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Archetypal analysis is an unsupervised machine learning method that summarizes data using a convex polytope. In its original formulation, for fixed k, the method finds a convex polytope with k vertices, called archetype points, such that the polytope is contained in the convex hull of the data and the mean squared Euclidean distance between the data and the polytope is minimal. In the present work, we consider an alternative formulation of archetypal analysis based on the Wasserstein metric, which we call Wasserstein archetypal analysis (WAA). In one dimension, there exists a unique solution of WAA and, in two dimensions, we prove the existence of a solution, as long as the data distribution is absolutely continuous with respect to the Lebesgue measure. We discuss obstacles to extending our result to higher dimensions and general data distributions. We then introduce an appropriate regularization of the problem, via a Rényi entropy, which allows us to obtain the existence of solutions of the regularized problem for general data distributions, in arbitrary dimensions. We prove a consistency result for the regularized problem, ensuring that if the data are iid samples from a probability measure, then as the number of samples is increased, a subsequence of the archetype points converges to the archetype points for the limiting data distribution, almost surely. Finally, we develop and implement a gradient-based computational approach for the two-dimensional problem, based on the semi-discrete formulation of the Wasserstein metric. Detailed numerical experiments are provided to support our theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract The knowledge of physical activity (PA) recommended for pregnant women and practical application of it has positive impact on the outcome. Nevertheless, it is estimated that in high-income countries over 40% of pregnant women are insufficiently physically active. One of the reasons is insufficient knowledge pregnant women have about allowed effort during pregnancy and both recommended and not recommended physical activities. Description of knowledge about physical activity the women have and distinguishing patterns of their knowledge is becoming an increasingly important issue. A common approach to handle survey data that reflect knowledge involves clustering methods or Principal Component Analysis (PCA). Nevertheless, new procedures of data analysis are still being sought. Using survey data collected by the Institute of Mother and Child Archetypal analysis has been applied to detect levels of knowledge reflected by answers given in a questionnaire and to derive patterns of knowledge contained in the data. Next, PHATE (Potential of Heat-diffusion for Affinity-based Trajectory Embedding) algorithm has been used to visualize the results and to get a deeper insight into the data structure. The results were compared with picture derived from PCA. Three archetypes representing three patterns of knowledge have been distinguished and described. The presentation of complex data in a low dimension was obtained with help of PHATE. The formations revealed by PHATE have been successfully described in terms of knowledge levels reflected by the survey. Finally, comparison of PHATE with PCA has been shown. Archetype analysis combined with PHATE provides novel opportunities in examining nonlinear structure of survey data and allows for visualization that captures complex relations in the data. PHATE has made it possible to distinguish sets of objects that have common features but were captured neither by Archetypal analysis nor PCA. Moreover, for our data, PHATE provides an image of data structure which is more detailed than interpretation of PCA.

The knowledge of physical activity (PA) recommended for pregnant women and practical application of it has positive impact on the outcome. Nevertheless, it is estimated that in high-income countries over 40% of pregnant women are insufficiently physically active. One of the reasons is insufficient knowledge pregnant women have about allowed effort during pregnancy and both recommended and not recommended physical activities. Description of knowledge about physical activity the women have and distinguishing patterns of their knowledge is becoming an increasingly important issue. A common approach to handle survey data that reflect knowledge involves clustering methods or Principal Component Analysis (PCA). Nevertheless, new procedures of data analysis are still being sought. Using survey data collected by the Institute of Mother and Child Archetypal analysis has been applied to detect levels of knowledge reflected by answers given in a questionnaire and to derive patterns of knowledge contained in the data. Next, PHATE (Potential of Heat-diffusion for Affinity-based Trajectory Embedding) algorithm has been used to visualize the results and to get a deeper insight into the data structure. The results were compared with picture derived from PCA. Three archetypes representing three patterns of knowledge have been distinguished and described. The presentation of complex data in a low dimension was obtained with help of PHATE. The formations revealed by PHATE have been successfully described in terms of knowledge levels reflected by the survey. Finally, comparison of PHATE with PCA has been shown. Archetype analysis combined with PHATE provides novel opportunities in examining nonlinear structure of survey data and allows for visualization that captures complex relations in the data. PHATE has made it possible to distinguish sets of objects that have common features but were captured neither by Archetypal analysis nor PCA. Moreover, for our data, PHATE provides an image of data structure which is more detailed than interpretation of PCA. [ABSTRACT FROM AUTHOR]

