# Invariance in Kernel Methods

Entwicklung effizienter Klassifikatoren. Vorrangig wird an Support Vektor Maschinen (SVM) gearbeitet.

Modern techniques for data analysis and machine learning are so called kernel methods. The most famous and successful one is represented by the support-vector machine for classification or regression tasks. The fundamental ingredient in these methods is the choice of a kernel function, which computes a similarity measure between two input objects. Many simple kernel functions already produce very good results on various application fields. Experience has demonstrated that these impressive results even can substantially be improved by incorporating problem specific a-priori knowledge. Intuitively this is also perspicuous, as e.g. elimination of known redundancies of data in a preprocessing stage will place emphasis on the non redundant contributions and simplify the further processing chain.

This project focusses on a certain kind of a-priori knowledge namely invariance knowledge. This comprises explicit or implicit knowledge of pattern transformations that do not or only slightly change the pattern's inherent meaning.

Explicit transformation knowledge means that one can explicitly parametrize the transformations of a pattern. Examples are global rigid transformations of 2D/ 3D objects in object detection or non rigid resp. only local transformation like slight stretching, shifting, rotation of characters in optical character recognition. The mathematical modelling is realized by transformation groups, subsets of transformations groups or arbitrary sets of transformations.

Implicit invariance means that the variations are implicitly captured by sophisticated comparison measures between objects. Examples are dynamic time warping techniques, which capture time variations in signals. Here an explicit parameterization would require arbitary many parameters. More generally, implicit invariances are often given by distance measures between objects.

These kinds of invariances are incorporated in kernel functions by approximation or integration techniques. Theoretical investigation of the kernels is performed and applicability is demonstrated by support vector classification of various types of data like optical characters, handwriting sequences or pollen classification.