In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
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Question: Minimum vertex cover problem is an NP-Hard problem with the aim of finding minimum number of vertices to cover graph. In this paper, a learning automaton based algorithm is proposed to find minimum vertex cover in graph. In the proposed algorithm, each vertex of graph is equipped with a learning automaton that has two actions in the candidate or noncandidate of the corresponding vertex cover set. Due to characteristics of learning automata, this algorithm significantly reduces the number of covering vertices of graph. The proposed algorithm based on learning automata iteratively minimize the candidate vertex cover through the update its action probability. As the proposed algorithm proceeds, a candidate solution nears to optimal solution of the minimum vertex cover problem. In order to evaluate the proposed algorithm, several experiments conducted on DIMACS dataset which compared to conventional methods. Experimental results show the major superiority of the proposed algorithm over the other methods. Keywords Minimum Vertex Cover; NP-Hard problems; Learning Automata; Distributed learning automata.

Answer: Solving Minimum Vertex Cover Problem Using Learning Automata

Question: In practice, pattern recognition applications often suffer from imbalanced data distributions between classes, which may vary during operations w.r.t. the design data. Two-class classification systems designed using imbalanced data tend to recognize the majority (negative) class better, while the class of interest (positive class) often has the smaller number of samples. Several data-level techniques have been proposed to alleviate this issue, where classifier ensembles are designed with balanced data subsets by up-sampling positive samples or under-sampling negative samples. However, some informative samples may be neglected by random under-sampling and adding synthetic positive samples through up-sampling adds to training complexity. In this paper, a new ensemble learning algorithm called Progressive Boosting (PBoost) is proposed that progressively inserts uncorrelated groups of samples into a Boosting procedure to avoid loosing information while generating a diverse pool of classifiers. Base classifiers in this ensemble are generated from one iteration to the next, using subsets from a validation set that grows gradually in size and imbalance. Consequently, PBoost is more robust when the operational data may have unknown and variable levels of skew. In addition, the computation complexity of PBoost is lower than Boosting ensembles in literature that use under-sampling for learning from imbalanced data because not all of the base classifiers are validated on all negative samples. In PBoost algorithm, a new loss factor is proposed to avoid bias of performance towards the negative class. Using this loss factor, the weight update of samples and classifier contribution in final predictions are set based on the ability to recognize both classes. Using the proposed loss factor instead of standard accuracy can avoid biasing performance in any Boosting ensemble. The proposed approach was validated and compared using synthetic data, videos from the Faces In Action dataset that emulates face re-identification applications, and KEEL collection of datasets. Results show that PBoost can outperform state of the art techniques in terms of both accuracy and complexity over different levels of imbalance and overlap between classes.

Answer: Progressive Boosting for Class Imbalance

Question: For large, real-world inductive learning problems, the number of training examples often must be limited due to the costs associated with procuring, preparing, and storing the training examples and/or the computational costs associated with learning from them. In such circumstances, one question of practical importance is: if only n training examples can be selected, in what proportion should the classes be represented? In this article we help to answer this question by analyzing, for a fixed training-set size, the relationship between the class distribution of the training data and the performance of classification trees induced from these data. We study twenty-six data sets and, for each, determine the best class distribution for learning. The naturally occurring class distribution is shown to generally perform well when classifier performance is evaluated using undifferentiated error rate (0/1 loss). However, when the area under the ROC curve is used to evaluate classifier performance, a balanced distribution is shown to perform well. Since neither of these choices for class distribution always generates the best-performing classifier, we introduce a "budget-sensitive" progressive sampling algorithm for selecting training examples based on the class associated with each example. An empirical analysis of this algorithm shows that the class distribution of the resulting training set yields classifiers with good (nearly-optimal) classification performance.

Answer:
Learning When Training Data are Costly: The Effect of Class Distribution on Tree Induction