[WIP] Refactor polynomial approximations and filtering in general

doc/history.rst

@@ -5,6 +5,20 @@ History
 0.6.0 (xxxx-xx-xx)
 ------------------
 
+* Filters approximated by Chebyshev polynomials are now implemented as separate
+  filters, i.e. you need to do Chebyshev(Heat(tau=1), order=10).filter(signal) to
+  filter a signal with a heat kernel approximated by a Chebyshev polynomial of
+  order 10. The reasons are multiple:
+  - They are arguably different filters.
+    Try Heat().plot() and Chebyshev(Heat(), order=1).plot().
+  - It allows to visualize the approximated filters in the spectral domain, and
+    compare them with their continuous counterpart or other approximations.
+  - One can now instantiates filters which are solely defined by their Chebyshev
+    coefficients. That is the case when learning them with back-propagation in a
+    neural network setting, and it's useful to (i) visualize the learned filters
+    in the spectral and vertex domains, and (ii) to compute and visualize the
+    feature maps.
+  See the new tutorial on filter approximations for usage.
 * print(graph) and print(filters) now show valuable information.
 * Building a graph object is much faster.
 * New rectangular filter (low-pass and band-pass).

pygsp/filters/__init__.py

@@ -20,6 +20,7 @@
     Filter.synthesize
     Filter.compute_frame
     Filter.estimate_frame_bounds
+    Filter.approximate
     Filter.plot
     Filter.localize
 
@@ -85,6 +86,10 @@
 
 **Chebyshev polynomials**
 
+.. autosummary::
+
+    Chebyshev
+
 .. autosummary::
 
     compute_cheby_coeff
@@ -130,7 +135,9 @@
     'lanczos_op'
 ]
 
-__all__ = _FILTERS + _APPROXIMATIONS
+__all__ = _FILTERS + _APPROXIMATIONS + ['Chebyshev']
 
 _utils.import_classes(_FILTERS, 'filters', 'filters')
-_utils.import_functions(_APPROXIMATIONS, 'filters.approximations', 'filters')
+_utils.import_functions(_APPROXIMATIONS, 'filters.approximations_old', 'filters')
+
+from .approximations import *