arXiv subjects

Alexandre Benatti

Publications and source records attributed to Alexandre Benatti.

At least 19 recordsLinked to original sources

arXiv2026

Non-Supervised Community Detection and Hierarchical Modularity Estimation in Complex Networks

This work extends to complex networks a recently described methodology (A. Benatti and L. da F Costa, Detecting Hierarchical Clusters and Estimating their Modularity Directly from Dendrograms, May 2026) for non-supervised hierarchical cluster detection and hierarchical modularity estimation. First, the edge betweenness centrality of a given complex network (or graph) is estimated, and a dendrogram is obtained from these values by using some linkage criterion (average linkage is considered in the present work). The mentioned concepts and methods can then be applied to the obtained dendrogram associated with the hierarchical structure of the nodes interrelationship, paving the way to community detection and hierarchical modularity estimation. Promising results are presented and discussed respectively to varying types of modular networks, namely fractal networks (which are intrinsically hierarchical) and prime partition networks, as well as to modular networks presenting just one (or a few) hierarchical levels.

physics.soc-ph↗

arXiv2026

Detecting Hierarchical Clusters and Estimating their Modularity Directly from Dendrograms

Identifying possible clusters in datasets and estimating their hierarchical modularity are central tasks in pattern recognition. In the present work, concepts and methodologies are described for performing these tasks while considering only the density of mergings obtained from hierarchical representations (dendrograms) of data inter-relationship along a scale variable. More specifically, the mergings of subclusters along the scale variable are obtained, yielding a respective merging density function. After this function is equalized along the scale variable, peak detection is applied in order to estimate, within a specified resolution, the main hierarchical levels and their clusters. After quantifying infinitesimal modularity of the dendrogram at a fixed scale value, taking into account the uniformity of the size of the identified clusters and their average size, the overall, average, and group hierarchical modularities are obtained. The potential of the reported approach is illustrated for some types of data and dendrograms and additive dendrograms obtained from DLA patterns, and the possibility of recursive cluster detection is also considered.

physics.soc-ph↗

arXiv2025

A Systematic Approach for Studying How Topological Measurements Respond to Complex Networks Modifications

Different types of graphs and complex networks have been characterized, analyzed, and modeled based on measurements of their respective topology. However, the available networks may constitute approximations of the original structure as a consequence of sampling incompleteness, noise, and/or error in the representation of that structure. Therefore, it becomes of particular interest to quantify how successive modifications may impact a set of adopted topological measurements, and how respectively undergone changes can be interrelated, which has been addressed in this paper by considering similarity networks and hierarchical clustering approaches. These studies are developed respectively to several topological measurements (accessibility, degree, hierarchical degree, clustering coefficient, betweenness centrality, assortativity, and average shortest path) calculated from complex networks of three main types (Erd\H{o}s-R\'enyi, Barab\'asi-Albert, and geographical) with varying sizes or subjected to progressive edge removal or rewiring. The coincidence similarity index, which can implement particularly strict comparisons, is adopted for two main purposes: to quantify and visualize how the considered topological measurements respond to the considered network alterations and to represent hierarchically the relationships between the observed changes undergone by the considered topological measurements. Several results are reported and discussed, including the identification of three types of topological changes taking place as a consequence of the modifications. In addition, the changes observed for the Erd\H{o}s-R\'enyi and Barab\'asi-Albert networks resulted mutually more similarly affected by topological changes than for the geometrical networks. The latter type of network has been identified to have more heterogeneous topological features than the other two types of networks.

cs.SI↗

arXiv2024

Partially Proportional and Adaptive Similarity Indices

A good deal of science and technology concepts and methods rely on comparing and relating entities in quantitative terms. Among the several possible approaches, similarity indices allow some interesting features, especially the ability to quantify how much two entities resemble one another. In this work, the Jaccard similarity for comparing non-zero real-valued vectors is modified so as to estimate similarity while focusing on the distinct parts of the signals. The resulting operator, which is called partially proportional similarity index, not only allows more strict comparisons, but also paves the way to develop an adaptive approach to similarity estimation in which the size and orientation of the comparisons adapt to those of a respective calibration field expressing how the observed features are related to original counterparts. Being a particularly relevant concept in data analysis and modeling, emphasis is placed on presenting and discussing the concept of calibration field and how they can be taken into account while performing similarity comparisons. Several results are described which illustrate the potential of the reported concepts and approaches for enhancing, and even simultaneously normalizing to some extent the representation of entities in terms of their features, as frequently required in scientific modeling and pattern recognition.

