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ormai universalmente riconosciuto che il concetto di povertà richiede un approccio multidimensionale che focalizzi la propria attenzione non solo sulle caratteristiche propriamente monetarie del fenomeno, ma anche su altri aspetti della vita quotidiana delle persone, quali lavoro, ambiente, relazioni sociali, sfera affettiva, conoscenza, salute. Tale approccio multidimensionale è ormai concretamente utilizzato dalle maggiori istituzioni internazionali e dalla stessa Unione Europea che individua nella lotta alla povertà (in stretta connessione al fenomeno dell’esclusione sociale) una delle priorità di azione anche nell’agenda strategica di Europa 2020. In questo quadro, la nostra ricerca è partita dal prendere in esame i tentativi messi in atto per misurare la povertà secondo un approccio “multidimensionale”, facendo riferimento all’indice Human Poverty Index (HPI), formulato dall’Human Development Report nel 1997 e all’indice Multidimensional Poverty Index (MPI). In questo lavoro, si propone, la costruzione di un indicatore composito model based ottenuto con l’utilizzo dei Modelli ad Equazioni Strutturale (Structural Equation Models, SEM), con metodo PLS Path Modeling.

In this chapter, a Higher-Order Construct Model is used to construct the Italian Social Cohesion Indicator with the use Elemaentary ordinal Indicators with suitable qualification and some Latent Variable mediation.

PLS-PM is one of the methods from the broad family of PLS techniques. Also known as the PLS approach to Structural Equation Modeling (SEM), it can be used to model theoretical concepts through constructs and connect these constructs via a structural model to study their relationships. Originally developed by Herman Wold to analyze high-dimensional data in a low-structure environment, PLS-PM has become a widely used variance- based estimator for SEM over the past decade. Consequently, PLS-PM has been applied, both in various fields of business administration research such as strategy, marketing, operations management, human resource management, tourism, both in social science researches to measure very complex phenomena like poverty, progress, wellbeing. The objective of this book is on the one hand to emphasize the basic concepts and some recent developments of the PLS-PM method, and on the other hand to present some realworld application of the PLS-PM method in social in science fields.

PLS-PM is one of the methods from the broad family of PLS techniques. Also known as the PLS approach to Structural Equation Modeling (SEM), it can be used to model theoretical concepts through constructs and connect these constructs via a structural model to study their relationships. Originally developed by Herman Wold to analyze high-dimensional data in a low-structure environment, PLS-PM has become a widely used variance- based estimator for SEM over the past decade. Consequently, PLS-PM has been applied, both in various fields of business administration research such as strategy, marketing, operations management, human resource management, tourism, both in social science researches to measure very complex phenomena like poverty, progress, wellbeing. The objective of this book is on the one hand to emphasize the basic concepts and some recent developments of the PLS-PM method, and on the other hand to present some realworld application of the PLS-PM method in social in science fields.

Sustainability is the biggest challenge of our generation, because civilization has reached a point where natural resources are in rapid decline. It’s a complex multidimensional phenomenon, which was studied for couple decades already. Nowadays different social concepts, such as sustainability, but also quality of life, satisfaction, are difficult and complex to define. The main problem for researchers is to find appropriate tools to obtain a composite indicator able to synthesize and represent these phenomena. The work focuses on building a system of composite indicators of Sustainability through to Structural Equation Modeling, specifically with the use of Partial Least Squares-Path Modeling. In recent years many advances have been developed, in the context of these models to solve some problems related to the role that the composite indicators play within that system; in particular on the aspects linked to the high level of abstraction, when a composite indicator is manifold, lacks its own manifest variables and is described by various underlying blocks. The aim of this paper is to demonstrate how these recent developments in Partial Least Square-Path Modeling could help you to build a SDGs system and to provide a better measure of this complex social phenomenon.

Gender violence is generally conceived as a phenomenon concerning only adults. Nonetheless, it is also perpetrated within teenagers&rsquo, relationships, as many empirical studies have shown. We therefore have focused our attention on a non-probabilistic sample consisting of 400 adolescents living in Naples (Italy), to study the association between sexism and the justification of violent attitudes. Generally, sexism is recognised as a discriminatory attitude towards people, based on their biological sex. However, it is conventional to talk about sexism as a prejudice against women. The Ambivalent Sexism Inventory (ASI) for adolescents was used to evaluate the two dimensions of ambivalent sexism, i.e., hostile sexism (HS) and benevolent sexism (BS). Moreover, the questionnaire regarding attitudes towards diversity and violence (CADV) was administered to assess participants&rsquo, attitudes towards violence. A Partial Least Square&ndash, Second Order Path Model reveals that girls&rsquo, ambivalent sexism is affected more by benevolent sexism than hostile sexism. On the contrary, among boys, hostile sexism has a higher impact. Finally, benevolent sexist girls justify domestic violence more than boys do.

