Mining Extremes through Fuzzy Clustering

Archetypes are extreme points that synthesize data representing "pure" individual types. Archetypes are assigned by the most discriminating features of data points, and are almost always useful in applications when one is interested in extremes and not on commonalities. Recent applications include talent analysis in sports and science, fraud detection, profiling of users and products in recommendation systems, climate extremes, as well as other machine learning applications. The furthest-sum Archetypal Analysis (FS-AA) (Mørup and Hansen, 2012) and the Fuzzy Clustering with Proportional Membership (FCPM) (Nascimento, 2005) propose distinct models to find clusters with extreme prototypes. Even though the FCPM model does not impose its prototypes to lie in the convex hull of data, it belongs to the framework of data recovery from clustering (Mirkin, 2005), a powerful property for unsupervised cluster analysis. The baseline version of FCPM, FCPM-0, provides central prototypes whereas its smooth version, FCPM-2 provides extreme prototypes as AA archetypes. The comparative study between FS-AA and FCPM algorithms conducted in this dissertation covers the following aspects. First, the analysis of FS-AA on data recovery from clustering using a collection of 100 data sets of diverse dimensionalities, generated with a proper data generator (FCPM-DG) as well as 14 real world data. Second, testing the robustness of the clustering algorithms in the presence of outliers, with the peculiar behaviour of FCPM-0 on removing the proper number of prototypes from data. Third, a collection of five popular fuzzy validation indices are explored on accessing the quality of clustering results. Forth, the algorithms undergo a study to evaluate how different initializations affect their convergence as well as the quality of the clustering partitions. The Iterative Anomalous Pattern (IAP) algorithm allows to improve the convergence of FCPM algorithm as well as to fine-tune the level of resolution to look at clustering results, which is an advantage from FS-AA. Proper visualization functionalities for FS-AA and FCPM support the easy interpretation of the clustering results

Validation of archetypal analysis

We use an information-theoretic criterion to assess the goodness-of-fit of the output of archetypal analysis (AA), also intended as a fuzzy clustering tool. It is an adaptation of an existing AIC-like measure to the specifics of AA. We test its effectiveness using artificial data and some data sets arising from real life problems. In most cases, the results achieved are similar to those provided by an external similarity index. The average reconstruction accuracy is about 93%.info:eu-repo/semantics/acceptedVersio