physics.soc-ph↗

arXiv2024

An Analytical Approach to the Jaccard Similarity Index

The Jaccard similarity index has often been employed in science and technology as a means to quantify the similarity between two sets. When modified to operate on real-valued values, the Jaccard similarity index can be applied to compare vectors, an operation which plays a central role in visualization, classification, and modeling. The present work aims at developing an analytical approach for estimating the probability density of the Jaccard similarity values as implied by set of data elements characterized by specific statistical densities, with emphasis on the uniform and normal cases. Several theoretical and practical situations can benefit directly from such an approach, as it allows several of the properties of the similarity comparisons among a given dataset to be better understood and anticipated. Situations in which the described approach can be applied include the estimation and visualization of data interrelationships in terms of similarity networks, as well as diverse problems in data analysis, pattern recognition and scientific modeling. In addition to presenting the analytical developments and results, examples are also provided in order to illustrate the potential of the approach. The work also includes extension of the reported developments to modifications of the Jaccard index intended for regularization and control of the sharpness of the implemented comparisons.

physics.data-an↗

arXiv2024

Normalization in Proportional Feature Spaces

The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of these activities and respective aspects. The selection of an appropriate normalization method needs to take into account the type and characteristics of the involved features, the methods to be used subsequently for the just mentioned data processing, as well as the specific questions being considered. After briefly considering how normalization constitutes one of the many interrelated parts typically involved in data analysis and modeling, the present work addressed the important issue of feature normalization from the perspective of uniform and proportional (right skewed) features and comparison operations. More general right skewed features are also considered in an approximated manner. Several concepts, properties, and results are described and discussed, including the description of a duality relationship between uniform and proportional feature spaces and respective comparisons, specifying conditions for consistency between comparisons in each of the two domains. Two normalization possibilities based on non-centralized dispersion of features are also presented, and also described is a modified version of the Jaccard similarity index which incorporates intrinsically normalization. Preliminary experiments are presented in order to illustrate the developed concepts and methods.

cs.LG↗

arXiv2024

Supervised Pattern Recognition Involving Skewed Feature Densities

Pattern recognition constitutes a particularly important task underlying a great deal of scientific and technologica activities. At the same time, pattern recognition involves several challenges, including the choice of features to represent the data elements, as well as possible respective transformations. In the present work, the classification potential of the Euclidean distance and a dissimilarity index based on the coincidence similarity index are compared by using the k-neighbors supervised classification method respectively to features resulting from several types of transformations of one- and two-dimensional symmetric densities. Given two groups characterized by respective densities without or with overlap, different types of respective transformations are obtained and employed to quantitatively evaluate the performance of k-neighbors methodologies based on the Euclidean distance an coincidence similarity index. More specifically, the accuracy of classifying the intersection point between the densities of two adjacent groups is taken into account for the comparison. Several interesting results are described and discussed, including the enhanced potential of the dissimilarity index for classifying datasets with right skewed feature densities, as well as the identification that the sharpness of the comparison between data elements can be independent of the respective supervised classification performance.

cs.LG↗

arXiv2024

Agglomerative Clustering in Uniform and Proportional Feature Spaces

Pattern comparison represents a fundamental and crucial aspect of scientific modeling, artificial intelligence, and pattern recognition. Three main approaches have typically been applied for pattern comparison: (i) distances; (ii) statistical joint variation; (iii) projections; and (iv) similarity indices, each with their specific characteristics. In addition to arguing for intrinsic interesting properties of multiset-based similarity approaches, the present work describes a respectively based hierarchical agglomerative clustering approach which inherits the several interesting characteristics of the coincidence similarity index -- including strict comparisons allowing distinguishing between closely similar patterns, inherent normalization, as well as substantial robustness to the presence of noise and outliers in datasets. Two other hierarchical clustering approaches are considered, namely a multiset-based method as well as the traditional Ward's approach. After characterizing uniform and proportional features spaces and presenting the main basic concepts and methods, a comparison of relative performance between the three considered hierarchical methods is reported and discussed, with several interesting and important results. In particular, though intrinsically suitable for implementing proportional comparisons, the coincidence similarity methodology also works effectively in several types of data in uniform feature spaces

physics.soc-ph↗

arXiv2024

Simple Games on Complex Networks

The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two teams playing according to a small set of simple rules, taking place on four types of complex networks. Starting from a minimalist game, characterized by full symmetry always leading to ties, four other games are described in progressive order of complexity, taking into account the presence of neighbors as well as strategies. Each of these five games, as well as their specific changes when implemented in four types of networks, are studied in terms of statistics of the total duration of the game as well as the number of victories and ties, with several interesting results that substantiate, in some cases, the importance of the network topology on the respective dynamics. As a subsidiary result, the visualization of relationships between the data elements in terms of coincidence similarity networks allowed a more complete and direct interpretation of the obtained results.