Partial least squares path modeling presents some inconsistencies in terms of coherence with the predictive directions specified in the inner model (i.e. the path directions), because the directions of the links in the inner model are not taken into account in the iterative algorithm. In fact, the procedure amplifies interdependence among blocks and fails to distinguish between dependent and explanatory blocks. The method proposed in this paper takes into account and respects the specified path directions, with the aim of improving the predictive ability of the model and to maintain the hypothesized theoretical inner model. To highlight its properties, the proposed method is compared to the classical PLS path modeling in terms of explained variability, predictive relevance and interpretation using artificial data through a real data application. A further development of the method allows to treat multi-dimensional blocks in composite-based path modeling.

Composite indicators (CIs), in the social sciences, are used more and more for measuring very complex phenomena as the poverty, the progress and the well-being. Using an approach Model Based in to build CIs, instead of an approach Data Driven, it is possible to consider the role (formative and reflective) of the manifest variables (MVs) and to model the relationships among the CIs. In this article, we begin introducing structural equation modeling (SEM) as a tool for building Model Based CIs. Secondly, among the several methods developed to estimate SEM, we show Partial Least Squares Path Modeling (PLS-PM), due to the key role that estimation of the latent variables (i.e. the CIs) plays in the estimation process. Moreover, we present some recent developments in PLS-PM for the treatment of non metric data, hierarchical data, longitudinal data and multi-block data. Finally, we demonstrate how these recent developments can strongly help in the building of CIs. It is easy to realize, for example, that as a consequence of considering nominal and ordinal data, the knowledge about a phenomenon synthesized by a CI is considerably extended and improved especially for operational use. In order to highlight the potentiality of the proposed approach, the construction of a CI is discussed. In particular, a CI of Social Cohesion, developed by using European Values Study data, will be described in detail.

In evaluating a policy, it is fundamental to represent its multiple dimensions and the targets it affects. Indeed, the impact of a policy generally involves a combination of socio-economic aspects that are difficult to represent. In this study, regional training policies are addressed, which are aimed at closing the huge gaps in employability and social inclusion of Italian trainees. Previous counterfactual estimates of the net impact of regional training policies reveal the need to observe and take into account the manifold aspects of trainees’ weaknesses. In fact, the target population consists of very disadvantaged individuals, who tend to experience difficult situations in the labour market. To overcome this shortfall, the present paper proposes Structural Equation Modelling (SEM) that considers the impact of trainees’ socio-economic conditions on the policy outcome itself. In particular, the ex ante human capital (HC) is estimated from the educational, social and individual backgrounds. Next, the labour and training policies augment the individual HC, affecting labour market outcomes jointly with individual job-search behaviour. All these phenomena are expressed by a wide set of manifest variables and synthesised by composite indicators calculated with Partial Least Squares SEM (SEM-PLS). The construction of the SEM is appraised and applied to the case of trainees in compulsory education.

Background Alopecia has been shown to have a significant impact on quality of life (QoL), particularly in women. However, there are no data for African populations. This study was conducted to pilot an original questionnaire and a model-based methodology to measure QoL and its determinants in a sample of South African Black women of African ancestry with alopecia. Methods Fifty participants aged 21–79 years were randomly chosen from patients presenting to dermatologists with alopecia. We used an original questionnaire consisting of 24 items grouped into those assessing the respective impacts of subjective symptoms, objective signs, and relationship issues, measured on a four-level scale. These were then combined using component-based structural equation modeling to return a QoL index (QLI) and to rank the factors contributing to this. Results On a scale ranging from 0 (high QoL) to 100 (severely decreased QoL), we found a mean QLI of 67.7. The negative impact of alopecia on QoL was higher in younger patients than older patients. The factors with the highest impact were those relating to the subjective experience of alopecia and self-image (56.3%), followed by those relevant to relationships and interaction with other people (34.8%). The presence of objective symptoms and signs such as pruritus was of minor importance (8.9%). Conclusions Although not a life-threatening condition, alopecia may seriously impair QoL, particularly by inducing anxiety and reducing self-esteem among African women. Healthcare practitioners should be mindful of this and intervene appropriately to mitigate these effects.

