Labeled Sample Compression Schemes for Complexes of Oriented Matroids

COMs: Complexes of oriented matroids

In his seminal 1983 paper, Jim Lawrence introduced lopsided sets and featured them as asymmetric counterparts of oriented matroids, both sharing the key property of strong elimination. Moreover, symmetry of faces holds in both structures as well as in the so-called affine oriented matroids. These two fundamental properties (formulated for covectors) together lead to the natural notion of “condi...

Labeled Compression Schemes for Extremal Classes

It is a long-standing open problem whether there exists a compression scheme whose size is of the order of the VapnikChervonienkis (VC) dimension d. Recently compression schemes of size exponential in d have been found for any concept class of VC dimension d. Previously, compression schemes of size d have been given for maximum classes, which are special concept classes whose size equals an upp...

On tope graphs of complexes of oriented matroids

We give two graph theoretical characterizations of tope graphs of (complexes of) oriented matroids. The first is in terms of excluded partial cube minors, the second is that all antipodal subgraphs are gated. A direct consequence is a third characterization in terms of zone graphs of tope graphs. Further corollaries include a characterization of topes of oriented matroids due to da Silva, anoth...

Fachbereich 3 Mathematik Oriented Matroids Oriented Matroids

Sample-oriented Domain Adaptation for Image Classification

Image processing is a method to perform some operations on an image, in order to get an enhanced image or to extract some useful information from it. The conventional image processing algorithms cannot perform well in scenarios where the training images (source domain) that are used to learn the model have a different distribution with test images (target domain). Also, many real world applicat...