Anna Cena

OM3: Ordered maxitive, minitive, and modular aggregation operators – Axiomatic and probabilistic properties in an arity-monotonic setting

The recently-introduced OM3 aggregation operators fulfill three appealing properties: they are simultaneously minitive, maxitive, and modular. Among the instances of OM3 operators we find e.g. OWMax and OWMin operators, the famous Hirsch h-index and all its natural generalizations. In this paper the basic axiomatic and probabilistic properties of extended, i.e. in an arity-dependent setting, OM3 aggregation operators are studied. We illustrate the di culties one is inevitably faced with when trying to combine the quality and quantity of numeric items into a single number. The discussion on such aggregation methods is particularly important in the information resources producers assessment problem, which aims to reduce the negative e ects of information overload. It turns out that the Hirsch-like indices of impact do not fulfill a set of very important properties, which puts the sensibility of their practical usage into question. Moreover, thanks to the probabilistic analysis of the operators in an i.i.d. model, we may better understand the relationship between the aggregated items’ quality and their producers’ productivity.

Hierarchical Clustering via Penalty-Based Aggregation and the Genie Approach

The paper discusses a generalization of the nearest centroid hierarchical clustering algorithm. A first extension deals with the incorporation of generic distance-based penalty minimizers instead of the classical aggregation by means of centroids. Due to that the presented algorithm can be applied in spaces equipped with an arbitrary dissimilarity measure (images, DNA sequences, etc.). Secondly, a correction preventing the formation of clusters of too highly unbalanced sizes is applied: just like in the recently introduced Genie approach, which extends the single linkage scheme, the new method averts a chosen inequity measure (e.g., the Gini-, de Vergottini-, or Bonferroni-index) of cluster sizes from raising above a predefined threshold. Numerous benchmarks indicate that the introduction of such a correction increases the quality of the resulting clusterings significantly.

OM3: Ordered Maxitive, Minitive, and Modular Aggregation Operators: Axiomatic Analysis under Arity-Dependence (I)

Recently, a very interesting relation between symmetric minitive, maxitive, and modular aggregation operators has been shown. It turns out that the intersection between any pair of the mentioned classes is the same. This result introduces what we here propose to call the OM3 operators. In the first part of our contribution on the analysis of the OM3 operators we study some properties that may be useful when aggregating input vectors of varying lengths. In Part II we will perform a thorough simulation study of the impact of input vectors’ calibration on the aggregation results.

Fuzzy K-Minpen Clustering and K-nearest-minpen Classification Procedures Incorporating Generic Distance-Based Penalty Minimizers

We discuss a generalization of the fuzzy (weighted) k-means clustering procedure and point out its relationships with data aggregation in spaces equipped with arbitrary dissimilarity measures. In the proposed setting, a data set partitioning is performed based on the notion of points’ proximity to generic distance-based penalty minimizers. Moreover, a new data classification algorithm, resembling the k-nearest neighbors scheme but less computationally and memory demanding, is introduced. Rich examples in complex data domains indicate the usability of the methods and aggregation theory in general.

Agent-based model for the h-index – exact solution

Abstract Hirsch’s h-index is perhaps the most popular citation-based measure of scientific excellence. In 2013, Ionescu and Chopard proposed an agent-based model describing a process for generating publications and citations in an abstract scientific community [G. Ionescu, B. Chopard, Eur. Phys. J. B 86, 426 (2013)]. Within such a framework, one may simulate a scientist’s activity, and – by extension – investigate the whole community of researchers. Even though the Ionescu and Chopard model predicts the h-index quite well, the authors provided a solution based solely on simulations. In this paper, we complete their results with exact, analytic formulas. What is more, by considering a simplified version of the Ionescu-Chopard model, we obtained a compact, easy to compute formula for the h-index. The derived approximate and exact solutions are investigated on a simulated and real-world data sets.

Problems and challenges of information resources producers’ clustering

Classically, unsupervised machine learning techniques are applied on data sets with fixed number of attributes (variables). However, many problems encountered in the field of informetrics face us with the need to extend these kinds of methods in a way such that they may be computed over a set of nonincreasingly ordered vectors of unequal lengths. Thus, in this paper, some new dissimilarity measures (metrics) are introduced and studied. Owing to that we may use, e.g. hierarchical clustering algorithms in order to determine an input data sets partition consisting of sets of producers that are homogeneous not only with respect to the quality of information resources, but also their quantity.

OM3: Ordered Maxitive, Minitive, and Modular Aggregation Operators. A Simulation Study (II)

This article is a second part of the contribution on the analysis of the recently-proposed class of symmetric maxitive, minitive and modular aggregation operators. Recent results (Gagolewski, Mesiar, 2012) indicated some unstable behavior of the generalized h-index, which is a particular instance of OM3, in case of input data transformation. The study was performed on a small, carefully selected real-world data set. Here we conduct some experiments to examine this phenomena more extensively.