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Purpose of Review: In this review, we will describe current methods for visual field testing in neuro-ophthalmic clinical practice and research, develop terminology that accurately describes patterns of field deficits, and discuss recent advances such as augmented or virtual reality-based perimetry and the use of artificial intelligence in visual field interpretation. Recent Findings: New testing strategies that reduce testing times, improve patient comfort, and increase sensitivity for detecting small central or paracentral scotomas have been developed for static automated perimetry. Various forms of machine learning-based tools such as archetypal analysis are being tested to quantitatively depict and monitor visual field abnormalities in optic neuropathies. Studies show that the combined use of optical coherence tomography and standard automated perimetry to determine the structure-function relationship improves clinical care in neuro-ophthalmic disorders. Summary: Visual field assessment must be performed in all patients with neuro-ophthalmic disorders affecting the afferent visual pathway. Quantitative visual field analysis using standard automated perimetry is critical in initial diagnosis, monitoring disease progression, and guidance of therapeutic plans. Visual field defects can adversely impact activities of daily living such as reading, navigation, and driving and thus impact quality of life. Visual field testing can direct appropriate occupational low vision rehabilitation in affected individuals. [ABSTRACT FROM AUTHOR]

Questions: The classification of plant communities is a well‐established practice in ecology. However, the factors that determine the distribution of common species and the extent of their dominance and overlap are still being debated. Large‐scale studies based on field data are of great interest in the face of biodiversity changes and climate change impacts. This research was designed to answer the following two questions: What are the dominant plant communities in the Patagonian steppes and how do they relate to environmental features, as measured by latitude, longitude, altitude, mean annual precipitation and mean temperature? What have been the recent changes in plant communities in terms of expansion and contraction of different types of communities? Location: Patagonian steppes (South America). Methods: We used a large database of species‐by‐species vegetation cover from 426 monitoring plots in the South American Patagonian steppes, surveyed between 2007 and 2019, with two different assessment dates at least 5 years apart. We applied archetypal analysis to identify different vegetation compositions at a regional scale (called floristic archetypes) and to track their changes over time. In addition, we analyzed the relationship between floristic archetypes and spatial and meteorological variables to assess the association between floristic composition and the environmental context. Results: Seven floristic archetypes were identified in the Patagonian steppes. The dominant and most widespread floristic archetype showed an expanding pattern in floristic trajectories and was positively associated with mean annual temperature. This floristic archetype was characterized by both drought‐ and grazing‐tolerant species. Two floristic archetypes located at the longitudinal extremes showed decreasing relative participation in the vegetation configurations, and the archetype located towards the west showed a positive relationship with annual precipitation, suggesting a threatened scenario in the face of drier conditions. Southern floristic archetypes either showed a slight decrease or remained stable. Conclusions: Patagonian steppes are dominated by both drought‐ and grazing‐tolerant species communities and their spatial distribution is expanding across different biomes, whereas the more forage‐preferred species were associated with a decreasing floristic archetype. A projected drier and hotter climate scenario may potentiate this pattern. The floristic archetypes framework has potential as a monitoring tool for tracking changes in vegetation composition at a mesoscale and for identifying hotspots of vulnerable vegetation in the face of environmental changes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algorithm based on archetypal analysis for blind hyperspectral unmixing, assuming linear mixing of endmembers. Archetypal analysis is a natural formulation for this task. This method does not require the presence of pure pixels (i.e., pixels containing a single material) but instead represents endmembers as convex combinations of a few pixels present in the original hyperspectral image. Our approach leverages an entropic gradient descent strategy, which (i) provides better solutions for hyperspectral unmixing than traditional archetypal analysis algorithms, and (ii) leads to efficient GPU implementations. Since running a single instance of our algorithm is fast, we also propose an ensembling mechanism along with an appropriate model selection procedure that make our method robust to hyper-parameter choices while keeping the computational complexity reasonable. By using six standard real datasets, we show that our approach outperforms state-of-the-art matrix factorization and recent deep learning methods. We also provide an open-source PyTorch implementation: https://github.com/inria-thoth/EDAA. [ABSTRACT FROM AUTHOR]

