On The Effect of Hyperedge Weights On Hypergraph Learning

Hypergraph is a powerful representation in several computer vision, machine learning and pattern recognition problems. In the last decade, many researchers have been keen to develop different hypergraph models. In contrast, no much attention has been paid to the design of hyperedge weights. However, many studies on pairwise graphs show that the choice of edge weight can significantly influence the performances of such graph algorithms. We argue that this also applies to hypegraphs. In this paper, we empirically discuss the influence of hyperedge weight on hypegraph learning via proposing three novel hyperedge weights from the perspectives of geometry, multivariate statistical analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE, Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to graph learning, several representative hyperedge weighting schemes can be concluded by our experimental studies. Moreover, the experiments also demonstrate that the combinations of such weighting schemes and conventional hypergraph models can get very promising classification and clustering performances in comparison with some recent state-of-the-art algorithms

Differential cross-section measurements for four-lepton production and implications for new physics

This thesis describes the analysis design and results of the ATLAS four-lepton measurement, using 139 fb−1 of data collected in 13 TeV proton-proton collisions at the Large Hadron Collider. The measurement is designed for maximal model-independence and inclusivity. Defined solely in terms of the final state particles, any process leading to the creation of four or more leptons is considered to be a part of the signal. The results are presented in the form of inclusive and fiducial differential cross-sections, and are corrected for detector effects via an iterative Bayesian technique. The measurement is compared to state- of-the-art Standard Model predictions, and the two are found to be consistent. Secondly, two re-interpretation studies are presented where existing precision fiducial measurements, including the aforementioned four-lepton measurement, are used to set constraints on two beyond the Standard Model theories. The first is a generic model of vector-like quarks, and the second is a model with a gauged and spontaneously broken B − L symmetry. These studies are conducted using the CONTUR re-interpretation toolkit. The derived limits are competitive with existing ATLAS limits, and exclude previously unexplored regions of parameter space