information into numerical values has been designed, in order to apply a numerical algorithm to the whole data set. On the other hand, a cost index has been developed, which will be optimized globally, to find the parameters of the local clusters that best define the output of the process. Each of the techniques has been applied to several experiments and results show the improvements over the actual techniques.Barceló Rico, F. (2009). New methods for discovering local behaviour in mixed databases. http://hdl.handle.net/10251/12739Archivo delegad

Survey of data mining approaches to user modeling for adaptive hypermedia

The ability of an adaptive hypermedia system to create tailored environments depends mainly on the amount and accuracy of information stored in each user model. Some of the difficulties that user modeling faces are the amount of data available to create user models, the adequacy of the data, the noise within that data, and the necessity of capturing the imprecise nature of human behavior. Data mining and machine learning techniques have the ability to handle large amounts of data and to process uncertainty. These characteristics make these techniques suitable for automatic generation of user models that simulate human decision making. This paper surveys different data mining techniques that can be used to efficiently and accurately capture user behavior. The paper also presents guidelines that show which techniques may be used more efficiently according to the task implemented by the applicatio

Identification and clustering of seasonality patterns for demand forecasting

Time series are essential in various domains and applications. Especially in retail business forecasting demand is a crucial task in order to make the appropriate business decisions. In this thesis we focus on a problem that can be characterized as a sub-problem in the field of demand forecasting: we attempt to form clusters of products that reflect the products’ annual seasonality patterns. We believe that these clusters would aid us in building more accurate forecast models. The seasonality patterns are identified from weekly sales time series, which in many cases are very sparse and noisy. In order to successfully identify the seasonality patterns from all the other factors contributing in a product’s sales, we build a pipeline to preprocess the data accordingly. This pipeline consist of first aggregating the sales of individual products over several stores to strengthen the sales signal, followed by solving a regularized weighted least squares objective to smooth the aggregates. Finally, the seasonality patterns are extracted using the STL decomposition procedure. These seasonality patterns are then used as input for the k-means algorithm and several hierarchical agglomerative clustering algorithms. We evaluate the clusters using two distinct approaches. In the first approach we manually label a subset of the data. These labeled subsets are then compared against the clusters provided by the clustering algorithms. In the second approach we form a simple forecast model that fits the clusters’ seasonality patterns back to the observed sales time series of individual products. In this approach we also build a secondary validation forecast model with the same objective, but instead of using the clusters provided by the algorithms, we use predetermined product categories as the clusters. These product categories should naturally provide a valid baseline for groups of products with similar seasonality as they reflect the structure of how similar products are organized within close proximity in physical stores. Our results indicate that we were able to find clear seasonal structure in the clusters. Especially the k-means algorithm and hierarchical agglomerative clustering algorithms with complete linkage and Ward’s method were able to form reasonable clusters, whereas hierarchical agglomerative clustering algorithm with single linkage was proven to be unsuitable given our data

Dynamic segmentation techniques applied to load profiles of electric energy consumption from domestic users

