Cover's Theorem
Encyclopedia
Cover's Theorem is a statement in computational learning theory
and is one of the primary theoretical motivations for the use of non-linear kernel methods
in machine learning
applications. The theorem states that given a set of training data that is not linearly separable
, one can with high probability transform it into a training set that is linearly separable by projecting it into a higher dimensional space via some non-linear transformation.
Computational learning theory
In theoretical computer science, computational learning theory is a mathematical field related to the analysis of machine learning algorithms.-Overview:Theoretical results in machine learning mainly deal with a type of...
and is one of the primary theoretical motivations for the use of non-linear kernel methods
Kernel methods
In computer science, kernel methods are a class of algorithms for pattern analysis, whose best known elementis the support vector machine...
in machine learning
Machine learning
Machine learning, a branch of artificial intelligence, is a scientific discipline concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases...
applications. The theorem states that given a set of training data that is not linearly separable
Linearly separable
In geometry, two sets of points in a two-dimensional space are linearly separable if they can be completely separated by a single line. In general, two point sets are linearly separable in n-dimensional space if they can be separated by a hyperplane....
, one can with high probability transform it into a training set that is linearly separable by projecting it into a higher dimensional space via some non-linear transformation.