Abstract
The properties of the VC-dimension under various compositions are well-understood, but this is much less the case for classes of continuous functions. In this brief, we show that a commonly used scale-sensitive dimension, \(V-\gamma \) , is much less well-behaved under Minkowski summation than its VC cousin, while the fat-shattering dimension retains some compositional similarity to the VC-dimension. As an application, we analyze the fat-shattering dimension of trigonometric functions and series.
Original language | English |
---|---|
Article number | 2327065 |
Pages (from-to) | 2309-2312 |
Number of pages | 4 |
Journal | IEEE Transactions on Neural Networks and Learning Systems |
Volume | 25 |
Issue number | 12 |
DOIs | |
State | Published - 1 Dec 2014 |
Keywords
- Combinatorial dimension
- Minkowski addition
- fat-shattering
- scale-sensitive.
ASJC Scopus subject areas
- Software
- Computer Science Applications
- Computer Networks and Communications
- Artificial Intelligence