Improve spectral clustering, correct bug in Modularity matrix

Author: Jonas1312

src/main.py

@@ -20,7 +20,7 @@ def main():
  #----------------------------------------------------------------------
  # Stochastic block model parameters
  #----------------------------------------------------------------------
- n_vertices = 3000 # number of vertices
+ n_vertices = 200 # number of vertices
  n_communities = 2 # number of communities
 
  # Fixing cin > cout is referred to as the assortative case, because vertices
@@ -29,7 +29,7 @@ def main():
  # is that any tractable algorithm will only detect communities if
  # abs(cin - cout) > n_communities*sqrt(c), where c is the average degree.
  cin = 15
- cout = 5
+ cout = 1
  probability_matrix = (1.0/n_vertices)*(np.full((n_communities,n_communities), cout, dtype=int) + np.diag([cin-cout]*n_communities)) # matrix of edge probabilities
  sbm = SBM(n_vertices, n_communities, probability_matrix)
  print("Average degree: {}, abs(cin - cout): {}, n_commuties*sqrt(c): {}".format(sbm.average_degree, abs(cin-cout), n_communities*np.sqrt(sbm.average_degree)))
@@ -57,13 +57,13 @@ def main():
  n_clusters = 2
  if n_clusters != n_communities:
  print("Number of clusters ({}) is not equal to number of communities generated by the SBM ({})!".format(n_clusters, n_communities))
- spectral_labels, eigvals, eigvects, W = SpectralClustering(n_clusters, BetheHessian(sbm.adjacency_matrix)) # spectral clustering
+ spectral_labels, eigvals, eigvects, W = SpectralClustering(n_clusters, ModularityMatrix(sbm.adjacency_matrix), "ModularityMatrix") # spectral clustering
  well_placed_vertices = pg.permutation_calculator(sbm.community_labels, spectral_labels, n_clusters)
  print("Spectral clustering accuracy: " + str(100*well_placed_vertices/n_vertices) + "%")
 
  # Eigenvalues and eigenvectors
  if n_vertices <= PLOT_MAX_NODES:
- plt.title("Histogram of Bethe Hessian matrix eigenvalues")
+ plt.title("Histogram of matrix eigenvalues")
  plt.hist(eigvals, bins=100) # plot histogram of the eigenvalues
  if n_clusters <= 2:
  plt.figure()

src/matrices.py

@@ -28,8 +28,8 @@ def ModularityMatrix(adjacency_matrix):
  :param matrix: np.array symetric square matrix
  :return: np.array square matrix
  """
- d = np.sum(adjacency_matrix, axis=0)
- return adjacency_matrix - (np.dot(d, d.T) / np.sum(d))
+ d = np.matrix(np.sum(adjacency_matrix, axis=0))
+ return adjacency_matrix - (np.dot(d.T, d).astype(float) / np.sum(d))
 
 # ----------------------------------------------------------------------
 def BetheHessian(adjacency_matrix, r=None):

src/spectralClustering.py

@@ -9,10 +9,15 @@
 from sklearn.cluster import KMeans
 
 #----------------------------------------------------------------------
-def SpectralClustering(n_clusters, matrix):
+def SpectralClustering(n_clusters, matrix, matrix_name):
  """"""
  eigvals, eigvects = np.linalg.eig(matrix) # eigvects[:,i] is the eigenvector corresponding to the eigenvalue eigvals[i]
- indices = eigvals.argsort()[:n_clusters] # find the 'n_clusters' smallest eigenvalues indices
+ if matrix_name in ["BetheHessian", "LaplacianMatrix"]:
+ indices = eigvals.argsort()[:n_clusters] # find the 'n_clusters' isolated eigenvalues
+ elif matrix_name in ["ModularityMatrix"]:
+ indices = eigvals.argsort()[-n_clusters:] # find the 'n_clusters' isolated eigenvalues
+ else:
+ raise ValueError("Unknown matrix name")
  W = eigvects[:,indices]
  kmeans = KMeans(n_clusters=n_clusters).fit(W) # kmeans
  return kmeans.labels_, eigvals, eigvects, W