instruction:
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.
question:
Normalized graph cut (NGC) has become a popular research topic due to its wide applications in a large variety of areas like machine learning and very large scale integration (VLSI) circuit design. Most of traditional NGC methods are based on pairwise relationships (similarities). However, in real-world applications relationships among the vertices (objects) may be more complex than pairwise, which are typically represented as hyperedges in hypergraphs. Thus, normalized hypergraph cut (NHC) has attracted more and more attention. Existing NHC methods cannot achieve satisfactory performance in real applications. In this paper, we propose a novel relaxation approach, which is called relaxed NHC (RNHC), to solve the NHC problem. Our model is defined as an optimization problem on the Stiefel manifold. To solve this problem, we resort to the Cayley transformation to devise a feasible learning algorithm. Experimental results on a set of large hypergraph benchmarks for clustering and partitioning in VLSI domain show that RNHC can outperform the state-of-the-art methods.
answer:
A New Relaxation Approach to Normalized Hypergraph Cut

question:
This manuscript presents a trust computation for international relations and its calculus, which related to Bayesian inference, Dempster-Shafer theory and subjective logic. We proposed a method that allows a trust computation which is previously subjective and incomputable. An example of case study for the trust computation is the United States of AmericaGreat Britain relations. The method supports decision makers in a government such as foreign ministry, defense ministry, presidential or prime minister office. The Department of Defense (DoD) may use our method to determine a nation that can be known as a friendly, neutral or hostile nation.
answer:
A Mathematical Trust Algebra for International Nation Relations Computation and Evaluation

question:
Stochastic gradient-boosted decision trees are widely employed for multivariate classification and regression tasks. This paper presents a speed-optimized and cache-friendly implementation for multivariate classification called FastBDT. FastBDT is one order of magnitude faster during the fitting-phase and application-phase, in comparison with popular implementations in software frameworks like TMVA, scikit-learn and XGBoost. The concepts used to optimize the execution time and performance studies are discussed in detail in this paper. The key ideas include: An equal-frequency binning on the input data, which allows replacing expensive floating-point with integer operations, while at the same time increasing the quality of the classification; a cache-friendly linear access pattern to the input data, in contrast to usual implementations, which exhibit a random access pattern. FastBDT provides interfaces to C/C++, Python and TMVA. It is extensively used in the field of high energy physics by the Belle II experiment.
answer:
A speed-optimized and cache-friendly implementation of stochastic gradient-boosted decision trees for multivariate classification