Clones in Graphs

Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context $(G,M,I)$ from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.Comment: 11 pages, 2 figures, 1 tabl

A Greedy Iterative Layered Framework for Training Feed Forward Neural Networks

info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FCCI-INF%2F29168%2F2017/PT" Custode, L. L., Tecce, C. L., Bakurov, I., Castelli, M., Cioppa, A. D., & Vanneschi, L. (2020). A Greedy Iterative Layered Framework for Training Feed Forward Neural Networks. In P. A. Castillo, J. L. Jiménez Laredo, & F. Fernández de Vega (Eds.), Applications of Evolutionary Computation - 23rd European Conference, EvoApplications 2020, Held as Part of EvoStar 2020, Proceedings (pp. 513-529). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12104 LNCS). Springer. https://doi.org/10.1007/978-3-030-43722-0_33In recent years neuroevolution has become a dynamic and rapidly growing research field. Interest in this discipline is motivated by the need to create ad-hoc networks, the topology and parameters of which are optimized, according to the particular problem at hand. Although neuroevolution-based techniques can contribute fundamentally to improving the performance of artificial neural networks (ANNs), they present a drawback, related to the massive amount of computational resources needed. This paper proposes a novel population-based framework, aimed at finding the optimal set of synaptic weights for ANNs. The proposed method partitions the weights of a given network and, using an optimization heuristic, trains one layer at each step while “freezing” the remaining weights. In the experimental study, particle swarm optimization (PSO) was used as the underlying optimizer within the framework and its performance was compared against the standard training (i.e., training that considers the whole set of weights) of the network with PSO and the backward propagation of the errors (backpropagation). Results show that the subsequent training of sub-spaces reduces training time, achieves better generalizability, and leads to the exhibition of smaller variance in the architectural aspects of the network.authorsversionpublishe

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Ants Constructing Rule-Based Classifiers

Book series: Studies in Computational Intelligencestatus: publishe

A penalty approach to a discretized double obstacle problem with derivative constraints

This work presents a penalty approach to a nonlinear optimization problem with linear box constraints arising from the discretization of an infinite-dimensional differential obstacle problem with bound constraints on derivatives. In this approach, we first propose a penalty equation approximating the mixed nonlinear complementarity problem representing the Karush-Kuhn-Tucker conditions of the optimization problem. We then show that the solution to the penalty equation converges to that of the complementarity problem with an exponential convergence rate depending on the parameters used in the equation. Numerical experiments, carried out on a non-trivial test problem to verify the theoretical finding, show that the computed rates of convergence match the theoretical ones well

A Spoonful of Math Helps the Medicine Go Down: An Illustration of How Healthcare can Benefit from Mathematical Modeling and Analysis

<p>Abstract</p> <p>Objectives</p> <p>A recent joint report from the Institute of Medicine and the National Academy of Engineering, highlights the benefits of--indeed, the need for--mathematical analysis of healthcare delivery. Tools for such analysis have been developed over decades by researchers in Operations Research (OR). An OR perspective typically frames a complex problem in terms of its essential mathematical structure. This article illustrates the use and value of the tools of operations research in healthcare. It reviews one OR tool, queueing theory, and provides an illustration involving a hypothetical drug treatment facility.</p> <p>Method</p> <p>Queueing Theory (QT) is the study of waiting lines. The theory is useful in that it provides solutions to problems of waiting and its relationship to key characteristics of healthcare systems. More generally, it illustrates the strengths of modeling in healthcare and service delivery.</p> <p>Queueing theory offers insights that initially may be hidden. For example, a queueing model allows one to incorporate randomness, which is inherent in the actual system, into the mathematical analysis. As a result of this randomness, these systems often perform much worse than one might have guessed based on deterministic conditions. Poor performance is reflected in longer lines, longer waits, and lower levels of server utilization.</p> <p>As an illustration, we specify a queueing model of a representative drug treatment facility. The analysis of this model provides mathematical expressions for some of the key performance measures, such as average waiting time for admission.</p> <p>Results</p> <p>We calculate average occupancy in the facility and its relationship to system characteristics. For example, when the facility has 28 beds, the average wait for admission is 4 days. We also explore the relationship between arrival rate at the facility, the capacity of the facility, and waiting times.</p> <p>Conclusions</p> <p>One key aspect of the healthcare system is its complexity, and policy makers want to design and reform the system in a way that affects competing goals. OR methodologies, particularly queueing theory, can be very useful in gaining deeper understanding of this complexity and exploring the potential effects of proposed changes on the system without making any actual changes.</p