cs.SI↗

arXiv2024

Subsuming Complex Networks by Node Walks

The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume complex networks. Three types of networks (Erd\'os- R\'eny, Barab\'asi-Albert, as well as a geometric model) are considered, while three node walks heuristics (uniformly random, largest degree, and smallest degree) are taken into account. Several interesting results are obtained and described, including the identification that the subsuming dynamics depend strongly on both the specific topology of the networks as well as the criteria controlling the node walks. The use of node walks as a model for studying the relationship between network topology and dynamics is motivated by this result. In addition, relatively high correlations between the initial node degree and the accumulated strength of the walking node were observed for some combinations of network types and dynamic rules, allowing some of the properties of the subsumption to be roughly predicted from the initial topology around the waking node which has been found, however, not to be enough for full determination of the subsumption dynamics. Another interesting result regards the quite distinct signatures (along the iterations) of walking node strengths obtained for the several considered combinations of network type and subsumption rules.

physics.soc-ph↗

arXiv2024

Node Accessibility Characterization of Radially-Grown Structures

Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties change along time, as new elements are incorporated into the existing structure. In the present work, an approach is the case in which systems grown radially around some straight axis of reference, such as particle deposition on electrodes, or urban expansion along avenues, roads, coastline, or rivers, among several other possibilities. More specifically, we aim at characterizing the topological properties of simulated growing structures, which are represented as graphs, in terms of a measurement corresponding to the accessibility of each involved node. The incorporation of new elements (nodes and links) is performed preferentially to the angular orientation respectively to the reference axis. Several interesting results are reported, including the tendency of structures grown preferentially to the orientation normal to the axis to have smaller accessibility.

cs.SI↗

arXiv2024

Distance-Based Hierarchical Cutting of Complex Networks with Non-Preferential and Preferential Choice of Seeds

Graphs and complex networks can be successively separated into connected components associated to respective seed nodes, therefore establishing a respective hierarchical organization. In the present work, we study the properties of the hierarchical structure implied by distance-based cutting of Erd\H{o}s-R\'enyi, Barab\'asi-Albert, and a specific geometric network. Two main situations are considered regarding the choice of the seeds: non-preferential and preferential to the respective node degree. Among the obtained findings, we have the tendency of geometrical networks yielding more balanced pairs of connected components along the network progressive separation, presenting little chaining effects, followed by the Erd\H{o}s-R\'enyi and Barab\'asi-Albert types of networks. The choice of seeds preferential to the node degree tended to enhance the balance of the connected components in the case of the geometrical networks.

physics.soc-ph↗

arXiv2024

Hierarchical Cutting of Complex Networks Performed by Random Walks

Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the situation in which the connections traversed by each step of a uniformly random walks are progressively removed, yielding a successively less interconnected structure that may break into two components, therefore establishing a respective hierarchy. The sizes of each of these pairs of sliced networks, as well as the permanence of each connected component, are studied in the present work. Several interesting results are reported, including the tendency of geometrical networks sometimes to be broken into two components with comparable large sizes.

cs.SI↗

arXiv2024

Detecting Groups in Directed and Non-Directed Bipartite Networks

Bipartite networks provide an effective resource for representing, characterizing, and modeling several abstract and real-world systems and structures involving binary relations, which include food webs, social interactions, and customer-product relationships. Of particular interest is the problem of, given a specific bipartite network, to identify possible respective groups or clusters characterized by similar interconnecting patterns. The present work approaches this issue by extending and complementing a previously described coincidence similarity methodology (Bioarxiv, doi.org/10.1101/2022.07.16.500294) in several manners, including the consideration of direct and non-directed bipartite networks, the characterization of groups in those networks, as well as considering synthetic bipartite networks presenting groups as a resource for studying the performance of the described methodology. Several interesting results are described and discussed, including the corroboration of the potential of the coincidence similarity methodology for achieving enhanced separation between the groups in bipartite networks.