Goal: The purpose of this study was to identify clinically relevant patterns of glaucomatous vision loss through convex representation to predict glaucoma several years prior to disease onset. Methods: We developed a deep archetypal analysis to identify patterns of glaucomatous vision loss, and then projected visual fields over the identified patterns. Projections provided a representation that was more accurate in detecting glaucomatous vision loss, thus, more appropriate for recognizing preclinical signs of glaucoma prior to disease development. To overcome the class imbalance in prediction, we implemented a class-balanced bagging with neural networks. Results: Using original visual field as features of the class-balanced bagging classification provided an area under the receiver-operating characteristic curve (AUC) of 0.55 for predicting glaucoma approximately four years prior to disease development. Using convex representation of the visual fields as input features provided an AUC of 0.61 while using deep convex representation as input features improved the AUC to 0.71. Relevance vector machine (RVM) achieved an AUC of 0.64. Conclusion: Deep archetypal analysis representation of visual functional features with balanced bagging classification could serve as an automated tool for predicting glaucoma. Significance: Glaucoma is the second leading cause of worldwide blindness. Most people with glaucoma have no early symptoms or pain, delaying diagnosis in many patients until they reach late irreversible vision loss stages. In fact, about 50% of people with glaucoma are unaware they have the disease. Deep archetypal analysis models may impact clinical practice in effectively identifying at-risk glaucoma patients well prior to disease development.

Archetypal analysis (AA) is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of AA in practice is the inherent computational complexity of the existing algorithms. In this paper, we provide a novel approximation approach to partially address this issue. Utilizing probabilistic ideas from high-dimensional geometry, we introduce two preprocessing techniques to reduce the dimension and representation cardinality of the data, respectively. We prove that provided data are approximately embedded in a low-dimensional linear subspace and the convex hull of the corresponding representations is well approximated by a polytope with a few vertices, our method can effectively reduce the scaling of AA. Moreover, the solution of the reduced problem is near-optimal in terms of prediction errors. Our approach can be combined with other acceleration techniques to further mitigate the intrinsic complexity of AA. We demonstrate the usefulness of our results by applying our method to summarize several moderately large-scale datasets. [ABSTRACT FROM AUTHOR]

The behavioral approach to leadership, which has introduced leadership styles, has been of great importance to the leadership field. Despite its importance, scholars have recently argued and demonstrated that these styles have various conceptual, methodological, and empirical limitations that could hamper further development of the leadership field. Consequently, they have called for alternative approaches to study leadership. We argue that taking a configurational or person-oriented approach to leadership behavior, which focuses on ideal-type configurations of leadership behaviors to identify leadership archetypes, offers such an alternative. We demonstrate the potential of such an approach via the use of archetypal analysis, for a dataset of 46 behaviors across 6 leadership styles, including more than 150,000 respondents. Our results offer a clear indication for the existence of archetypes of leadership. We also suggest how the resulting archetypes can get a meaningful interpretation, and discuss implications for future research. [ABSTRACT FROM AUTHOR]