This chapter deals with the predictive use of PLS-PM and related component-based methods in an attempt to contribute to the recent debates on the suitability of PLS-PM for predictive purposes. Appropriate measures and evaluation criteria for the assessment of models in terms of predictive ability are more and more desirable in PLS-PM. The performance of the models can be improved by choosing the appropriate parameter estimation procedure among the different existing ones or by making developments and modifications of the latter. A recent example of this type of work is the non-symmetrical approach for component-based path modeling, which leads to a new method, called non-symmetrical composite-based path modeling. In the composites construction stage, this new method explicitly takes into account the directions of the relationships in the inner model. Results are promising for this new method, especially in terms of predictive relevance.

A common misunderstanding found in the literature is that only PLS-PM allows the estimation of SEM including formative blocks. However, if certain model specification conditions are satisfied the model is identified, and it is possible to estimate a covariance-based SEM with formative blocks. Due to the complexity of both SEM estimation methods, we studied their relative performance in the framework of the same simulation design. The simulation results showed that the effect of measurement model misspecification is much larger on the ML-SEM parameter estimates. For a model that includes a correctly specified formative block, we found that the inter-correlation level among formative MVs and the magnitude of the variance of the disturbance in the formative block have evident effects on the bias and the variability of the estimates. For high inter-correlation levels among formative MVs, PLS-PM outperforms ML-SEM, regardless of the magnitude of the disturbance variance. For a low inter-correlation level among formative MVs the performance of the two methods depends also on the magnitude of the disturbance variance. For a small disturbance variance, PLS-PM performs slightly better compared to ML-SEM. On the contrary, as the disturbance variance increases ML-SEM outperforms PLS-PM.

Many phenomena are complex and therefore difficult to measure and to evaluate. Research, in the last years, has been focusing on the development and use of a system of Composite Indicators in order to obtain a global description of a complex phenomenon and to convey a suitable synthesis of information. The existing literature offers several alternative methods for obtaining a Composite Indicators. The work focuses on building them through to Structural Equation Modeling, specifically with the use of Partial Least Squares-Path Modeling. In recent years many advances have been developed, in the context of these models to solve some problems related to the role that the Composite Indicators play within that system; in particular, the research focuses on a particular aspect linked to the high level of abstraction, when a Composite Indicator is manifold, lacks its own manifest variables and is described by various underlying blocks. In this regard we have proposed two alternative methods for analyzing and studying higher-order construct Composite Indicator, on the calculation of the estimates for the determination of endogenous block, so as to be the best estimated and represented by the blocks below.

PLS-PM presents some inconsistencies in terms of coherence with the direction of the relationships specified in the path diagram (i.e., the path directions). The PLS-PM iterative algorithm analyzes interdependence among blocks and misses to distinguish explicitly between dependent and explanatory blocks in the structural model. This inconsistency of PLS-PM is illustrated using the simple two-blocks model. For the case of more than two blocks of variables, it is necessary to have a close look at the different criteria optimized by PLS-PM to show this issue. In general, the role of latent variables in the structural model depends on the way the outer weights are calculated. A recently proposed method, called Non-Symmetrical Component-based Path Modeling, which is based on the optimization of a redundancy-related criterion in a multi-block framework, respects the direction of the relationships specified in the structural model. In order to assess the quality of the model, we provide a new goodness-of-fit index based on redundancy criterion and prediction capability. Furthermore, we provide a procedure to address the problem of multicollinearity within blocks of variables.

