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.

Ex Input:
There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their solutions. This paper introduces effective and compact, complete symmetry breaking constraints for small graph search. Enumerating with these symmetry breaks generates all and only non-isomorphic solutions. For small search problems, with up to 10 vertices, we compute instance independent symmetry breaking constraints. For small search problems with a larger number of vertices we demonstrate the computation of instance dependent constraints which are complete. We illustrate the application of complete symmetry breaking constraints to extend two known sequences from the OEIS related to graph enumeration.

Ex Output:
Breaking Symmetries in Graph Search with Canonizing Sets

Ex Input:
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.

Ex Output:
Progressive Boosting for Class Imbalance

Ex Input:
Many real systems have been modelled in terms of network concepts, and written texts are a particular example of information networks. In recent years, the use of network methods to analyze language has allowed the discovery of several interesting findings, including the proposition of novel models to explain the emergence of fundamental universal patterns. While syntactical networks, one of the most prevalent networked models of written texts, display both scale-free and small-world properties, such representation fails in capturing other textual features, such as the organization in topics or subjects. In this context, we propose a novel network representation whose main purpose is to capture the semantical relationships of words in a simple way. To do so, we link all words co-occurring in the same semantic context, which is defined in a threefold way. We show that the proposed representations favours the emergence of communities of semantically related words, and this feature may be used to identify relevant topics. The proposed methodology to detect topics was applied to segment selected Wikipedia articles. We have found that, in general, our methods outperform traditional bag-of-words representations, which suggests that a high-level textual representation may be useful to study semantical features of texts.

Ex Output:
Topic segmentation via community detection in complex networks