Fast, practical and effective algorithms for clustering with advice. To maintain a safe and healthy society, government and industry need high quality immunization and national security databases. Since we cannot afford to have duplicate, incomplete and conflicting records that refer to the same person, we unify them by identifying clusters of related records.
In the emerging field of functional genomics, diagnosis of certain diseases is enhanced by determining which genes act together. Diffe ....Fast, practical and effective algorithms for clustering with advice. To maintain a safe and healthy society, government and industry need high quality immunization and national security databases. Since we cannot afford to have duplicate, incomplete and conflicting records that refer to the same person, we unify them by identifying clusters of related records.
In the emerging field of functional genomics, diagnosis of certain diseases is enhanced by determining which genes act together. Different experimental runs might result in different clusterings of genes: we need one consensus clustering that summarizes the experimental outcomes.
Cleaning databases and combining clusterings by hand would require vast amounts of time. This project will result in faster and more accurate computational procedures.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE150100240
Funder
Australian Research Council
Funding Amount
$315,000.00
Summary
Geometry and Conditioning in Structured Conic Problems. Conic programming allows one to model and solve large industrial problems via modern optimisation methods, such as interior-point algorithms. These methods are efficient and reliable in solving a vast number of problems, however, they fail on a relatively small but significant set of ill-posed instances, thus affecting the overall reliability of the technique. The reason for such behaviour is profound and constitutes one of the major unsolv ....Geometry and Conditioning in Structured Conic Problems. Conic programming allows one to model and solve large industrial problems via modern optimisation methods, such as interior-point algorithms. These methods are efficient and reliable in solving a vast number of problems, however, they fail on a relatively small but significant set of ill-posed instances, thus affecting the overall reliability of the technique. The reason for such behaviour is profound and constitutes one of the major unsolved problems in real complexity: there is no known algorithm that solves conic problems with real data in polynomial time. The project aims to develop a deep understanding of the geometry of conic problems, aiming for the resolution of this fundamental problem in computational theory.Read moreRead less
Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unit ....Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.Read moreRead less