Annabella Astorino - Academia.edu (original) (raw)

Papers by Annabella Astorino

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We consider the directional sensor network lifetime maximization problem (DSLMP). Given a set of ... more We consider the directional sensor network lifetime maximization problem (DSLMP). Given a set of directional sensor and target locations, the problem consists in assigning, at each time unit of a given time horizon, the action radius, the aperture angle, and the orientation direction to all sensors. The objective is to maximize the number of time units when all targets are covered, under certain constraints on sensor available energy. We present a mixed integer nonlinear programming formulation and tackle it by Lagrangean decomposition and subgradient optimization. The algorithm is equipped with a repairing heuristics aimed at finding good‐quality feasible solutions to DSLMP. The results of the application of the proposed approach to a number of problem instances are also reported.

European Journal of Operational Research

2017 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 2017

We present an application of a Multiple Instance Learning (MIL) approach to image classification.... more We present an application of a Multiple Instance Learning (MIL) approach to image classification. In particular we focus on a recent MIL method for binary classification where the objective is to discriminate between positive and negative sets of points. Such sets are called bags and the points inside the bags are called instances. In the case of two classes of instances (positive and negative), a bag is defined positive if it contains at least a positive instance and it is negative if it contains only negative instances. For such kind of problems there exist in literature two different approaches: the bag-level approach and the instance level approach. While in the former the total entity of each bag is considered, in the latter a classifier is obtained on the basis of the characteristics of the instances, without looking at the whole entity of each bag. The presented method is an instance-level approach and it is based on the application of the Lagrangian relaxation technique to a Support Vector Machine (SVM) type model. Preliminary numerical tests are discussed on a set of simple grey-level images.

Proceedings of the 22nd International Database Engineering & Applications Symposium on - IDEAS 2018, 2018

After a brief survey on well established methods for image classification, we focus on a recently... more After a brief survey on well established methods for image classification, we focus on a recently proposed Multiple Istance Learning (MIL) method which is suitable for applications in image processing. In particular the method is based on a mixed integer nonlinear formulation of the optimization problem to be solved for MIL purposes. The algorithm is applied to a set of color images (Red, Green, Blue, RGB) with the objective of classifying the images containing some specific pattern. The results of our experimentation are reported.

Soft Computing, 2021

We consider polyhedral separation of sets as a possible tool in supervised classification. In par... more We consider polyhedral separation of sets as a possible tool in supervised classification. In particular, we focus on the optimization model introduced by Astorino and Gaudioso (J Optim Theory Appl 112(2):265–293, 2002) and adopt its reformulation in difference of convex (DC) form. We tackle the problem by adapting the algorithm for DC programming known as DCA. We present the results of the implementation of DCA on a number of benchmark classification datasets.

Soft Computing, 2020

We tackle the problem of separating two finite sets of samples by means of a spherical surface, f... more We tackle the problem of separating two finite sets of samples by means of a spherical surface, focusing on the case where the center of the sphere is fixed. Such approach reduces to the minimization of a convex and nonsmooth function of just one variable (the radius), revealing very effective in terms of computational time. In particular, we analyze the case where the center of the sphere is selected far from both the two sets, embedding the grossone idea and obtaining a kind of linear separation. Some numerical results are presented on classical binary data sets drawn from the literature.

Interdisciplinary Sciences: Computational Life Sciences, 2019

We present an application to melanoma detection of a multiple instance learning (MIL) approach, w... more We present an application to melanoma detection of a multiple instance learning (MIL) approach, whose objective, in the binary case, is to discriminate between positive and negative sets of items. In the MIL terminology these sets are called bags and the items inside the bags are called instances. Under the hypothesis that a bag is positive if at least one of its instances is positive and it is negative if all its instances are negative, the MIL paradigm fits very well with images classification, since an image (bag) is in general classified on the basis of some its subregions (instances). In this work we have applied a MIL algorithm on some clinical data constituted by color dermoscopic images, with the aim to discriminate between melanomas (positive images) and common nevi (negative images). In comparison with standard classification approaches, such as the well known support vector machine, our method performs very well in terms both of accuracy and sensitivity. In particular, using a leave-one-out validation on a data set constituted by 80 melanomas and 80 common nevi, we have obtained the following results: accuracy = 92.50%, sensitivity = 97.50% and specificity = 87.50%. Since the results appear promising, we conclude that a MIL technique could be at the basis of more sophisticated tools useful to physicians in melanoma detection.

IEEE Transactions on Neural Networks and Learning Systems, 2019

In the standard classification problems, the objective is to categorize points into different cla... more In the standard classification problems, the objective is to categorize points into different classes. Multiple instance learning (MIL), instead, is aimed at classifying bags of points, each point being an instance. The main peculiarity of a MIL problem is that, in the learning phase, only the label of each bag is known whereas the labels of the instances are unknown. We discuss an instance-level learning approach for a binary MIL classification problem characterized by two classes of instances, positive and negative, respectively. In such a problem, a negative bag is constituted only by negative instances, while a bag is positive if it contains at least one positive instance. We start from a mixed integer nonlinear optimization model drawn from the literature and the main result we obtain is to prove that a Lagrangian relaxation approach, equipped with a dual ascent scheme, allows us to obtain an optimal solution of the original problem. The relaxed problem is tackled by means of a block coordinate descent (BCD) algorithm. We provide, finally, the results of our implementation on some benchmark data sets.

AIP Conference Proceedings, 2016

The Directional Sensors Continuous Coverage Problem (DSCCP) aims at covering a given set of targe... more The Directional Sensors Continuous Coverage Problem (DSCCP) aims at covering a given set of targets in a plane by means of a set of directional sensors. The location of these sensors is known in advance and they are characterized by a discrete set of possible radii and aperture angles. Decisions to be made are about orientation (which in our approach can vary continuously), radius and aperture angle of each sensor. The objective is to get a minimum cost coverage of all targets, if any. We introduce a MINLP formulation of the problem and define a Lagrangian heuristics based on a dual ascent procedure operating on one multiplier at a time. Finally we report the results of the implementation of the method on a set of test problems.