Wind Turbine Fault Detection: an Unsupervised vs Semi-Supervised Approach

The need for renewable energy has been growing in recent years for the reasons we all know, wind power is no exception. Wind turbines are complex and expensive structures and the need for maintenance exists. Conditioning Monitoring Systems that make use of supervised machine learning techniques have been recently studied and the results are quite promising. Though, such systems still require the physical presence of professionals but with the advantage of gaining insight of the operating state of the machine in use, to decide upon maintenance interventions beforehand. The wind turbine failure is not an abrupt process but a gradual one. The main goal of this dissertation is: to compare semi-supervised methods to at tack the problem of automatic recognition of anomalies in wind turbines; to develop an approach combining the Mahalanobis Taguchi System (MTS) with two popular fuzzy partitional clustering algorithms like the fuzzy c-means and archetypal analysis, for the purpose of anomaly detection; and finally to develop an experimental protocol to com paratively study the two types of algorithms. In this work, the algorithms Local Outlier Factor (LOF), Connectivity-based Outlier Factor (COF), Cluster-based Local Outlier Factor (CBLOF), Histogram-based Outlier Score (HBOS), k-nearest-neighbours (k-NN), Subspace Outlier Detection (SOD), Fuzzy c-means (FCM), Archetypal Analysis (AA) and Local Minimum Spanning Tree (LoMST) were explored. The data used consisted of SCADA data sets regarding turbine sensorial data, 8 to tal, from a wind farm in the North of Portugal. Each data set comprises between 1070 and 1096 data cases and characterized by 5 features, for the years 2011, 2012 and 2013. The analysis of the results using 7 different validity measures show that, the CBLOF al gorithm got the best results in the semi-supervised approach while LoMST won in the unsupervised scenario. The extension of both FCM and AA got promissing results.A necessidade de produzir energia renovável tem vindo a crescer nos últimos anos pelas razões que todos sabemos, a energia eólica não é excepção. As turbinas eólicas são es truturas complexas e caras e a necessidade de manutenção existe. Sistemas de Condição Monitorizada utilizando técnicas de aprendizagem supervisionada têm vindo a ser estu dados recentemente e os resultados são bastante promissores. No entanto, estes sistemas ainda exigem a presença física de profissionais, mas com a vantagem de obter informa ções sobre o estado operacional da máquina em uso, para decidir sobre intervenções de manutenção antemão. O principal objetivo desta dissertação é: comparar métodos semi-supervisionados para atacar o problema de reconhecimento automático de anomalias em turbinas eólicas; desenvolver um método que combina o Mahalanobis Taguchi System (MTS) com dois mé todos de agrupamento difuso bem conhecidos como fuzzy c-means e archetypal analysis, no âmbito de deteção de anomalias; e finalmente desenvolver um protocolo experimental onde é possível o estudo comparativo entre os dois diferentes tipos de algoritmos. Neste trabalho, os algoritmos Local Outlier Factor (LOF), Connectivity-based Outlier Factor (COF), Cluster-based Local Outlier Factor (CBLOF), Histogram-based Outlier Score (HBOS), k-nearest-neighbours (k-NN), Subspace Outlier Detection (SOD), Fuzzy c-means (FCM), Archetypal Analysis (AA) and Local Minimum Spanning Tree (LoMST) foram explorados. Os conjuntos de dados utilizados provêm do sistema SCADA, referentes a dados sen soriais de turbinas, 8 no total, com origem num parque eólico no Norte de Portugal. Cada um está compreendendido entre 1070 e 1096 observações e caracterizados por 5 caracte rísticas, para os anos 2011, 2012 e 2013. A ánalise dos resultados através de 7 métricas de validação diferentes mostraram que, o algoritmo CBLOF obteve os melhores resultados na abordagem semi-supervisionada enquanto que o LoMST ganhou na abordagem não supervisionada. A extensão do FCM e do AA originou resultados promissores

No Pattern, No Recognition: a Survey about Reproducibility and Distortion Issues of Text Clustering and Topic Modeling

Extracting knowledge from unlabeled texts using machine learning algorithms can be complex. Document categorization and information retrieval are two applications that may benefit from unsupervised learning (e.g., text clustering and topic modeling), including exploratory data analysis. However, the unsupervised learning paradigm poses reproducibility issues. The initialization can lead to variability depending on the machine learning algorithm. Furthermore, the distortions can be misleading when regarding cluster geometry. Amongst the causes, the presence of outliers and anomalies can be a determining factor. Despite the relevance of initialization and outlier issues for text clustering and topic modeling, the authors did not find an in-depth analysis of them. This survey provides a systematic literature review (2011-2022) of these subareas and proposes a common terminology since similar procedures have different terms. The authors describe research opportunities, trends, and open issues. The appendices summarize the theoretical background of the text vectorization, the factorization, and the clustering algorithms that are directly or indirectly related to the reviewed works

Development of statistical methodologies applied to anthropometric data oriented towards the ergonomic design of products

