arXiv subjects

Panos M. Pardalos

Publications and source records attributed to Panos M. Pardalos.

27 records · Page 2Linked to original sources

arXiv2020

A Statistical Density-Based Analysis of Graph Clustering Algorithm Performance

Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences and a step-by-step routine for clustering quality assessment. Our null hypothesis does not rely on any generative model for the graph, unlike modularity which uses the configuration model as a null model. Our measures are shown to meet the axioms of a good clustering quality function, unlike the very commonly used modularity measure. They also have an intuitive graph-theoretic interpretation, a formal statistical interpretation and can be easily tested for significance. Our work is centered on the idea that well clustered graphs will display a significantly larger intra-cluster density than inter-cluster density. We develop tests to validate the existence of such a cluster structure. We empirically explore the behavior of our measures under a number of stress test scenarios and compare their behavior to the commonly used modularity and conductance measures. Empirical stress test results confirm that our measures compare very favorably to the established ones. In particular, they are shown to be more responsive to graph structure and less sensitive to sample size and breakdowns during numerical implementation and less sensitive to uncertainty in connectivity. These features are especially important in the context of larger data sets or when the data may contain errors in the connectivity patterns.

cs.SI↗

arXiv2019

Combining Stochastic Adaptive Cubic Regularization with Negative Curvature for Nonconvex Optimization

We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global convergence guarantees and ability to escape from strict saddle points. This method uses a trust region-like scheme to determine if an iteration is successful or not, and updates only when it is successful. In this paper, we suggest an algorithm combining negative curvature with the adaptive cubic regularized Newton method to update even at unsuccessful iterations. We call this new method Stochastic Adaptive cubic regularization with Negative Curvature (SANC). Unlike the previous method, in order to attain stochastic gradient and Hessian estimators, the SANC algorithm uses independent sets of data points of consistent size over all iterations. It makes the SANC algorithm more practical to apply for solving large-scale machine learning problems. To the best of our knowledge, this is the first approach that combines the negative curvature method with the adaptive cubic regularized Newton method. Finally, we provide experimental results including neural networks problems supporting the efficiency of our method.

math.OC↗

arXiv2018

A Smooth Double Proximal Primal-Dual Algorithm for a Class of Distributed Nonsmooth Optimization Problem

This technical note studies a class of distributed nonsmooth convex consensus optimization problem. The cost function is a summation of local cost functions which are convex but nonsmooth. Each of the local cost functions consists of a twice differentiable convex function and two lower semi-continuous convex functions. We call this problem as single-smooth plus double-nonsmooth (SSDN) problem. Under mild conditions, we propose a distributed double proximal primal-dual optimization algorithm. The double proximal operator is designed to deal with the difficulty caused by the unproximable property of the summation of those two nonsmooth functions. Besides, it can also guarantee that the proposed algorithm is locally Lipschitz continuous. An auxiliary variable in the double proximal operator is introduced to estimate the subgradient of the second nonsmooth function. Theoretically, we conduct the convergence analysis by employing Lyapunov stability theory. It shows that the proposed algorithm can make the states achieve consensus at the optimal point. In the end, nontrivial simulations are presented and the results demonstrate the effectiveness of the proposed algorithm.

math.OC↗

arXiv2018

Extended Vertical Lists for Temporal Pattern Mining from Multivariate Time Series

Temporal Pattern Mining (TPM) is the problem of mining predictive complex temporal patterns from multivariate time series in a supervised setting. We develop a new method called the Fast Temporal Pattern Mining with Extended Vertical Lists. This method utilizes an extension of the Apriori property which requires a more complex pattern to appear within records only at places where all of its subpatterns are detected as well. The approach is based on a novel data structure called the Extended Vertical List that tracks positions of the first state of the pattern inside records. Extensive computational results indicate that the new method performs significantly faster than the previous version of the algorithm for TMP. However, the speed-up comes at the expense of memory usage.