cs.SI↗

arXiv2023

Random Walks Performed by Topologically-Specific Agents on Complex Networks

Random walks by single-node agents have been systematically conducted on various types of complex networks in order to investigate how their topologies can affect the dynamics of the agents. However, by fitting any network node, these agents do not engage in topological interactions with the network. In the present work, we describe random walks on complex networks performed by agents that are actually small graphs. These agents can only occupy admissible portions of the network onto which they fit topologically, hence their name being taken as topologically-specific agents. These agents are also allowed to move to adjacent subgraphs in the network, which have each node adjacent to a distinct original respective node of the agent. Given a network and a specific agent, it is possible to obtain a respective associated network, in which each node corresponds to a possible instance of the agent and the edges indicate adjacent positions. Associated networks are obtained and studied respectively to three types of topologically-specific agents (triangle, square, and slashed square) considering three types of complex networks (geometrical, Erd\H{o}s-R\'enyi, and Barab\'asi-Albert). Uniform random walks are also performed on these structures, as well as networks respectively obtained by removing the five nodes with the highest degree, and studied in terms of the number of covered nodes along the walks. Several results are reported and discussed, including the fact that substantially distinct associated networks can be obtained for each of the three considered agents and for varying average node degrees. Respectively to the coverage of the networks by uniform random walks, the square agent led to the most effective coverage of the nodes, followed by the triangle and slashed square agents. In addition, the geometric network turned out to be less effectively covered.

physics.soc-ph↗

arXiv2023

Parallel and Sequential Resources Networks

A large number of real and abstract systems involve the transformation of some basic resource into respective products under the action of multiple processing agents, which can be understood as multiple-agent production systems (MAP). At each discrete time instant, for each agent, a fraction of the resources is assumed to be kept, forwarded to other agents, or converted into work with some efficiency. The present work describes a systematic study of nine basic MAP architectures subdivided into two main groups, namely parallel and sequential distribution of resources from a single respective source. Several types of interconnections among the involved processing agents are also considered. The resulting MAP architectures are studied in terms of the total amount of work, the dispersion of the resources (states) among the agents, and the transition times from the start of operation until the respective steady state. Several interesting results are obtained and discussed, including the observation that some of the parallel designs were able to yield maximum work and minimum state dispersion, achieved at the expense of the transition time and use of several interconnections between the source and the agents. The results obtained for the sequential designs indicate that relatively high performance can be obtained for some specific cases.

cs.MA↗

arXiv2023

Simple Bundles of Complex Networks

Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree, shortest paths, and modularity. In the present work, we develop an approach aimed at identifying and characterizing simple bundles of interconnections between pairs of nodes (source and destination) in complex networks. More specifically, simple bundles can be understood as corresponding to the bundle of paths obtained while traveling through successive neighborhoods after departing from a given source node. Because no node appears more than once along a given bundle, these structures have been said to be simple, in analogy to the concept of a simple path. In addition to describing simple bundles and providing a possible methodology for their identification, we also consider how their respective effective width can be estimated in terms of diffusion flow and exponential entropy of transition probabilities. The potential of the concepts and methods described in this work is then illustrated respectively to the characterization and analysis of model-theoretic networks, with several interesting results.

cs.SI↗

arXiv2023

Multilayer Multiset Neuronal Networks -- MMNNs

The coincidence similarity index, based on a combination of the Jaccard and overlap similarity indices, has noticeable properties in comparing and classifying data, including enhanced selectivity and sensitivity, intrinsic normalization, and robustness to data perturbations and outliers. These features allow multiset neurons, which are based on the coincidence similarity operation, to perform effective pattern recognition applications, including the challenging task of image segmentation. A few prototype points have been used in previous related approaches to represent each pattern to be identified, each of them being associated with respective multiset neurons. The segmentation of the regions can then proceed by taking into account the outputs of these neurons. The present work describes multilayer multiset neuronal networks incorporating two or more layers of coincidence similarity neurons. In addition, as a means to improve performance, this work also explores the utilization of counter-prototype points, which are assigned to the image regions to be avoided. This approach is shown to allow effective segmentation of complex regions despite considering only one prototype and one counter-prototype point. As reported here, the balanced accuracy landscapes to be optimized in order to identify the weight of the neurons in subsequent layers have been found to be relatively smooth, while typically involving more than one attraction basin. The use of a simple gradient-based optimization methodology has been demonstrated to effectively train the considered neural networks with several architectures, at least for the given data type, configuration of parameters, and network architecture.

cs.NE↗