The high cosine similarity between some single-base substitution mutational signatures and their characteristic flat profiles could suggest the presence of overfitting and mathematical artefacts. The newest version (v3.3) of the signature database available in the Catalogue Of Somatic Mutations In Cancer (COSMIC) provides a collection of 79 mutational signatures, which has more than doubled with respect to previous version (30 profiles available in COSMIC signatures v2), making more critical the associations between signatures and specific mutagenic processes. This study both provides a systematic assessment of the de novo extraction task through simulation scenarios based on the latest version of the COSMIC signatures and highlights, through a novel approach using archetypal analysis, which COSMIC signatures are redundant and more likely to be considered as mathematical artefacts. 29 archetypes were able to reconstruct the profile of all the COSMIC signatures with cosine similarity > 0.8. Interestingly, these archetypes tend to group similar original signatures sharing either the same aetiology or similar biological processes. We believe that these findings will be useful to encourage the development of new de novo extraction methods avoiding the redundancy of information among the signatures while preserving the biological interpretation. [ABSTRACT FROM AUTHOR]

The high cosine similarity between some single-base substitution mutational signatures and their characteristic flat profiles could suggest the presence of overfitting and mathematical artefacts. The newest version (v3.3) of the signature database available in the Catalogue Of Somatic Mutations In Cancer (COSMIC) provides a collection of 79 mutational signatures, which has more than doubled with respect to previous version (30 profiles available in COSMIC signatures v2), making more critical the associations between signatures and specific mutagenic processes. This study both provides a systematic assessment of the de novo extraction task through simulation scenarios based on the latest version of the COSMIC signatures and highlights, through a novel approach using archetypal analysis, which COSMIC signatures are redundant and more likely to be considered as mathematical artefacts. 29 archetypes were able to reconstruct the profile of all the COSMIC signatures with cosine similarity >0.8. Interestingly, these archetypes tend to group similar original signatures sharing either the same aetiology or similar biological processes. We believe that these findings will be useful to encourage the development of new de novo extraction methods avoiding the redundancy of information among the signatures while preserving the biological interpretation.

The behavioral approach to leadership, which has introduced leadership styles, has been of great importance to the leadership field. Despite its importance, scholars have recently argued and demonstrated that these styles have various conceptual, methodological, and empirical limitations that could hamper further development of the leadership field. Consequently, they have called for alternative approaches to study leadership. We argue that taking a configurational or person-oriented approach to leadership behavior, which focuses on ideal-type configurations of leadership behaviors to identify leadership archetypes, offers such an alternative. We demonstrate the potential of such an approach via the use of archetypal analysis, for a dataset of 46 behaviors across 6 leadership styles, including more than 150,000 respondents. Our results offer a clear indication for the existence of archetypes of leadership. We also suggest how the resulting archetypes can get a meaningful interpretation, and discuss implications for future research.

Metastable microstates in electro- and magnetoencephalographic (EEG and MEG) measurements are usually determined using modified k-means accounting for polarity invariant states. However, hard state assignment approaches assume that the brain traverses microstates in a discrete rather than continuous fashion. We present multimodal, multisubject directional archetypal analysis as a scale and polarity invariant extension to archetypal analysis using a loss function based on the Watson distribution. With this method, EEG/MEG microstates are modeled using subject- and modality-specific archetypes that are representative, distinct topographicmaps between which the brain continuously traverses. Archetypes are specified as convex combinations of unit norm input data based on a shared generator matrix, thus assuming that the timing of neural responses to stimuli is consistent across subjects and modalities. The input data is reconstructed as convex combinations of archetypes using a subject-and-modality-specific continuous archetypal mixing matrix. We showcase the model on synthetic data and an openly available face perception event-related potential data set with concurrently recorded EEG and MEG. In synthetic and unimodal experiments, we compare our model to conventional Euclidean multisubject archetypal analysis. We also contrast our model to a directional clustering model with discrete state assignments to highlight the advantages of modeling state trajectories rather than hard assignments. We find that our approach successfully models scale and polarity invariant data, such as microstates, accounting for intersubject and intermodal variability. The model is readily extendable to other modalities ensuring component correspondence while elucidating spatiotemporal signal variability. [ABSTRACT FROM AUTHOR]

