Cohomological parametrization

model/decoding.py

@@ -1,4 +1,4 @@
- # -*- coding: utf-8 -*-
+# -*- coding: utf-8 -*-
 """
 Use cohomology to decode datasets with circular parameters
 
@@ -14,7 +14,7 @@ from tqdm import trange
 
 import ripser
 
-from persistence import persistence
+from .persistence import persistence
 
 EPSILON = 0.0000000000001
 
@@ -48,18 +48,19 @@ def shortest_cycle(graph, node2, node1):
     while (math.isnan(prev_nodes[node1])):
         distances_buffer = distances
         for j in range(N):
-            possible_path_lengths = distances_buffer + graph[:,j]
+            possible_path_lengths = distances_buffer + graph[:, j]
             if (np.min(possible_path_lengths) < distances[j]):
                 prev_nodes[j] = np.argmin(possible_path_lengths)
                 distances[j] = np.min(possible_path_lengths)
     prev_nodes = prev_nodes.astype(int)
     cycle = [node1]
     while (cycle[0] != node2):
-        cycle.insert(0,prev_nodes[cycle[0]])
-    cycle.insert(0,node1)
+        cycle.insert(0, prev_nodes[cycle[0]])
+    cycle.insert(0, node1)
     return cycle
 
-def cohomological_parameterization(X ,cocycle_number=1, coeff=2,weighted=False):
+
+def cohomological_parameterization(X, cocycle_number=1, coeff=2, weighted=False):
     """
     Compute an angular parametrization on the data set corresponding to a given
     1-cycle
@@ -89,67 +90,67 @@ def cohomological_parameterization(X ,cocycle_number=1, coeff=2,weighted=False):
     cocycles = result['cocycles']
     D = result['dperm2all']
     dgm1 = diagrams[1]
-    idx = np.argsort(dgm1[:, 1] - dgm1[:, 0])[-cocycle_number] 
+    idx = np.argsort(dgm1[:, 1] - dgm1[:, 0])[-cocycle_number]
     cocycle = cocycles[1][idx]
     persistence(X, homdim=1, coeff=coeff, show_largest_homology=0,
                 Nsubsamples=0, save_path=None, cycle=idx)
-    thresh = dgm1[idx, 1]-EPSILON
-    
+    thresh = dgm1[idx, 1] - EPSILON
+
     # Compute connectivity
     N = X.shape[0]
-    connectivity = np.zeros([N,N])
+    connectivity = np.zeros([N, N])
     for i in range(N):
         for j in range(i):
             if D[i, j] <= thresh:
-                connectivity[i,j] = 1
-    cocycle_array = np.zeros([N,N])
-    
+                connectivity[i, j] = 1
+    cocycle_array = np.zeros([N, N])
+
     # Lift cocycle
     for i in range(cocycle.shape[0]):
-        cocycle_array[cocycle[i,0],cocycle[i,1]] = (
-            ((cocycle[i,2] + coeff/2) % coeff) - coeff/2
-            )
-        
+        cocycle_array[cocycle[i, 0], cocycle[i, 1]] = (
+                ((cocycle[i, 2] + coeff / 2) % coeff) - coeff / 2
+        )
+
     # Weights
     if (weighted):
         def real_cocycle(x):
-            real_cocycle =(
-                connectivity * (cocycle_array + np.subtract.outer(x, x))
-                )
+            real_cocycle = (
+                    connectivity * (cocycle_array + np.subtract.outer(x, x))
+            )
             return np.ravel(real_cocycle)
-        
+
         # Compute graph
         x0 = np.zeros(N)
         res = least_squares(real_cocycle, x0)
         real_cocyle_array = res.fun
-        real_cocyle_array = real_cocyle_array.reshape(N,N)
+        real_cocyle_array = real_cocyle_array.reshape(N, N)
         real_cocyle_array = real_cocyle_array - np.transpose(real_cocyle_array)
-        graph = np.array(real_cocyle_array>0).astype(float)
-        graph[graph==0] = np.inf
-        graph = (D + EPSILON) * graph   # Add epsilon to avoid NaNs
-        
+        graph = np.array(real_cocyle_array > 0).astype(float)
+        graph[graph == 0] = np.inf
+        graph = (D + EPSILON) * graph  # Add epsilon to avoid NaNs
+
         # Compute weights
-        cycle_counts = np.zeros([N,N])  
+        cycle_counts = np.zeros([N, N])
         iterator = trange(0, N, position=0, leave=True)
         iterator.set_description("Computing weights for decoding")
         for i in iterator:
             for j in range(N):
-                if (graph[i,j] != np.inf):
+                if (graph[i, j] != np.inf):
                     cycle = shortest_cycle(graph, j, i)
-                    for k in range(len(cycle)-1):
-                        cycle_counts[cycle[k], cycle[k+1]] += 1
-                
-        weights = cycle_counts / (D + EPSILON)**2
+                    for k in range(len(cycle) - 1):
+                        cycle_counts[cycle[k], cycle[k + 1]] += 1
+
+        weights = cycle_counts / (D + EPSILON) ** 2
         weights = np.sqrt(weights)
     else:
-        weights = np.outer(np.ones(N),np.ones(N))
-        
+        weights = np.outer(np.ones(N), np.ones(N))
+
     def real_cocycle(x):
-        real_cocycle =(
-            weights * connectivity * (cocycle_array + np.subtract.outer(x, x))
-            )
+        real_cocycle = (
+                weights * connectivity * (cocycle_array + np.subtract.outer(x, x))
+        )
         return np.ravel(real_cocycle)
-    
+
     # Smooth cocycle
     print("Decoding...", end=" ")
     x0 = np.zeros(N)
@@ -157,7 +158,7 @@ def cohomological_parameterization(X ,cocycle_number=1, coeff=2,weighted=False):
     decoding = res.x
     decoding = np.mod(decoding, 1)
     print("done")
-    
+
     decoding = pd.DataFrame(decoding, columns=["decoding"])
     decoding = decoding.set_index(X.index)
     return decoding
@@ -180,9 +181,9 @@ def remove_feature(X, decoding, shift=0, cut_amplitude=1.0):
         Amplitude of the cut
     """
     cuts = np.zeros(X.shape)
-    decoding = decoding.to_numpy()[:,0]
+    decoding = decoding.to_numpy()[:, 0]
     for i in range(X.shape[1]):
         effective_amplitude = cut_amplitude * (np.max(X[i]) - np.min(X[i]))
-        cuts[:,i] = effective_amplitude * ((decoding - shift) % 1)
+        cuts[:, i] = effective_amplitude * ((decoding - shift) % 1)
     reduced_data = X + cuts
-    return reduced_data
+    return reduced_data

model/persistence.py

@@ -16,7 +16,7 @@ import ripser
 from persim import plot_diagrams
 import gudhi
 
-from decorators import multi_input
+from .decorators import multi_input
 
     
 def hausdorff(data1, data2, homdim, coeff):