[EN] The electricity sector is currently undergoing a process of liberalization and separation of roles, which is being implemented under the regulatory auspices of each Member State of the European Union and, therefore, with different speeds, perspectives and objectives that must converge on a common horizon, where Europe will benefit from an interconnected energy market in which producers and consumers can participate in free competition. This process of liberalization and separation of roles involves two consequences or, viewed another way, entails a major consequence from which other immediate consequence, as a necessity, is derived. The main consequence is the increased complexity in the management and supervision of a system, the electrical, increasingly interconnected and participatory, with connection of distributed energy sources, much of them from renewable sources, at different voltage levels and with different generation capacity at any point in the network. From this situation the other consequence is derived, which is the need to communicate information between agents, reliably, safely and quickly, and that this information is analyzed in the most effective way possible, to form part of the processes of decision taking that improve the observability and controllability of a system which is increasing in complexity and number of agents involved. With the evolution of Information and Communication Technologies (ICT), and the investments both in improving existing measurement and communications infrastructure, and taking the measurement and actuation capacity to a greater number of points in medium and low voltage networks, the availability of data that informs of the state of the network is increasingly higher and more complete. All these systems are part of the so-called Smart Grids, or intelligent networks of the future, a future which is not so far. One such source of information comes from the energy consumption of customers, measured on a regular basis (every hour, half hour or quarter-hour) and sent to the Distribution System Operators from the Smart Meters making use of Advanced Metering Infrastructure (AMI). This way, there is an increasingly amount of information on the energy consumption of customers, being stored in Big Data systems. This growing source of information demands specialized techniques which can take benefit from it, extracting a useful and summarized knowledge from it. This thesis deals with the use of this information of energy consumption from Smart Meters, in particular on the application of data mining techniques to obtain temporal patterns that characterize the users of electrical energy, grouping them according to these patterns in a small number of groups or clusters, that allow evaluating how users consume energy, both during the day and during a sequence of days, allowing to assess trends and predict future scenarios. For this, the current techniques are studied and, proving that the current works do not cover this objective, clustering or dynamic segmentation techniques applied to load profiles of electric energy consumption from domestic users are developed. These techniques are tested and validated on a database of hourly energy consumption values for a sample of residential customers in Spain during years 2008 and 2009. The results allow to observe both the characterization in consumption patterns of the different types of residential energy consumers, and their evolution over time, and to assess, for example, how the regulatory changes that occurred in Spain in the electricity sector during those years influenced in the temporal patterns of energy consumption.[ES] El sector eléctrico se halla actualmente sometido a un proceso de liberalización y separación de roles, que está siendo aplicado bajo los auspicios regulatorios de cada Estado Miembro de la Unión Europea y, por tanto, con distintas velocidades, perspectivas y objetivos que deben confluir en un horizonte común, en donde Europa se beneficiará de un mercado energético interconectado, en el cual productores y consumidores podrán participar en libre competencia. Este proceso de liberalización y separación de roles conlleva dos consecuencias o, visto de otra manera, conlleva una consecuencia principal de la cual se deriva, como necesidad, otra consecuencia inmediata. La consecuencia principal es el aumento de la complejidad en la gestión y supervisión de un sistema, el eléctrico, cada vez más interconectado y participativo, con conexión de fuentes distribuidas de energía, muchas de ellas de origen renovable, a distintos niveles de tensión y con distinta capacidad de generación, en cualquier punto de la red. De esta situación se deriva la otra consecuencia, que es la necesidad de comunicar información entre los distintos agentes, de forma fiable, segura y rápida, y que esta información sea analizada de la forma más eficaz posible, para que forme parte de los procesos de toma de decisiones que mejoran la observabilidad y controlabilidad de un sistema cada vez más complejo y con más agentes involucrados. Con el avance de las Tecnologías de Información y Comunicaciones (TIC), y las inversiones tanto en mejora de la infraestructura existente de medida y comunicaciones, como en llevar la obtención de medidas y la capacidad de actuación a un mayor número de puntos en redes de media y baja tensión, la disponibilidad de datos sobre el estado de la red es cada vez mayor y más completa. Todos estos sistemas forman parte de las llamadas Smart Grids, o redes inteligentes del futuro, un futuro ya no tan lejano. Una de estas fuentes de información proviene de los consumos energéticos de los clientes, medidos de forma periódica (cada hora, media hora o cuarto de hora) y enviados hacia las Distribuidoras desde los contadores inteligentes o Smart Meters, mediante infraestructura avanzada de medida o Advanced Metering Infrastructure (AMI). De esta forma, cada vez se tiene una mayor cantidad de información sobre los consumos energéticos de los clientes, almacenada en sistemas de Big Data. Esta cada vez mayor fuente de información demanda técnicas especializadas que sepan aprovecharla, extrayendo un conocimiento útil y resumido de la misma. La presente Tesis doctoral versa sobre el uso de esta información de consumos energéticos de los contadores inteligentes, en concreto sobre la aplicación de técnicas de minería de datos (data mining) para obtener patrones temporales que caractericen a los usuarios de energía eléctrica, agrupándolos según estos mismos patrones en un número reducido de grupos o clusters, que permiten evaluar la forma en que los usuarios consumen la energía, tanto a lo largo del día como durante una secuencia de días, permitiendo evaluar tendencias y predecir escenarios futuros. Para ello se estudian las técnicas actuales y, comprobando que los trabajos actuales no cubren este objetivo, se desarrollan técnicas de clustering o segmentación dinámica aplicadas a curvas de carga de consumo eléctrico diario de clientes domésticos. Estas técnicas se prueban y validan sobre una base de datos de consumos energéticos horarios de una muestra de clientes residenciales en España durante los años 2008 y 2009. Los resultados permiten observar tanto la caracterización en consumos de los distintos tipos de consumidores energéticos residenciales, como su evolución en el tiempo, y permiten evaluar, por ejemplo, cómo influenciaron en los patrones temporales de consumos los cambios regulatorios que se produjeron en España en el sector eléctrico durante esos años.