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oapen-20.500.12657-460362023-01-31T18:46:10Z Graphs for Pattern Recognition Gainanov, Damir Computers Artificial Intelligence Computer Vision & Pattern Recognition Technology & Engineering Agriculture bic Book Industry Communication::U Computing & information technology::UY Computer science::UYQ Artificial intelligence::UYQV Computer vision bic Book Industry Communication::T Technology, engineering, agriculture::TV Agriculture & farming This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition. Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important special subclass of infeasible systems of constraints with a monotonicity property – systems whose multi-indices of feasible subsystems form abstract simplicial complexes (independence systems), which are fundamental objects of combinatorial topology. The methods of data mining and machine learning discussed in this monograph form the foundation of technologies like big data and deep learning, which play a growing role in many areas of human-technology interaction and help to find solutions, better solutions and excellent solutions. 2021-01-12T04:31:59Z 2021-01-12T04:31:59Z 2016 book 9783110481068 https://library.oapen.org/handle/20.500.12657/46036 eng application/pdf n/a external_content.pdf De Gruyter De Gruyter https://doi.org/10.1515/9783110481068 https://doi.org/10.1515/9783110481068 2b386f62-fc18-4108-bcf1-ade3ed4cf2f3 b818ba9d-2dd9-4fd7-a364-7f305aef7ee9 9783110481068 Knowledge Unlatched (KU) De Gruyter Knowledge Unlatched open access
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This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition.
Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important special subclass of infeasible systems of constraints with a monotonicity property – systems whose multi-indices of feasible subsystems form abstract simplicial complexes (independence systems), which are fundamental objects of combinatorial topology.
The methods of data mining and machine learning discussed in this monograph form the foundation of technologies like big data and deep learning, which play a growing role in many areas of human-technology interaction and help to find solutions, better solutions and excellent solutions.
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