Ergonomics is the scientific discipline that studies the interactions between human beings and the elements of a system and presents multiple applications in areas such as clothing and footwear design or both working and household environments. In each of these sectors, knowing the anthropometric dimensions of the current target population is fundamental to ensure that products suit as well as possible most of the users who make up the population. Anthropometry refers to the study of the measurements and dimensions of the human body and it is considered a very important branch of Ergonomics because its considerable influence on the ergonomic design of products. Human body measurements have usually been taken using rules, calipers or measuring tapes. These procedures are simple and cheap to carry out. However, they have one major drawback: the body measurements obtained and consequently, the human shape information, is imprecise and inaccurate. Furthermore, they always require interaction with real subjects, which increases the measure time and data collecting. The development of new three-dimensional (3D) scanning techniques has represented a huge step forward in the way of obtaining anthropometric data. This technology allows 3D images of human shape to be captured and at the same time, generates highly detailed and reproducible anthropometric measurements. The great potential of these new scanning systems for the digitalization of human body has contributed to promoting new anthropometric studies in several countries, such as United Kingdom, Australia, Germany, France or USA, in order to acquire accurate anthropometric data of their current population. In this context, in 2006 the Spanish Ministry of Health commissioned a 3D anthropometric survey of the Spanish female population, following the agreement signed by the Ministry itself with the Spanish associations and companies of manufacturing, distribution, fashion design and knitted sectors. A sample of 10415 Spanish females from 12 to 70 years old, randomly selected from the official Postcode Address File, was measured. The two main objectives of this study, which was conducted by the Biomechanics Institute of Valencia, were the following: on the one hand, to characterize the shape and body dimensions of the current Spanish women population to develop a standard sizing system that could be used by all clothing designers. On the other hand, to promote a healthy image of beauty through the representation of suited mannequins. In order to tackle both objectives, Statistics plays an essential role. Thus, the statistical methodologies presented in this PhD work have been applied to the database obtained from the Spanish anthropometric study. Clothing sizing systems classify the population into homogeneous groups (size groups) based on some key anthropometric dimensions. All members of the same group are similar in body shape and size, so they can wear the same garment. In addition, members of different groups are very different with respect to their body dimensions. An efficient and optimal sizing system aims at accommodating as large a percentage of the population as possible, in the optimum number of size groups that better describes the shape variability of the population. Besides, the garment fit for the accommodated individuals must be as good as possible. A very valuable reference related to sizing systems is the book Sizing in clothing: Developing effective sizing systems for ready-to-wear clothing, by Susan Ashdown. Each clothing size is defined from a person whose body measurements are located toward the central value for each of the dimensions considered in the analysis. The central person, which is considered as the size representative (the size prototype), becomes the basic pattern from which the clothing line in the same size is designed. Clustering is the statistical tool that divides a set of individuals in groups (clusters), in such a way that subjects of the same cluster are more similar to each other than to those in other groups. In addition, clustering defines each group by means of a representative individual. Therefore, it arises in a natural way the idea of using clustering to try to define an efficient sizing system. Specifically, four of the methodologies presented in this PhD thesis aimed at segmenting the population into optimal sizes, use different clustering methods. The first one, called trimowa, has been published in Expert Systems with Applications. It is based on using an especially defined distance to examine differences between women regarding their body measurements. The second and third ones (called biclustAnthropom and TDDclust, respectively) will soon be submitted in the same paper. BiclustAnthropom adapts to the field of Anthropometry a clustering method addressed in the specific case of gene expression data. Moreover, TDDclust uses the concept of statistical depth for grouping according to the most central (deep) observation in each size. As mentioned, current sizing systems are based on using an appropriate set of anthropometric dimensions, so clustering is carried out in the Euclidean space. In the three previous proposals, we have always worked in this way. Instead, in the fourth and last approach, called kmeansProcrustes, a clustering procedure is proposed for grouping taking into account the women shape, which is represented by a set of anatomical markers (landmarks). For this purpose, the statistical shape analysis will be fundamental. This contribution has been submitted for publication. A sizing system is intended to cover the so-called standard population, discarding the individuals with extreme sizes (both large and small). In mathematical language, these individuals can be considered outliers. An outlier is an observation point that is distant from other observations. In our case, a person with extreme anthopometric measurements would be considered as a statistical outlier. Clothing companies usually design garments for the standard sizes so that their market share is optimal. Nevertheless, with their foreign expansion, a lot of brands are spreading their collection and they already have a special sizes section. In last years, Internet shopping has been an alternative for consumers with extreme sizes looking for clothes that follow trends. The custom-made fabrication is other possibility with the advantage of making garments according to the customers' preferences. The four aforementioned methodologies (trimowa, biclustAnthropom, TDDclust and kmeansProcrustes) have been adapted to only accommodate the standard population. Once a particular garment has been designed, the assessing and analysis of fit is performed using one or more fit models. The fit model represents the body dimensions selected by each company to define the proportional relationships needed to achieve the fit the company has determined. The definition of an efficient sizing system relies heavily on the accuracy and representativeness of the fit models regarding the population to which it is addressed. In this PhD work, a statistical approach is proposed to identify representative fit models. It is based on another clustering method originally developed for grouping gene expression data. This method, called hipamAnthropom, has been published in Decision Support Systems. From well-defined fit models and prototypes, representative and accurate mannequins of the population can be made. Unlike clothing design, where representative cases correspond with central individuals, in the design of working and household environments, the variability of human shape is described by extreme individuals, which are those that have the largest or smallest values (or extreme combinations) in the dimensions involved in the study. This is often referred to as the accommodation problem. A very interesting reference in this area is the book entitled Guidelines for Using Anthropometric Data in Product Design, published by The Human Factors and Ergonomics Society. The idea behind this way of proceeding is that if a product fits extreme observations, it will also fit the others (less extreme). To that end, in this PhD thesis we propose two methodological contributions based on the statistical archetypal analysis. An archetype in Statistics is an extreme individual that is obtained as a convex combination of other subjects of the sample. The first of these methodologies has been published in Computers and Industrial Engineering, whereas the second one has been submitted for publication. The outline of this PhD report is as follows: Chapter 1 reviews the state of the art of Ergonomics and Anthropometry and introduces the anthropometric survey of the Spanish female population. Chapter 2 presents the trimowa, biclustAnthropom and hipamAnthropom methodologies. In Chapter 3 the kmeansProcrustes proposal is detailed. The TDDclust methodology is explained in Chapter 4. Chapter 5 presents the two methodologies related to the archetypal analysis. Since all these contributions have been programmed in the statistical software R, Chapter 6 presents the Anthropometry R package, that brings together all the algorithms associated with each approach. In this way, from Chapter 2 to Chapter 6 all the methodologies and results included in this PhD thesis are presented. At last, Chapter 7 provides the most important conclusions