Background Alopecia areata (AA) is an autoimmune disease affecting about 2% of the population, which has a considerable impact on quality of life (QoL). There are no disease-specific questionnaires to assess QoL in patients suffering from AA. Objective To validate a new disease-specific questionnaire for AA, named AA-QLI, and to compare the consequent Quality of Life Index (QLI) with the commonly known Dermatology Life Quality Index (DLQI) to verify if it can provide a more comprehensive tool for patients. Methods A total of 50 patients affected by AA were administered both the AA-QLI, created by us, and the well-known DLQI. With the aim to detect suitable QLI, we propose to use two multivariate analyses: • a principal component analysis approach on the data collected with both questionnaires to compare their capability to measure the QoL; • a structural equation modelling on our AA-QLI to identify which category of symptoms mostly affects the QoL. Results The scores of both the questionnaires are quite close, except for a few cases. Statistical analysis shows a higher specificity of the AA-QLI for evaluating QoL. Among the three areas in which AA-QLI is divided, ‘Relationship’ has a major impact on the QLI, followed by ‘Subjective symptoms’; ‘Objective signs’ has a lower weight on the QLI. Conclusion AA-QLI is a good instrument to evaluate the real impact of AA on QoL. It can be helpful both for the physician and for the patient.

Objective: Patient satisfaction can be measured by criteria inspired by currently available marketing research methods. Among the latter, qualitative methods can be performed on limited population samples and be based on latent variables, i.e., variables that are not directly observed but deducted from mathematical analysis (i.e., quality of life). Qualitative research methods include the partial least squares (PLS) path modelling aimed at defining optimal linear relations among latent variables in order to assemble the best set of predictions. Methods: In the February-May 2007 period, 73 patients (41 males and 32 females) consecutively discharged from the Division of Thoracic Surgery of the National Cancer Institute at Naples underwent an adaptation of the PLS path modelling by accepting to file an itemized questionnaire on 29 different aspects of hospitalization. The sampled population represented about 32% of all patients operated by a single surgeon and about 21% of all patients admitted to a 12-bed thoracic surgical ward in 2007. Five categories of performance were identified, i.e., quality of the facilities, quality and clarity of provided Information, quality of relationship with surgeons and nurses, quality of the received care, overall patient satisfaction. Results: During the analyzed period, the overall patient satisfaction reached 91% (±15). The mean scores were 62% (±33), 80% (±28), 84% (±21), 81% (±19), 88% (±15) for ward facilities, information provided, relationship with personnel, clinical services, and, perceived quality, respectively. In addition, overall perceived quality, relationship with personnel and the provision of information were the variables with greatest positive impact on patient satisfaction. Conversely, waiting times for radiological procedures, quality of meals and duration of visiting hours adversely affected the level of satisfaction. Conclusions: In the setting of a thorough audit of current clinical practice, PLS path modelling may represent another valuable tool to measure quality in the setting of managed health care since it allows for the identification of areas where the service can be improved.

Advances in computer technology have made large data ubiquitous and have determined the need to handle these data accordingly. In particular they need to be aggregated using some functions, but this process can lead to a loss of information. Beanplot series, in this context, can represent a solution in terms of special symbolic data: in fact the parameters of the density models based on a mixture of distributions represent the original data accordingly and contribute to solving the problem of data storage. In this work we propose an approach to beanplot data analysis by PCA on the parameters of the models. The aim is to build a synthesis of multiple beanplot time series as indicators which can have relevant applications in Finance, in Risk Management and in other disciplines.

We propose in this work a new approach for modelling, forecasting and clustering beanplot financial time series. The beanplot time series like the histogram time series or the interval time series can be very useful to model the intra-period variability of the series. These types of new time series can be very useful with High Frequency financial data, data collected with often irregularly spaced observations

Real world data analysis is often affected by different types of errors as: measurement errors, computation errors, imprecision related to the method adopted for estimating the data. The uncertainty in the data, which is strictly connected to the above errors, may be treated by considering, rather than a single value for each data, the interval of values in which it may fall: the interval data. Statistical units described by interval data can be assumed as a special case of Symbolic Object (SO). In Symbolic Data Analysis (SDA), these data are represented as boxes. Accordingly, purpose of the present work is the extension of Principal Component analysis (PCA) to obtain a visualisation of such boxes, on a lower dimensional space pointing out of the relationships among the variables, the units, and between both of them. The aim is to use, when possible, the interval algebra instruments to adapt the mathematical models, on the basis of the classical PCA, to the case in which an interval data matrix is given. The proposed method has been tested on a real data set and the numerical results, which are in agreement with the theory, are reported.

A presentation of the Partial Least Squares approach to Structural Equation Modeling (or PLS Path Modeling) is given together with a discussion of its extensions. This approach is compared with the estimation of Structural Equation Modeling by means of maximum likelihood (SEM-ML). Notwithstanding, this approach still shows some weaknesses. In this respect, some new improvements are proposed. Furthermore, PLS path modeling can be used for analyzing multiple tables so as to be related to more classical data analysis methods used in this field. Finally, a complete treatment of a real example is shown through the available software.