Metastable microstates in electro- and magnetoencephalographic (EEG and MEG) measurements are usually determined using modified k-means accounting for polarity invariant states. However, hard state assignment approaches assume that the brain traverses microstates in a discrete rather than continuous fashion. We present multimodal, multisubject directional archetypal analysis as a scale and polarity invariant extension to archetypal analysis using a loss function based on the Watson distribution. With this method, EEG/MEG microstates are modeled using subject- and modality-specific archetypes that are representative, distinct topographic maps between which the brain continuously traverses. Archetypes are specified as convex combinations of unit norm input data based on a shared generator matrix, thus assuming that the timing of neural responses to stimuli is consistent across subjects and modalities. The input data is reconstructed as convex combinations of archetypes using a subject- and modality-specific continuous archetypal mixing matrix. We showcase the model on synthetic data and an openly available face perception event-related potential data set with concurrently recorded EEG and MEG. In synthetic and unimodal experiments, we compare our model to conventional Euclidean multisubject archetypal analysis. We also contrast our model to a directional clustering model with discrete state assignments to highlight the advantages of modeling state trajectories rather than hard assignments. We find that our approach successfully models scale and polarity invariant data, such as microstates, accounting for intersubject and intermodal variability. The model is readily extendable to other modalities ensuring component correspondence while elucidating spatiotemporal signal variability.

Accessible risk predictors are crucial for improving the early detection and prognosis of breast cancer. Blood samples are widely available and contain proteins that provide important information about human health and disease, however, little is still known about the contribution of circulating proteins to breast cancer risk prediction. We profiled EDTA plasma samples collected before diagnosis from the Swedish KARMA breast cancer cohort to evaluate circulating proteins as molecular predictors. A data-driven analysis strategy was applied to the molecular phenotypes built on 700 circulating proteins to identify and annotate clusters of women. The unsupervised analysis of 183 future breast cancer cases and 366 age-matched controls revealed five stable clusters with distinct proteomic plasma profiles. Among these women, those in the most stable cluster (N = 19; mean Jaccard index: 0.70 ± 0.29) were significantly more likely to have used menopausal hormonal therapy (MHT), get a breast cancer diagnosis, and were older compared to the remaining clusters. The circulating proteins associated with this cluster (FDR < 0.001) represented physiological processes related to cell junctions (F11R, CLDN15, ITGAL), DNA repair (RBBP8), cell replication (TJP3), and included proteins found in female reproductive tissue (PTCH1, ZP4). Using a data-driven approach on plasma proteomics data revealed the potential long-lasting molecular effects of menopausal hormonal therapy (MHT) on the circulating proteome, even after women had ended their treatment. This provides valuable insights concerning proteomics efforts to identify molecular markers for breast cancer risk prediction.

We summarize the results of an intensive simulation study carried out to compare the performance of three approaches to archetypal analysis regarded as a fuzzy clustering tool: the original approach, namely that of Cutler and Breiman (Technometrics 36(4):338–347, 1994), the Ding et al. (IEEE Trans Pattern Anal Mach Intell 32(1):45–55, 2010) proposal, and the factorized fuzzy c-means algorithm. The artificial data we use in our experiment are generated from polytopes in low-dimensional R n spaces 2 ≤ n ≤ 7 , and comprise a diversity of cluster contexts. The simulation results show that the original proposal is generally a more accurate method to uncover the cluster structure hidden in the data and to reproduce the data themselves. However, this supremacy, if any, is not clear for the data generated from real life problems, and devoted to unsupervised clustering problems. [ABSTRACT FROM AUTHOR]