[CA] El sector elèctric es troba actualment sotmès a un procés de liberalització i separació de rols, que s'està aplicant davall els auspicis reguladors de cada estat membre de la Unió Europea i, per tant, amb distintes velocitats, perspectives i objectius que han de confluir en un horitzó comú, on Europa es beneficiarà d'un mercat energètic interconnectat, en el qual productors i consumidors podran participar en lliure competència. Aquest procés de liberalització i separació de rols comporta dues conseqüències o, vist d'una altra manera, comporta una conseqüència principal de la qual es deriva, com a necessitat, una altra conseqüència immediata. La conseqüència principal és l'augment de la complexitat en la gestió i supervisió d'un sistema, l'elèctric, cada vegada més interconnectat i participatiu, amb connexió de fonts distribuïdes d'energia, moltes d'aquestes d'origen renovable, a distints nivells de tensió i amb distinta capacitat de generació, en qualsevol punt de la xarxa. D'aquesta situació es deriva l'altra conseqüència, que és la necessitat de comunicar informació entre els distints agents, de forma fiable, segura i ràpida, i que aquesta informació siga analitzada de la manera més eficaç possible, perquè forme part dels processos de presa de decisions que milloren l'observabilitat i controlabilitat d'un sistema cada vegada més complex i amb més agents involucrats. Amb l'avanç de les tecnologies de la informació i les comunicacions (TIC), i les inversions, tant en la millora de la infraestructura existent de mesura i comunicacions, com en el trasllat de l'obtenció de mesures i capacitat d'actuació a un nombre més gran de punts en xarxes de mitjana i baixa tensió, la disponibilitat de dades sobre l'estat de la xarxa és cada vegada major i més completa. Tots aquests sistemes formen part de les denominades Smart Grids o xarxes intel·ligents del futur, un futur ja no tan llunyà. Una d'aquestes fonts d'informació prové dels consums energètics dels clients, mesurats de forma periòdica (cada hora, mitja hora o quart d'hora) i enviats cap a les distribuïdores des dels comptadors intel·ligents o Smart Meters, per mitjà d'infraestructura avançada de mesura o Advanced Metering Infrastructure (AMI). D'aquesta manera, cada vegada es té una major quantitat d'informació sobre els consums energètics dels clients, emmagatzemada en sistemes de Big Data. Aquesta cada vegada major font d'informació demanda tècniques especialitzades que sàpiguen aprofitar-la, extraient-ne un coneixement útil i resumit. La present tesi doctoral versa sobre l'ús d'aquesta informació de consums energètics dels comptadors intel·ligents, en concret sobre l'aplicació de tècniques de mineria de dades (data mining) per a obtenir patrons temporals que caracteritzen els usuaris d'energia elèctrica, agrupant-los segons aquests mateixos patrons en una quantitat reduïda de grups o clusters, que permeten avaluar la forma en què els usuaris consumeixen l'energia, tant al llarg del dia com durant una seqüència de dies, i que permetent avaluar tendències i predir escenaris futurs. Amb aquesta finalitat, s'estudien les tècniques actuals i, en comprovar que els treballs actuals no cobreixen aquest objectiu, es desenvolupen tècniques de clustering o segmentació dinàmica aplicades a corbes de càrrega de consum elèctric diari de clients domèstics. Aquestes tècniques es proven i validen sobre una base de dades de consums energètics horaris d'una mostra de clients residencials a Espanya durant els anys 2008 i 2009. Els resultats permeten observar tant la caracterització en consums dels distints tipus de consumidors energètics residencials, com la seua evolució en el temps, i permeten avaluar, per exemple, com van influenciar en els patrons temporals de consums els canvis reguladors que es van produir a Espanya en el sector elèctric durant aquests anys.Benítez Sánchez, IJ. (2015). Dynamic segmentation techniques applied to load profiles of electric energy consumption from domestic users [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/59236TESI

3rd Workshop in Symbolic Data Analysis: book of abstracts

This workshop is the third regular meeting of researchers interested in Symbolic Data Analysis. The main aim of the event is to favor the meeting of people and the exchange of ideas from different fields - Mathematics, Statistics, Computer Science, Engineering, Economics, among others - that contribute to Symbolic Data Analysis

Clustering of Multiple Dissimilarity Data Tables for Documents Categorization

ISBN 978-3-7908-2603-6 e-ISBN 978-3-7908-2604-3International audienceThis paper introduces a clustering algorithm that is able to partition objects taking into account simultaneously their relational descriptions given by multiple dissimilarity matrices. These matrices could have been generated using different sets of variables and a fixed dissimilarity function, using a fixed set of variables and different dissimilarity functions or using different sets of variables and dissimilarity functions. This method, which is based on the dynamic hard clustering algorithm for relational data, is designed to provided a partition and a prototype for each cluster as well as to learn a relevance weight for each dissimilarity matrix by optimizing an adequacy criterion that measures the fit between clusters and their representatives. These relevance weights change at each algorithm iteration and are different from one cluster to another. Experiments aiming at obtaining a categorization of a document data base demonstrate the usefulness of this partitional clustering method