Comparative Analysis of Student Learning: Technical, Methodological and Result Assessing of PISA-OECD and INVALSI-Italian Systems .

PISA is the most extensive international survey promoted by the OECD in the field of education, which measures the skills of fifteen-year-old students from more than 80 participating countries every three years. INVALSI are written tests carried out every year by all Italian students in some key moments of the school cycle, to evaluate the levels of some fundamental skills in Italian, Mathematics and English. Our comparison is made up to 2018, the last year of the PISA-OECD survey, even if INVALSI was carried out for the last edition in 2022. Our analysis focuses attention on the common part of the reference populations, which are the 15-year-old students of the 2nd class of secondary schools of II degree, where both sources give a similar picture of the students

Statistical Data Modeling and Machine Learning with Applications

The modeling and processing of empirical data is one of the main subjects and goals of statistics. Nowadays, with the development of computer science, the extraction of useful and often hidden information and patterns from data sets of different volumes and complex data sets in warehouses has been added to these goals. New and powerful statistical techniques with machine learning (ML) and data mining paradigms have been developed. To one degree or another, all of these techniques and algorithms originate from a rigorous mathematical basis, including probability theory and mathematical statistics, operational research, mathematical analysis, numerical methods, etc. Popular ML methods, such as artificial neural networks (ANN), support vector machines (SVM), decision trees, random forest (RF), among others, have generated models that can be considered as straightforward applications of optimization theory and statistical estimation. The wide arsenal of classical statistical approaches combined with powerful ML techniques allows many challenging and practical problems to be solved. This Special Issue belongs to the section “Mathematics and Computer Science”. Its aim is to establish a brief collection of carefully selected papers presenting new and original methods, data analyses, case studies, comparative studies, and other research on the topic of statistical data modeling and ML as well as their applications. Particular attention is given, but is not limited, to theories and applications in diverse areas such as computer science, medicine, engineering, banking, education, sociology, economics, among others. The resulting palette of methods, algorithms, and applications for statistical modeling and ML presented in this Special Issue is expected to contribute to the further development of research in this area. We also believe that the new knowledge acquired here as well as the applied results are attractive and useful for young scientists, doctoral students, and researchers from various scientific specialties

SIS 2017. Statistics and Data Science: new challenges, new generations

The 2017 SIS Conference aims to highlight the crucial role of the Statistics in Data Science. In this new domain of ‘meaning’ extracted from the data, the increasing amount of produced and available data in databases, nowadays, has brought new challenges. That involves different fields of statistics, machine learning, information and computer science, optimization, pattern recognition. These afford together a considerable contribute in the analysis of ‘Big data’, open data, relational and complex data, structured and no-structured. The interest is to collect the contributes which provide from the different domains of Statistics, in the high dimensional data quality validation, sampling extraction, dimensional reduction, pattern selection, data modelling, testing hypotheses and confirming conclusions drawn from the data