Data-driven anomaly detection is one of the central issues for the implementation of predictive maintenance in cyber–physical systems (CPS). The increasing nonstationary dynamics in CPS lead to complex shapes of collected process data, e.g., convex and nonconvex. Algorithms with the ability of handling nonconvex data are desired for anomaly detection tasks in CPS. Archetypal analysis selects extreme points (archetypes) to represent a dataset—mainly to improve run times, e.g., for anomaly detection. The classic archetypal analysis uses convex combinations of archetypes to represent a set of observations (data points). This leads to the performance depression of the classic archetypal analysis methods for anomaly detection tasks on nonconvex datasets. Such nonconvex sets are typical for CPS. In this article, the anomaly detection tasks are considered as one-class classification problem due to the lack of abnormal samples. A novel nonconvex archetypal one-class classification algorithm is proposed to address the challenge of nonconvex data, which combines the random projection and the AdaBoost algorithm. The major advantages of this method are its high efficiency, flexibility, and its ability to handle both convex and nonconvex datasets, i.e., it can be applied to CPS analysis tasks. The usefulness of the presented approach is evaluated for fault diagnosis tasks in CPS. [ABSTRACT FROM AUTHOR]

Goal: The purpose of this study was to identify clinically relevant patterns of glaucomatous vision loss through convex representation to predict glaucoma several years prior to disease onset. Methods: We developed a deep archetypal analysis to identify patterns of glaucomatous vision loss, and then projected visual fields over the identified patterns. Projections provided a representation that was more accurate in detecting glaucomatous vision loss, thus, more appropriate for recognizing preclinical signs of glaucoma prior to disease development. To overcome the class imbalance in prediction, we implemented a class-balanced bagging with neural networks. Results: Using original visual field as features of the class-balanced bagging classification provided an area under the receiver-operating characteristic curve (AUC) of 0.55 for predicting glaucoma approximately four years prior to disease development. Using convex representation of the visual fields as input features provided an AUC of 0.61 while using deep convex representation as input features improved the AUC to 0.71. Relevance vector machine (RVM) achieved an AUC of 0.64. Conclusion: Deep archetypal analysis representation of visual functional features with balanced bagging classification could serve as an automated tool for predicting glaucoma. Significance: Glaucoma is the second leading cause of worldwide blindness. Most people with glaucoma have no early symptoms or pain, delaying diagnosis in many patients until they reach late irreversible vision loss stages. In fact, about 50% of people with glaucoma are unaware they have the disease. Deep archetypal analysis models may impact clinical practice in effectively identifying at-risk glaucoma patients well prior to disease development.

Archetypes represent extreme manifestations of a population with respect to specific characteristic traits or features. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. As mixing of archetypes is performed directly on the input data, linear Archetypal Analysis requires additivity of the input, which is a strong assumption unlikely to hold e.g. in case of image data. To address this problem, we propose learning an appropriate latent feature space while simultaneously identifying suitable archetypes. We thus introduce a generative formulation of the linear archetype model, parameterized by neural networks. By introducing the distance-dependent archetype loss, the linear archetype model can be integrated into the latent space of a deep variational information bottleneck and an optimal representation, together with the archetypes, can be learned end-to-end. Moreover, the information bottleneck framework allows for a natural incorporation of arbitrarily complex side information during training. As a consequence, learned archetypes become easily interpretable as they derive their meaning directly from the included side information. Applicability of the proposed method is demonstrated by exploring archetypes of female facial expressions while using multi-rater based emotion scores of these expressions as side information. A second application illustrates the exploration of the chemical space of small organic molecules. By using different kinds of side information we demonstrate how identified archetypes, along with their interpretation, largely depend on the side information provided. [ABSTRACT FROM AUTHOR]

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix. The templates are chosen so that as far as possible only the initial data set can be represented this way. However, the templates are not required to be nonnegative nor convex combinations of the original data. [ABSTRACT FROM AUTHOR]

