Abstract
Kernels have proven useful for machine learning, data mining, and computer vision as they provide a means to derive non-linear variants of learning, optimization or classification strategies from linear ones. A central question when applying a kernel-based method is the choice and the design of the kernel function. This paper provides a novel view on kernels based on fuzzy logical concepts that allows to incorporate prior knowledge in the design process. It is demonstrated that kernels that map to the unit interval and have constantly 1 in their diagonals can be represented by a commonly used fuzzy-logical formula for representing fuzzy relations. This means that a large and important class of kernels can be represented by fuzzy logical concepts. Beside this result which only guarantees the existence of such a representation, constructive examples are presented.
| Original language | English |
|---|---|
| Title of host publication | Proc. 15th IEEE Int. Conf. on Fuzzy Systems |
| Pages | 10217-10223 |
| Number of pages | 7 |
| Publication status | Published - Jul 2006 |
Fields of science
- 101004 Biomathematics
- 101027 Dynamical systems
- 101028 Mathematical modelling
- 101029 Mathematical statistics
- 101014 Numerical mathematics
- 101015 Operations research
- 101016 Optimisation
- 101017 Game theory
- 101018 Statistics
- 101019 Stochastics
- 101024 Probability theory
- 101026 Time series analysis
- 102 Computer Sciences
- 102001 Artificial intelligence
- 102003 Image processing
- 102004 Bioinformatics
- 102013 Human-computer interaction
- 102018 Artificial neural networks
- 102019 Machine learning
- 103029 Statistical physics
- 106005 Bioinformatics
- 106007 Biostatistics
- 202017 Embedded systems
- 202035 Robotics
- 202036 Sensor systems
- 202037 Signal processing
- 305901 Computer-aided diagnosis and therapy
- 305905 Medical informatics
- 305907 Medical statistics
- 102032 Computational intelligence
- 102033 Data mining
- 101031 Approximation theory