The present paper deals with the study of continuous interval data by means of suitable Principal Component Analyses (PCA). Statistical units described by interval data can be assumed as special cases of Symbolic Objects (SO) (Diday, 1987). In Symbolic Data Analysis (SDA), these data are represented as hypercubes. In the present paper, we propose some extensions of the PCA with the aim of representing, in a space of reduced dimensions, images of such hypercubes, pointing out differences and similarities according to their structural features.

The aim of this paper is to give an overview of the methodological contribution given by Italian researchers in introducing a priori information into multidimensional data analysis techniques, paying special attention to categorical variables. The basic method is Non-Symmetrical Correspondence Analysis, which enables the analysis of a contingency table when the behaviour of one variable is supposed to be dependent on the other cross-classified variable. As usual correspondence analysis decomposes an association index (Pearson's Φ2), in a principal component sense, the proposed method is based on a decomposition of a predictability index (Goodman and Kruskal's τb). Non-symmetrical correspondence analysis has been extended to more than one dependent/explanatory variable(s), by means of proper flattening procedures, i.e. by the use of multiple tables, and the decomposition of Gray and Williams' multiple and partial τb's. In doing so multiple and partial versions have been proposed. A forward selection procedure for choosing the variables with higher predictive power is presented. After a brief review of non-symmetrical correspondence analysis confirmatory approach, the problem of validating results in terms of analytical stability and replication stability is faced by means of influence functions and resampling techniques. Copyright © 1999 John Wiley & Sons, Ltd.

The article is about the problem of the treatment of qualitative variables in the Structural Equation Models with attention to the case of Partial Least Squares Path Modeling. In literature there are some proposals based on the application of known statistical tecniques to quantify the qualitative variables. Starting from these works we propose an external quantification for only qualitative variables by the Alternating Least Squares, obtaining the optimal quantification (vectors of optimal scaling), a future objective to develop an algorithm that computes simultaneously the vectors of optimal scaling and the optimal regression coefficients, between the variables. We will present an application of our method to a real dataset.

Aim of this paper is to underline the main contributions in the context of Factorial Conjoint Analysis. The integration of Conjoint Analysis with the exploratory tools of Multidimensional Data Analysis is the basis of different research strategies, proposed by the authors, combining the common estimation method with its geometrical representation. Here we present a systematic and unitary review of some of these methodologies by taking into account their contribution to several open ended problems.

To regress one or more quantitative response variables on a set of predictor variables of different nature, it is necessary to transform non-quantitative predictors in such a way that they can be analyzed together with the other variables measured on an interval scale. Here, a new proposal to cope with this issue in Partial Least Squares (PLS) regression framework is presented. The approach consists in quantifying each non-quantitative predictor according to Hayashi’s first quantification method, using the dependent variable (or, in the multivariate case, a linear combination of the response variables) as an external criterion. The PLS weight of each variable which is quantified according to the proposed approach is coherent with the statistical relationship between its original non-quantitative variable and the response variable(s) as expressed in terms of Pearson’s correlation ratio. Firstly, the case where one variable depends on a set of both categorical and quantitative variables is discussed; then, a modified PLS algorithm, called PLS-CAP, is proposed to obtain the quantifications of the categorical predictors in the multi-response case. An application on real data is presented in order to enhance the properties of the quantification approach based on the PLS-CAP with respect to the classical approach based on the dummy code of the categorical variables.

Technical education and training is now interested by a reform process, trying to integrate the different paths that a student can follow to get a technical degree: the professional schools and training courses. Another challenge is that of integrating in the new system the lessons coming from best innovative practices in the field of the fight to early school living. For this reason the level of application of subsidiarity principle can help to explain differences in the job and social outcome for students. The paper analyses the methodological aspects to be afforded to design a research on the level and effects of subsidiarity in the technical educational system.