Context The rapid evolvement of software development effort estimation models created the need for empirical evaluation of their quality. The empirical evaluation is based either on hypothesis tests with respect to a single criterion or on aggregating methods for multiple criteria. However, a model can be considered as a multidimensional entity performing differently on alternative datasets and its performance can be divergent when expressed by alternative criteria. Objective: In this study, we explore this multidimensional nature of models by considering them as points in two different spaces (domain and criteria spaces). Method: Introducing an alternative approach for data‐driven benchmarking, a new framework based on archetypal analysis is proposed for evaluation purposes of multiple models. Results: The benefits of the framework are illustrated through a large‐scale experimental setup on a set of 93 effort estimation models, trained and tested on 10 datasets under 8 criteria providing answers to critical research questions. Conclusion: The results indicate that a small minority of reference models is enough to define the performance of the bulk of all models. The framework focuses on models that have behavior close to archetypes and especially those that are close to a "best" archetype. [ABSTRACT FROM AUTHOR]

Software teams are often asked to deliver new features within strict deadlines leading developers to deliberately or inadvertently serve "not quite right code" compromising software quality and maintainability. This non-ideal state of software is efficiently captured by the Technical Debt (TD) metaphor, which reflects the additional effort that has to be spent to maintain software. Although several tools are available for assessing TD, each tool essentially checks software against a particular ruleset. The use of different rulesets can often be beneficial as it leads to the identification of a wider set of problems; however, for the common usage scenario where developers or researchers rely on a single tool, diverse estimates of TD and the identification of different mitigation actions limits the credibility and applicability of the findings. The objective of this study is two-fold: First, we evaluate the degree of agreement among leading TD assessment tools. Second, we propose a framework to capture the diversity of the examined tools with the aim of identifying few "reference assessments" (or class/file profiles) representing characteristic cases of classes/files with respect to their level of TD. By extracting sets of classes/files exhibiting similarity to a selected profile (e.g., that of high TD levels in all employed tools) we establish a basis that can be used either for prioritization of maintenance activities or for training more sophisticated TD identification techniques. The proposed framework is illustrated through a case study on fifty (50) open source projects and two programming languages (Java and JavaScript) employing three leading TD tools. [ABSTRACT FROM AUTHOR]

Archetypal criticism is one of the approaches of contemporary literary criticism that explores and explains the influence of myths and archetypes as well as their role in literature. Individualization is one of the most prominent archetypes of Jung's archetypal theory. In the story of Khorshid-Va- Mahpareh, Khorshid, as the hero of the story, encounters a lot of hardships and sequels to reach his beloved, including magical Arghavan, crafy Ainbalay, cannibal Negros, rival Marzban, stormy sea, etc. In addition to the archetypal phenomena in the collection such as magic, witches, supernatural actions, and archetypal symbols, archetypes such as journey, individuality, dream, mother, hero, and so on have been used to investigate and analyze individualization from the perspective of Jung's archetypal theory. Accordingly, Khorshid, the protagonist of the story, reached out to his beloved after going through a heroic journey, overcoming shadows and negative anima, and achieved self-individuality through the help of the Old Wise Man and the essence of love, and then had a rebirthed. [ABSTRACT FROM AUTHOR]

One of the goals of macroeconomic analysis is to rank and segment enterprises described by many financial indicators. The segmentation can be used for investment strategies or risk evaluation. The aim of this research was to distinguish groups of similar objects and visualize the results in a low dimensional space. In order to obtain clusters of similar objects, the authors applied a DEA BCC model and archetypal analysis for a set of companies described by financial indicators and listed on the Warsaw Stock Exchange. The authors showed that both methods give consistent results. To get a better insight into the data structure as well as a visualization of the similarities between objects, the authors used a new approach called the PHATE algorithm. It allowed the results of DEA and archetypal analysis to be visualized in a low dimensional space.