Neural Computing and Applications, 2016

We introduce and test a binary classification method aimed at detecting malicious URL on the basi... more We introduce and test a binary classification method aimed at detecting malicious URL on the basis of some information on both the URL syntax and its domain properties. Our method belongs to the class of supervised machine learning models, where, in particular, classification is performed by using information coming from a set of URL’s (samples in machine learning parlance) whose class membership is known in advance. The main novelty of our approach is in the use of a spherical separation-based algorithm, instead of SVM-type methods, which are based on hyperplanes as separation surfaces in the sample space. In particular we adopt a simplified spherical separation model which runs in O(tlogt) time (t is the number of samples in the training set), and thus is suitable for large-scale applications. We test our approach using different sets of features and report the results in terms of training correctness according to the well-established tenfold cross-validation paradigm.

Journal of Optimization Theory and Applications, 2002

We address the problem of discriminating between two finite point sets A and B in the n-dimension... more We address the problem of discriminating between two finite point sets A and B in the n-dimensional space by h hyperplanes generating a convex polyhedron. If the intersection of the convex hull of A with B is empty, the two sets can be strictly separated (polyhedral separability). We introduce an error function which is piecewise linear, but not convex nor concave, and define a descent procedure based on the iterative solution of the LP descent direction finding subproblems.

Optimization Letters, 2016

We introduce a method for edge detection which is based on clustering the pixels representing any... more We introduce a method for edge detection which is based on clustering the pixels representing any given digital image into two sets (the edge pixels and the non-edge ones). The process is based on associating to each pixel an appropriate vector representing the differences in brightness w.r.t. the surrounding pixels. Clustering is driven by the norms of such vectors, thus it takes place in R, which allows us to use a (simple) DC (Difference of Convex) optimization algorithm to get the clusters. A novel thinning technique, based on calculation of the edge phase angles, refines the classification obtained by the clustering algorithm. The results of some numerical experiments are also provided.

Optimization and Engineering, 2015

Let fa i : i 2 Ig be a finite set in R n. The illumination problem addressed in this work concern... more Let fa i : i 2 Ig be a finite set in R n. The illumination problem addressed in this work concerns the optimal location and orientation of a conic light beam R À z; y; s Á ¼ x 2 R n : s kx À zk À hy; x À zi 0 f g : The aperture angle # ¼ 2 arccos s of the conic light beam is a decreasing function of the sharpness coefficient s 2 ½0; 1. The problem at hand is to select an apex z in a prescribed compact region Z R n and a unit vector y 2 R n so that the conic light beam R(z, y, s) fulfils two conflicting requirements: it captures as many points a i as possible and, at the same time, it has a sharpness coefficient s as large as possible.

IEEE Transactions on Neural Networks and Learning Systems, 2016

We propose a bilevel cross-validation scheme for support vector machine (SVM) model selection bas... more We propose a bilevel cross-validation scheme for support vector machine (SVM) model selection based on the construction of the entire regularization path. Since such path is a particular case of the more general proximal trajectory concept from nonsmooth optimization, we propose for its construction an algorithm based on solving a finite number of structured linear programs. Our methodology, differently from other approaches, works directly on the primal form of SVM. Numerical results are presented on binary data sets drawn from literature.

Journal of Convex Analysis

This work addresses the issue of separating two finite sets in ℝ n by means of a suitable revolut... more This work addresses the issue of separating two finite sets in ℝ n by means of a suitable revolution cone Γ(z,y,s)={x∈ℝ n :s∥x-z∥-y T (x-z)=0}· The specific challenge at hand is to determine the aperture coefficient s, the axis y, and the apex z of the cone. These parameters have to be selected in such a way as to meet certain optimal separation criteria. Part I of this work focusses on the homogeneous case in which the apex of the revolution cone is the origin of the space. The homogeneous case deserves a separated treatment, not just because of its intrinsic interest, but also because it helps to built up the general theory. Part II of this work concerns the non-homogeneous case in which the apex of the cone can move in some admissible region. The non-homogeneous case is structurally more involved and leads to challenging nonconvex nonsmooth optimization problems.

Applied Mathematical Modelling, 2015

ABSTRACT

Optimization Letters, 2014

Wireless sensor coverage problem has been extensively studied in the last years, with growing att... more Wireless sensor coverage problem has been extensively studied in the last years, with growing attention to energy efficient configurations. In the paper we consider the problem of determining the radius of a given number of sensors, covering a set of targets, with the objective of minimizing the total coverage energy consumption. The problem has a non linear objective function and non convex constraints. To solve it we adopt a penalty function approach which allows us to state the problem in difference of convex functions form. Some numerical results are presented on a set of randomly generated test problems.

Computational Optimization and Applications, 2015

We introduce a new notion of central axis for a finite set {a 1 ,. .. , a m } of vectors in R n. ... more We introduce a new notion of central axis for a finite set {a 1 ,. .. , a m } of vectors in R n. In tandem, we discuss different ways of measuring the dispersion of the data points a i 's around the central axis. Finally, we explain how to detect numerically the most peripheral points of the given dataset.

Nonconvex Optimization and Its Applications, 2001

Abstract Different problems of practical importance, such as problems of pattern recognition, med... more Abstract Different problems of practical importance, such as problems of pattern recognition, medical and technical diagnostics, identification, study of experimental data etc., can be described by mathematical models which require the solution of the problem of separation of two or more sets. In many cases the sets mentioned are inseparable, and the problem arises