cs.LG↗

arXiv2017

Information transmission on hybrid networks

Many real-world communication networks often have hybrid nature with both fixed nodes and moving modes, such as the mobile phone networks mainly composed of fixed base stations and mobile phones. In this paper, we discuss the information transmission process on the hybrid networks with both fixed and mobile nodes. The fixed nodes (base stations) are connected as a spatial lattice on the plane forming the information-carrying backbone, while the mobile nodes (users), which are the sources and destinations of information packets, connect to their current nearest fixed nodes respectively to deliver and receive information packets. We observe the phase transition of traffic load in the hybrid network when the packet generation rate goes from below and then above a critical value, which measures the network capacity of packets delivery. We obtain the optimal speed of moving nodes leading to the maximum network capacity. We further improve the network capacity by rewiring the fixed nodes and by considering the current load of fixed nodes during packets transmission. Our purpose is to optimize the network capacity of hybrid networks from the perspective of network science, and provide some insights for the construction of future communication infrastructures.

cs.NI↗

arXiv2017

Heuristic for Maximizing Grouping Efficiency in the Cell Formation Problem

In our paper we consider the Cell Formation Problem in Group Technology with grouping efficiency as an objective function. We present a heuristic approach for obtaining high-quality solutions of the CFP. The suggested heuristic applies an improvement procedure to obtain solutions with high grouping efficiency. This procedure is repeated many times for randomly generated cell configurations. Our computational experiments are performed for popular benchmark instances taken from the literature with sizes from 10x20 to 50x150. Better solutions unknown before are found for 23 instances of the 24 considered.

cs.DM↗

arXiv2017

Optimal statistical decision for Gaussian graphical model selection

Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language, information retrieval and others. Gaussian graphical model selection is a statistical problem to identify the Gaussian graphical model from a sample of a given size. Different approaches for Gaussian graphical model selection are suggested in the literature. One of them is based on considering the family of individual conditional independence tests. The application of this approach leads to the construction of a variety of multiple testing statistical procedures for Gaussian graphical model selection. An important characteristic of these procedures is its error rate for a given sample size. In existing literature great attention is paid to the control of error rates for incorrect edge inclusion (Type I error). However, in graphical model selection it is also important to take into account error rates for incorrect edge exclusion (Type II error). To deal with this issue we consider the graphical model selection problem in the framework of the multiple decision theory. The quality of statistical procedures is measured by a risk function with additive losses. Additive losses allow both types of errors to be taken into account. We construct the tests of a Neyman structure for individual hypotheses and combine them to obtain a multiple decision statistical procedure. We show that the obtained procedure is optimal in the sense that it minimizes the linear combination of expected numbers of Type I and Type II errors in the class of unbiased multiple decision procedures.

stat.ML↗

arXiv2015

Information Theory Perspective on Network Robustness

A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures. In this work, we propose a dynamical definition of network's robustness based on Information Theory, that considers measurements of the structural changes caused by failures of the network's components. Failures are defined here, as a temporal process defined in a sequence. The robustness of the network is then evaluated by measuring dissimilarities between topologies after each time step of the sequence, providing a dynamical information about the topological damage. We thoroughly analyze the efficiency of the method in capturing small perturbations by considering both, the degree and distance distributions. We found the network's distance distribution more consistent in capturing network structural deviations, as better reflects the consequences of the failures. Theoretical examples and real networks are used to study the performance of this methodology.

physics.soc-ph↗

arXiv2013

Concepts of Stability in Discrete Optimization Involving Generalized Addition Operations

The paper addresses the tolerance approach to the sensitivity analysis of optimal solutions to the nonlinear optimization problem of the form $$\mbox{$\bigoplus\limits_{y\in S}C(y)\to\min$\quad over\quad $S\in\mathcal{S}$,}$$ where $\mathcal{S}$ is a collection of nonempty subsets of a finite set $X$ such that the union of $\mathcal{S}$ is $X$ and the intersection of $\mathcal{S}$ is empty, $C$ is a cost (or weight) function from $X$ into $\mathbb{R}^+=[0,\infty)$ or $(0,\infty)$, and $\oplus$ is a continuous, associative, commutative, nondecreasing and unbounded binary operation of generalized addition on $\mathbb{R}^+$, called an A-operation. We evaluate and present sharp estimates for upper and lower bounds of costs of elements from $X$, for which an optimal solution to the above problem remains stable. These bounds present new results in the sensitivity analysis as well as extend most known results in a unified way. We define an invariant of the optimization problem---the tolerance function, which is independent of optimal solutions, and establish its basic properties, among which we mention a characterization of the set of all optimal solutions, the uniqueness of optimal solutions and extremal values of the tolerance function on an optimal solution.

math.FA↗