No abstract

Prototypes, as Rosch (1973) defined the term in the cognitive sciences field, are ideal exemplars that summarize and\ud represent groups of objects (or categories) and that are “typical” according to their internal resemblance and external dissimilarity\ud vis-`a-vis other groups or categories. In line with the cognitive approach, we propose a data-driven procedure for identifying\ud prototypes that is based on archetypal analysis and compositional data analysis. The procedure presented here exploits the properties of archetypes, both in terms of their external dissimilarity in relation to other points in the data set and in terms of their ability to represent the data through compositions in a simplex in which it is possible to cluster all of the observations. The proposed procedure is useful not only for the usual real data points; it may also be used for interval-valued data, functional data, and relational data, and it provides well-separated and clearly profiled prototypes

Archetypal analysis aims at synthesizing single‐valued data sets through a few (not necessarily observed) points that are called archetypes, under the constraint that all points can be represented as a convex combination of the archetypes themselves and that the archetypes are a convex combination of the data. In this paper, we extend this methodology to the case of interval‐valued data, which represent a special case of set‐valued data, where the sets are compact and identified by ordered pairs of values. In addition, we propose to use interval archetypes as a tool in an analysis strategy to explore and mine complex data sets. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012

In this paper we propose a method to analyze and synthesize a set of N networks that refer to a common scenario and that are comparable among each other. Examples of this type of data are: a set of collaboration networks, each defined for a different scientific field; or a set of ego networks, where egos belong to a same category; a set of governance networks, etc. For these kind of sets of networks it can be of interest to find a small number of representative networks that can serve as a condensed view of the data set. In a statistical perspective this goal amount to find a small number of networks that are able to typify the network structures starting from the observed ones. In addition, these networks should have a clear and interpretable profile in terms of their most relevant features and their specificity in contrast to the others. Given the set of N networks, we propose to find these representative networks by using the archetypal analysis, yielding what we call Archetypal Networks. The Archetypal Networks can serve to understand the data structure, as benchmarks for the other networks, and are useful also to compare networks among each other. We exemplify the proposed procedure by analyzing a set of 36 governance networks of public structures devoted to provide youth services and referring to 36 different territorial districts in Campania region in Italy. Our results highlight the presence of different network structures that can be interpreted in terms of the governance forms established in literature

This paper deals with the problem of identifying multiple outliers in multivariate data. Detection of anomalous values is achieved by looking at the variations in the convex hull of the data set as block of observations are deleted.