Contributed Session Thu.3.H 2013

Thursday, 15:15 - 16:45 h, Room: H 2013

Cluster 11: Integer & mixed-integer programming [...]

Topology, clustering and separation


Chair: Timo Berthold



Thursday, 15:15 - 15:40 h, Room: H 2013, Talk 1

Marcia Fampa
MILP formulation for the software clustering problem

Coauthors: Olinto Araújo, Viviane Kohler


We present a mixed integer linear programming (MILP) formulation for the Software Clustering
Problem (SCP), where we divide the modules of a software system into groups or clusters, to
facilitate the work of the software maintainers. We discuss a preprocessing that reduces the size
of the instances of the SCP and introduce some valid inequalities that have been shown to be very effective in tightening the MILP formulation. Numerical results presented compare the results
obtained with the formulation proposed with the solutions obtained by the exhaustive algorithm
supported by the freely available Bunch clustering tool, for benchmark problems.



Thursday, 15:45 - 16:10 h, Room: H 2013, Talk 2

Pedro G. Guillén
Natural languages with the morphosyntactic distance as a topological space

Coauthors: Juan Castellanos, Alejandro De Santos, Eduardo Villa


The main aim of this paper is to give a proof of the computability of morphosyntactic distance (M.D.) over an arbitrary set of data. Since here, M.D. (defined in the works of De Santos, Villa and Guillén) can be defined over the elements of this group. Distance d induces a topological space, that we call morphosyntactic space. Based on these hypothesis, studying the properties of this space from a topological point of view. Let the associated lexical space built, that haves a semigroup structure, and could be treated as a set, regardless of its algebraic properties. Using the fact that the meaning function is inyective, it is possible to define on it the M.D. d.
In the first section, several topological properties of morphosyntactic space are proved: total disconnection, compactness and separability. Then a comparison is proposed between different structures and morphosyntactic space.
Under the latter theorem, reasonable time to implement algorithms can be assumed over morphosyntactic space. In these conditions, is easy to conclude that the model designed to define the morphosyntactic space is computable, and therefore the algorithm of M.D. is solvable.



Thursday, 16:15 - 16:40 h, Room: H 2013, Talk 3

Inácio Andruski-Guimarães
Comparison of techniques based on linear programming to detect separation


Separation is a key feature in logistic regression. In fact, is well known that, in case of complete separation, iterative methods commonly used to maximize the likelihood, like for example Newton's method, do not converge to finite values. This phenomenon is also known as monotone likelihood, or infinite parameters. Linear programming techniques to detect separation have been proposed in the literature for logistic regression with binary response variable. But, for polytomous response variable, the time required to perform these techniques can be greater than that for fitting the model using an iterative method. The purpose with this job is to develop and implement an alternative approach to detect separation for the parameter estimation in polytomous logistic regression. This approach proposes to use as covariates a reduced set of optimum principal components of the original covariates. Principal components analysis allows the reduction of the number of dimensions and avoiding the multicollinearity of these variables. Examples on datasets taken from the literature show that the approach is feasible and works better than other techniques, in terms of amount of computing.


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