Data analysis is often affected by different types of errors as: measurement errors, computation errors, imprecision related to the method adopted for estimating the data. The methods which have been proposed for treating errors in the data, may also be applied to different kinds of data that in real life are of interval type. The uncertainty in the data, which is strictly connected to the above errors, may be treated by considering, rather than a single value for each data, the interval of values in which it may fall: the interval data. The purpose of the present paper is to introduce methods for analyzing the interdependence and dependence among interval-valued variables. Statistical units described by interval-valued variables can be assumed as a special case of Symbolic Object (SO). In Symbolic Data Analysis (SDA), these data are represented as boxes. Accordingly, the purpose of the present work is the extension of the Principal Component Analysis to obtain a visualization of such boxes, on a lower dimensional space. Furthermore, a new method for fitting an interval simple linear regression equation is developed. With difference to other approaches proposed in the literature that work on scalar recoding of the intervals using classical tools of analysis, we make extensively use of the interval algebra tools combined with some optimization techniques.

Many real world phenomena are better represented by non-precise data rather than by single-valued data. In fact, non-precise data represent two sources of variability: the natural phenomena variability and the variability or uncertainty induced by measurement errors or determined by specific experimental conditions. The latter variability source is named imprecision. When there are information about the imprecision distribution the fuzzy data coding is used to represent the imprecision. However, in many cases imprecise data are natively defined only by the minimum and maximum values. Technical specifications, stock-market daily prices, survey data are some examples of such kind of data. In these cases, interval data represent a good data coding to take into account the imprecision. This paper aims at describing multiple imprecise data by means of a suitable Principal Component Analysis that is based on specific interval data coding taking into account both sources of variation.

Classification, within a PLS regression framework, is classically meant in the sense of the SIMCA methodology, i.e. as the assignment of statistical units to a-priori defined classes. As a matter of fact, PLS components are built with the double objective of describing the set of explanatory variables while predicting the set of response variables. Taking into account this objective, a classification algorithm is developed that allows to build typologies of statistical units whose different local PLS models have an intrinsic explanatory power higher than the initial global PLS model. The typology induced by the algorithm may undergo a non parametric validation procedure based on bootstrap. Finally, the definition of a compromise model is investigated.

In this paper, we propose a new approach to Principal Component Analysis, for interval-valued data. On the basis of the interval arithmetic we show that any continuous interval can be expressed in terms of a midpoint (location) and of a radius (variation). Moving from this result, we propose a well suited factorial analysis, which exploits this characteristic of interval data. Both the location and variation information are represented on maps.

In the framework of Factorial Data Analysis on Symbolic Objects (SO’s), we propose new kinds of SO’s visualizations on factorial planes alternative to rectangular shapes (Minimum Covering Area Rectangle MCAR). MCAR were mainly proposed in PCA on SO’s to represent in reduced bi-dimensional subspace symbolic data described by interval variables and represented by hypercubes. The new representations of SO’s are based on the convex hulls (CH) of the projected hypercube vertices. In particular, we propose a compromise between the MCAR and CH visualizations by means of particular closed shapes, that contains the CH and it is contained by MCAR. The main advantage of this kind of SO representation is its interpretation and lower over-fitting than MCAR. Furthermore, some indexes of quality of representation and over-fitting are developed.

Data visualization plays an outstanding role in descriptive statistics. Human eye has a strong ability in detecting regularities in the data and, in many cases, the analysis of graphed data can drive the analyst towards the choice of the most suitable analytical tools. Symbolic Data Analysis (SDA) aims at defining statistical methods to analyze complex data structures no longer based on the classical tabular model. In the SDA context, this paper proposes a thinking on the Symbolic Data visualization and, at the same time, new methods capable of representing complex data and preserving the statistical interpretation.

International audience; The major focus of the book is on using the methods suitable for an on-line and off-line process control both in the univariate and multivariate case. The authors do not only concentrate on the standard situation when the errors accompanying the observed process are normally distributed, but also describe in detail the more general situations that call for the use of the robust and non-parametric approaches. Within these approaches, the use of recent methods of the multivariate analysis in the total quality control is enhanced with particular reference to the customer satisfaction area, the monitoring of interval data and the comparison of patterns generated from multioccasion observations. The authors cover both pratical computational aspects of the problem and the necessary mathematical background, taking into account requirements of total quality control.

In the present paper we initially intend to show the fundamental ideas behind the methodological achievements of Non Symmetrical Data Analysis from a geometrical point of view. We then focus on some of the most recent extensions by stressing and giving insights on their application aspects. Finally, we outline what seem to be the most promising directions of further research in this field.