Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem

We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning problem, being NP-hard in the general case of having edge weights of different signs. We propose a new method of estimating an upper bound of the objective function that we combine with the classical branch-and-bound technique to find the exact solution. We evaluate our approach on a broad range of random graphs and real-world networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.Comment: 20 pages, 3 figure

A Multi-cut Formulation for Joint Segmentation and Tracking of Multiple Objects

Recently, Minimum Cost Multicut Formulations have been proposed and proven to be successful in both motion trajectory segmentation and multi-target tracking scenarios. Both tasks benefit from decomposing a graphical model into an optimal number of connected components based on attractive and repulsive pairwise terms. The two tasks are formulated on different levels of granularity and, accordingly, leverage mostly local information for motion segmentation and mostly high-level information for multi-target tracking. In this paper we argue that point trajectories and their local relationships can contribute to the high-level task of multi-target tracking and also argue that high-level cues from object detection and tracking are helpful to solve motion segmentation. We propose a joint graphical model for point trajectories and object detections whose Multicuts are solutions to motion segmentation {\it and} multi-target tracking problems at once. Results on the FBMS59 motion segmentation benchmark as well as on pedestrian tracking sequences from the 2D MOT 2015 benchmark demonstrate the promise of this joint approach

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Communities in Networks

We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and open problems, and discuss why scientists from diverse backgrounds are interested in these problems. As a running theme, we emphasize the connections of community detection to problems in statistical physics and computational optimization.Comment: survey/review article on community structure in networks; published version is available at http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pd

ピアアセスメントのための項目反応理論と整数計画法を用いたグループ構成最適化

In recent years, large-scale e-learning environments such as Massive Online Open Courses (MOOCs) have become increasingly popular. In such environments, peer assessment, which is mutual assessment among learners, has been used to evaluate reports and programming assignments. When the number of learners increases as in MOOCs, peer assessment is often conducted by dividing learners into multiple groups to reduce the learners’ assessment workload. In this case, however, the accuracy of peer assessment depends on the way to form groups. To solve the problem, this study proposes a group optimization method based on item response theory (IRT) and integer programming. The proposed group optimization method is formulated as an integer programming problem that maximizes the Fisher information, which is a widely used index of ability assessment accuracy in IRT. Experimental results, however, show that the proposed method cannot sufficiently improve the accuracy compared to the random group formulation. To overcome this limitation, this study introduces the concept of external raters and proposes an external rater selection method that assigns a few appropriate external raters to each learner after the groups were formed using the proposed group optimization method. In this study, an external rater is defined as a peer-rater who belongs to different groups. The proposed external rater selection method is formulated as an integer programming problem that maximizes the lower bound of the Fisher information of the estimated ability of the learners by the external raters. Experimental results using both simulated and real-world peer assessment data show that the introduction of external raters is useful to improve the accuracy sufficiently. The result also demonstrates that the proposed external rater selection method based on IRT models can significantly improve the accuracy of ability assessment than the random selection.近年，MOOCsなどの大規模型eラーニングが普及してきた．大規模な数の学習者が参加している場合には，教師が一人で学習者のレポートやプログラム課題などを評価することは難しい．大規模の学習者の評価手法の一つとして，学習者同士によるピアアセスメントが注目されている．MOOCsのように学習者数が多い場合のピアアセスメントは，評価の負担を軽減するために学習者を複数のグループに分割してグループ内のメンバ同士で行うことが多い．しかし，この場合，グループ構成の仕方によって評価結果が大きく変化してしまう問題がある．この問題を解決するために，本研究では，項目反応理論と整数計画法を用いて，グループで行うピアアセスメントの精度を最適化するグループ構成手法を提案する．具体的には，項目反応理論において学習者の能力測定精度を表すフィッシャー情報量を最大化する整数計画問題としてグループ構成問題を定式化する．実験の結果，ランダムグループ構成と比べて，提案手法はおおむね測定精度を改善したが，それは限定的な結果であることが明らかとなった．そこで，本研究ではさらに，異なるグループから数名の学習者を外部評価者として各学習者に割り当て外部評価者選択手法を提案する．シミュレーションと実データ実験により，提案手法を用いることで能力測定精度を大幅に改善できることを示す．電気通信大学201

A Multi-cut Formulation for Joint Segmentation and Tracking of Multiple Objects

Recently, Minimum Cost Multicut Formulations have been proposed and proven to be successful in both motion trajectory segmentation and multi-target tracking scenarios. Both tasks benefit from decomposing a graphical model into an optimal number of connected components based on attractive and repulsive pairwise terms. The two tasks are formulated on different levels of granularity and, accordingly, leverage mostly local information for motion segmentation and mostly high-level information for multi-target tracking. In this paper we argue that point trajectories and their local relationships can contribute to the high-level task of multi-target tracking and also argue that high-level cues from object detection and tracking are helpful to solve motion segmentation. We propose a joint graphical model for point trajectories and object detections whose Multicuts are solutions to motion segmentation {\it and} multi-target tracking problems at once. Results on the FBMS59 motion segmentation benchmark as well as on pedestrian tracking sequences from the 2D MOT 2015 benchmark demonstrate the promise of this joint approach