changed doc

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/kernels@3829 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 77b9c8a4cd00555c2930229d083a88c298c22db5

2 files changed, 20 insertions, 7 deletions

diff --git a/src/Persistence_representations/doc/Persistence_representations_doc.h b/src/Persistence_representations/doc/Persistence_representations_doc.h
index 3aa99315..a8f8ba8b 100644
--- a/src/Persistence_representations/doc/Persistence_representations_doc.h
+++ b/src/Persistence_representations/doc/Persistence_representations_doc.h
@@ -227,9 +227,19 @@ namespace Persistence_representations {
  to diagonal are given then sometimes the kernel have support that reaches the region
  below the diagonal. If the value of this parameter is true, then the values below diagonal can be erased.
 
- We also provide two methods to perform exact calculations. In both methods, the kernel is no longer provided as a filter (i.e. a square matrix---see parameters above), but rather as
- a function assigning a real value to a 2D point. In the first method, calculations are done on a grid, leading to a finite-dimensional representation.
- On the other hand, in the second method, we do not use grids, meaning that diagrams are represented as functions. Thus, only scalar products are available.
+ In addition to the previous method, we also provide two more methods to perform exact calculations, in the sense that we use functions
+ instead of matrices to define the kernel between the points of the diagrams.
+ Indeed, in both of these exact methods, the kernel is no longer provided as a square matrix, or a filter (see parameters above), but rather as
+ a function assigning a real value to a 2D point in the plane.
+
+ In the first of these exact methods, we aim at obtaining a finite-dimensional representation of the diagram, so we still use a grid of pixels.
+ On the other hand, in the second exact method, we represent diagrams implicitly as functions (i.e. infinite-dimensional representations). This way, we no longer require grids,
+ but only scalar products and distances are available with these implicit representations. This type of representations is known as
+ kernel methods (see \ref sec_persistence_kernels below for more details on kernels).
+
+ Names can be a bit confusing so we recall that, with this second exact method, we implicitly define a kernel representation of diagrams that is built from a kernel between points
+ in the plane. Hence, we have two kernels here, which are independent. One is defined between points in the plane (its type in the code is Kernel2D), and is a parameter,
+ whereas the other is defined between persistence diagrams (it is the scalar product of the infinite-dimensional representations of the diagrams).
 
  \section sec_persistence_vectors Persistence vectors
  <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Vector_distances_in_diagram <br>
@@ -255,7 +265,7 @@ namespace Persistence_representations {
 
   \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>
+ <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Persistence_heat_maps <br>
 
  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
@@ -265,9 +275,9 @@ namespace Persistence_representations {
  Examples of such algorithms include Support Vector Machines, Principal Component Analysis and Ridge Regression.
 
  There have been several attempts at defining kernels, i.e., positive semi-definite functions, between persistence diagrams within the last few years. We provide implementation
- for the <i>Sliced Wasserstein Kernel</i>---see \cite pmlr-v70-carriere17a, which takes the form of a Gaussian kernel with a specific distance between persistence diagrams
- called the <i>Sliced Wasserstein Distance</i>: \f$k(D_1,D_2)={\rm exp}\left(-\frac{SW(D_1,D_2)}{2\sigma^2}\right)\f$. Other kernels such as the Persistence Weighted Gaussian Kernel or
- the Persistence Scale Space Kernel are implemented in Persistence_heat_maps.
+ for the <i>Sliced Wasserstein kernel</i>---see \cite pmlr-v70-carriere17a, which takes the form of a Gaussian kernel with a specific distance between persistence diagrams
+ called the <i>Sliced Wasserstein distance</i>: \f$k(D_1,D_2)={\rm exp}\left(-\frac{SW(D_1,D_2)}{2\sigma^2}\right)\f$. Other kernels such as the Persistence Weighted Gaussian kernel or
+ the Persistence Scale Space kernel are implemented in Persistence_heat_maps.
 
  When launching:
 
diff --git a/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h b/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h
index 6f67f7bc..2e23f69e 100644
--- a/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h
+++ b/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h
@@ -38,6 +38,9 @@ namespace Persistence_representations {
  * \ingroup Persistence_representations
  *
  * \details
+ * In this class, we compute infinite-dimensional representations of persistence diagrams by using the
+ * Sliced Wasserstein kernel (see \ref sec_persistence_kernels for more details on kernels). We recall that infinite-dimensional
+ * representations are defined implicitly, so only scalar products and distances are available for the representations defined in this class.
  * The Sliced Wasserstein kernel is defined as a Gaussian-like kernel between persistence diagrams, where the distance used for
  * comparison is the Sliced Wasserstein distance \f$SW\f$ between persistence diagrams, defined as the integral of the 1-norm
  * between the sorted projections of the diagrams onto all lines passing through the origin: