Doc+armijo

Author: tvayer

ot/gromov.py

@@ -33,12 +33,12 @@ def init_matrix(C1, C2, p, q, loss_fun='square_loss'):
         * C2 : Metric cost matrix in the target space
         * T : A coupling between those two spaces
 
-    The square-loss function L(a,b)=(1/2)*|a-b|^2 is read as :
+    The square-loss function L(a,b)=|a-b|^2 is read as :
         L(a,b) = f1(a)+f2(b)-h1(a)*h2(b) with :
-            * f1(a)=(a^2)/2
-            * f2(b)=(b^2)/2
+            * f1(a)=(a^2)
+            * f2(b)=(b^2)
             * h1(a)=a
-            * h2(b)=b
+            * h2(b)=2*b
 
     The kl-loss function L(a,b)=a*log(a/b)-a+b is read as :
         L(a,b) = f1(a)+f2(b)-h1(a)*h2(b) with :
@@ -269,7 +269,7 @@ def update_kl_loss(p, lambdas, T, Cs):
     return np.exp(np.divide(tmpsum, ppt))
 
 
-def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, amijo=False, **kwargs):
+def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs):
     """
     Returns the gromov-wasserstein transport between (C1,p) and (C2,q)
 
@@ -307,8 +307,8 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, amijo=False, **kwargs)
         Print information along iterations
     log : bool, optional
         record log if True
-    amijo : bool, optional
-        If True the steps of the line-search is found via an amijo research. Else closed form is used.
+    armijo : bool, optional
+        If True the steps of the line-search is found via an armijo research. Else closed form is used.
         If there is convergence issues use False.
     **kwargs : dict
         parameters can be directly pased to the ot.optim.cg solver
@@ -344,14 +344,14 @@ def df(G):
         return gwggrad(constC, hC1, hC2, G)
 
     if log:
-        res, log = cg(p, q, 0, 1, f, df, G0, log=True, amijo=amijo, C1=C1, C2=C2, constC=constC, **kwargs)
+        res, log = cg(p, q, 0, 1, f, df, G0, log=True, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)
         log['gw_dist'] = gwloss(constC, hC1, hC2, res)
         return res, log
     else:
-        return cg(p, q, 0, 1, f, df, G0, amijo=amijo, C1=C1, C2=C2, constC=constC, **kwargs)
+        return cg(p, q, 0, 1, f, df, G0, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)
 
 
-def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, amijo=False, **kwargs):
+def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, armijo=False, **kwargs):
     """
     Computes the FGW distance between two graphs see [3]
     .. math::
@@ -363,6 +363,7 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5,
     - M is the (ns,nt) metric cost matrix
     - :math:`f` is the regularization term ( and df is its gradient)
     - a and b are source and target weights (sum to 1)
+    - L is a loss function to account for the misfit between the similarity matrices
     The algorithm used for solving the problem is conditional gradient as discussed in  [1]_
     Parameters
     ----------
@@ -386,8 +387,8 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5,
         Print information along iterations
     log : bool, optional
         record log if True
-    amijo : bool, optional
-        If True the steps of the line-search is found via an amijo research. Else closed form is used.
+    armijo : bool, optional
+        If True the steps of the line-search is found via an armijo research. Else closed form is used.
         If there is convergence issues use False.
     **kwargs : dict
         parameters can be directly pased to the ot.optim.cg solver
@@ -415,10 +416,10 @@ def f(G):
     def df(G):
         return gwggrad(constC, hC1, hC2, G)
 
-    return cg(p, q, M, alpha, f, df, G0, amijo=amijo, C1=C1, C2=C2, constC=constC, **kwargs)
+    return cg(p, q, M, alpha, f, df, G0, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)
 
 
-def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, amijo=False, **kwargs):
+def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs):
     """
     Returns the gromov-wasserstein discrepancy between (C1,p) and (C2,q)
 
@@ -456,8 +457,8 @@ def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, amijo=False, **kwargs
         Print information along iterations
     log : bool, optional
         record log if True
-    amijo : bool, optional
-        If True the steps of the line-search is found via an amijo research. Else closed form is used.
+    armijo : bool, optional
+        If True the steps of the line-search is found via an armijo research. Else closed form is used.
         If there is convergence issues use False.
     Returns
     -------
@@ -487,7 +488,7 @@ def f(G):
 
     def df(G):
         return gwggrad(constC, hC1, hC2, G)
-    res, log = cg(p, q, 0, 1, f, df, G0, log=True, amijo=amijo, C1=C1, C2=C2, constC=constC, **kwargs)
+    res, log = cg(p, q, 0, 1, f, df, G0, log=True, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)
     log['gw_dist'] = gwloss(constC, hC1, hC2, res)
     log['T'] = res
     if log:
@@ -890,7 +891,7 @@ def fgw_barycenters(N, Ys, Cs, ps, lambdas, alpha, fixed_structure=False, fixed_
                     p=None, loss_fun='square_loss', max_iter=100, tol=1e-9,
                     verbose=False, log=True, init_C=None, init_X=None):
     """
-    Compute the fgw barycenter as presented eq (5) in [3].
+    Compute the fgw barycenter as presented eq (5) in [24].
     ----------
     N : integer
         Desired number of samples of the target barycenter
@@ -1065,7 +1066,7 @@ def update_sructure_matrix(p, lambdas, T, Cs):
 
 def update_feature_matrix(lambdas, Ys, Ts, p):
     """
-    Updates the feature with respect to the S Ts couplings. See "Solving the barycenter problem with Block Coordinate Descent (BCD)" in [3]
+    Updates the feature with respect to the S Ts couplings. See "Solving the barycenter problem with Block Coordinate Descent (BCD)" in [24]
     calculated at each iteration
     Parameters
     ----------

ot/optim.py

@@ -73,13 +73,13 @@ def phi(alpha1):
 
 
 def do_linesearch(cost, G, deltaG, Mi, f_val,
-                  amijo=True, C1=None, C2=None, reg=None, Gc=None, constC=None, M=None):
+                  armijo=True, C1=None, C2=None, reg=None, Gc=None, constC=None, M=None):
     """
     Solve the linesearch in the FW iterations
     Parameters
     ----------
     cost : method
-        The FGW cost
+        Cost in the FW for the linesearch
     G : ndarray, shape(ns,nt)
         The transport map at a given iteration of the FW
     deltaG : ndarray (ns,nt)
@@ -88,21 +88,21 @@ def do_linesearch(cost, G, deltaG, Mi, f_val,
         Cost matrix of the linearized transport problem. Corresponds to the gradient of the cost
     f_val :  float
         Value of the cost at G
-    amijo : bool, optionnal
-            If True the steps of the line-search is found via an amijo research. Else closed form is used.
+    armijo : bool, optionnal
+            If True the steps of the line-search is found via an armijo research. Else closed form is used.
             If there is convergence issues use False.
     C1 : ndarray (ns,ns), optionnal
-        Structure matrix in the source domain. Only used when amijo=False
+        Structure matrix in the source domain. Only used when armijo=False
     C2 : ndarray (nt,nt), optionnal
-        Structure matrix in the target domain. Only used when amijo=False
+        Structure matrix in the target domain. Only used when armijo=False
     reg : float, optionnal
-          Regularization parameter. Corresponds to the alpha parameter of FGW. Only used when amijo=False
+          Regularization parameter. Only used when armijo=False
     Gc : ndarray (ns,nt)
-        Optimal map found by linearization in the FW algorithm. Only used when amijo=False
+        Optimal map found by linearization in the FW algorithm. Only used when armijo=False
     constC : ndarray (ns,nt)
-             Constant for the gromov cost. See [3]. Only used when amijo=False
+             Constant for the gromov cost. See [24]. Only used when armijo=False
     M : ndarray (ns,nt), optionnal
-        Cost matrix between the features. Only used when amijo=False
+        Cost matrix between the features. Only used when armijo=False
     Returns
     -------
     alpha : float
@@ -118,7 +118,7 @@ def do_linesearch(cost, G, deltaG, Mi, f_val,
         "Optimal Transport for structured data with application on graphs"
         International Conference on Machine Learning (ICML). 2019.
     """
-    if amijo:
+    if armijo:
         alpha, fc, f_val = line_search_armijo(cost, G, deltaG, Mi, f_val)
     else:  # requires symetric matrices
         dot1 = np.dot(C1, deltaG)