Mobile map applications are increasingly used in various aspects of our lives, leading to an increase in different map use situations and, therefore, map use contexts. Several empirical usability studies have identified how map design is associated with and impacted by selected map use context attributes. This research seeks to expand on these studies and analyzes combinations of map use contexts to identify relevant contextual factors that influence mobile map design usability. In a study with 50 participants from Colombia, we assessed in an online survey the usability of 27 map design variations (consisting of three map-reading tasks, three base map styles, and three interactivity variants). We found that the overall map design is critical in supporting map-reading activities (e.g., identifying a location on a map was supported by a simplified base map, whereas selecting points on the map was supported by a more detailed base map). We then evaluated user patterns in the collected data with archetypal analysis. It was possible to create archetypal representations of the participants with a corresponding map design profile and establish a workflow for modeling patterns in usability and context data. We recommend that future research continues assessing archetypal analysis as it provides a means for context-based decision-making on map design adaptation and transferability.

The development of powerful new 3D scanning techniques has enabled the generation of large up-to-date anthropometric databases which provide highly valued data to improve the ergonomic design of products adapted to the user population. As a consequence, Ergonomics and Anthropometry are two increasingly quantitative fields, so advanced statistical methodologies and modern software tools are required to get the maximum benefit from anthropometric data. This paper presents a new R package, called Anthropometry, which is available on the Comprehensive R Archive Network. It brings together some statistical methodologies concerning clustering, statistical shape analysis, statistical archetypal analysis and the statistical concept of data depth, which have been especially developed to deal with anthropometric data. They are proposed with the aim of providing effective solutions to some common anthropometric problems, such as clothing design or workstation design (focusing on the particular case of aircraft cockpits). The utility of the package is shown by analyzing the anthropometric data obtained from a survey of the Spanish female population performed in 2006 and from the 1967 United States Air Force survey. This manuscript is also contained in Anthropometry as a vignette.

Statistics and analytic methods are becoming increasingly important in basketball. In particular, predicting players' performance using past observations is a considerable challenge. The purpose of this study is to forecast the future behavior of basketball players. The available data are sparse functional data, which are very common in sports. So far, however, no forecasting method designed for sparse functional data has been used in sports. A methodology based on two methods to handle sparse and irregular data, together with the analogous method and functional archetypoid analysis is proposed. Results in comparison with traditional methods show that our approach is competitive and additionally provides prediction intervals. The methodology can also be used in other sports when sparse longitudinal data are available. [ABSTRACT FROM AUTHOR]

Aim: Understanding the mechanisms determining species richness is a primary goal of biogeography. Richness patterns of sub‐groups within a taxon are usually assumed to be driven by similar processes. However, if richness of distinct ecological strategies respond differently to the same processes, inferences made for an entire taxon may be misleading. We deconstruct the global lizard assemblage into functional groups and examine the congruence among richness patterns between them. We further examine the species richness – functional richness relationship to elucidate the way functional diversity contributes to the overall species richness patterns. Location: Global. Methods: Using comprehensive biological trait databases we classified the global lizard assemblage into ecological strategies based on body size, diet, activity times and microhabitat preferences, using Archetypal Analysis. We then examined spatial gradients in the richness of each strategy at the one‐degree grid cell, biome, and realm scales. Results: We found that lizards can best be characterized by seven "ecological strategies": scansorial, terrestrial, nocturnal, herbivorous, fossorial, large, and semi‐aquatic. There are large differences among the global richness patterns of these strategies. While the major richness hotspot for lizards in general is in Australia, several strategies exhibit highest richness in the Amazon Basin. Importantly, the global maximum in lizard species richness is achieved at intermediate values of functional diversity and increasing functional diversity further result in a slow decline of species richness. Main conclusions: The deconstruction of the global lizard assemblage along multiple ecological axes offers a new way to conceive lizard diversity patterns. It suggests that local lizard richness mostly increases when species belonging to particular ecological strategies become hyper‐diverse there, and not because more ecological types are present in the most species rich localities. Thus maximum richness and maximum ecological diversity do not overlap. These results shed light on the global richness pattern of lizards, and highlight previously unidentified spatial patterns in understudied functional groups. [ABSTRACT FROM AUTHOR]