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Using the one-versus-rest strategy with samples balancing to improve pairwise coupling classification

Chmielnicki W., Stąpor K.

International Journal of Applied Mathematics and Computer Science

2016

Vol. 26, no. 1

191--201

The simplest classification task is to divide a set of objects into two classes, but most of the problems we find in real life applications are multi-class. There are many methods of decomposing such a task into a set of smaller classification problems involving two classes only. Among the methods, pairwise coupling proposed by Hastie and Tibshirani (1998) is one of the best known. Its principle is to separate each pair of classes ignoring the remaining ones. Then all objects are tested against these classifiers and a voting scheme is applied using pairwise class probability estimates in a joint probability estimate for all classes. A closer look at the pairwise strategy shows the problem which impacts the final result. Each binary classifier votes for each object even if it does not belong to one of the two classes which it is trained on. This problem is addressed in our strategy. We propose to use additional classifiers to select the objects which will be considered by the pairwise classifiers. A similar solution was proposed by Moreira and Mayoraz (1998), but they use classifiers which are biased according to imbalance in the number of samples representing classes.

Analysis of semantic modularity for genetic programming

Krawiec K., Wieloch B.

Foundations of Computing and Decision Sciences

2009

Vol. 34, No. 4

265-285

In this paper we analyze the properties of functional modularity, a concept introduced in [14] for detecting and measuring modularity in problems of automatic program synthesis, in particular by means of genetic programming. The basic components of functional modularity approach are subgoals - entities that embody module's semantic - and monotonicity, a measure for assessing subgoals' potential utility for searching for good modules. For a given subgoal and a sample of solutions decomposed into parts and contexts according to module definition, monotonicity measures the correlation of distance between semantics of solution's part and the fitness of the solution. The central tenet of this approach is that highly monotonous subgoals can be used to decompose the task and improve search convergence. In the experimental part we investigate the properties of functional modularity using eight instances of problems of Boolean function synthesis. The results show that monotonicity varies depending on problem's structure of modularity and correctly identifies good subgoals, potentially enabling automatic program decomposition.