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| author | mcarrier <mcarrier@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2018-04-23 15:22:13 +0000 |
|---|---|---|
| committer | mcarrier <mcarrier@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2018-04-23 15:22:13 +0000 |
| commit | 541284f6f1bf7d4a76daac8a52850c7162a765cb (patch) | |
| tree | 2ebecae35daf30dbcfb9c683f9587b93e117f443 /src/Persistence_representations/doc | |
| parent | 5e24206f945f66575c7c179d74e9661cf60ca3df (diff) | |
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/kernels@3387 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: 3fe2ae4af0c7cadf507fc5148c05dcf664c5e151
Diffstat (limited to 'src/Persistence_representations/doc')
| -rw-r--r-- | src/Persistence_representations/doc/Persistence_representations_doc.h | 5 |
1 files changed, 2 insertions, 3 deletions
diff --git a/src/Persistence_representations/doc/Persistence_representations_doc.h b/src/Persistence_representations/doc/Persistence_representations_doc.h index 6d4cc96c..ca283017 100644 --- a/src/Persistence_representations/doc/Persistence_representations_doc.h +++ b/src/Persistence_representations/doc/Persistence_representations_doc.h @@ -24,7 +24,6 @@ #define DOC_GUDHI_STAT_H_ namespace Gudhi { - namespace Persistence_representations { /** \defgroup Persistence_representations Persistence representations @@ -254,11 +253,11 @@ namespace Persistence_representations { -\section sec_persistence_kernels Kernels on Persistence Diagrams +\section sec_persistence_kernels Kernels on persistence diagrams <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Sliced_Wasserstein <br> <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Persistence_weighted_gaussian <br> - Kernels for Persistence Diagrams can be regarded as infinite-dimensional vectorizations. More specifically, + Kernels for persistence diagrams can be regarded as infinite-dimensional vectorizations. More specifically, they are similarity functions whose evaluations on pairs of persistence diagrams equals the scalar products between images of these pairs under a map \f$\Phi\f$ taking values in a specific (possibly non Euclidean) Hilbert space \f$k(D_i, D_j) = \langle \Phi(D_i),\Phi(D_j)\rangle\f$. Reciprocally, classical results of learning theory ensure that such a \f$\Phi\f$ exists for a given similarity function \f$k\f$ if and only if \f$k\f$ is <i>positive semi-definite</i>. |