def join_CCs_simple(X, W, num_ccs=1, verbose=False):
"""Old method for connecting the graph. Use join_CCs now."""
n, labels = connected_components(W, directed=False, return_labels=True)
CC_labels = labels
while n > num_ccs:
if verbose:
print n, 'connected components'
Dcenter, min_edge_idxs = inter_cluster_distance(X, n, labels)
p_inds,q_inds = min_k_indices(Dcenter, 2).T # self + 1 == 2
ii,jj = min_edge_idxs[p_inds,q_inds].T
W[ii,jj] = 1
W[jj,ii] = 1
n, labels = connected_components(W, directed=False, return_labels=True)
return CC_labels
def grow_trees(X, W, embed_dim, verbose=False):
W = W.astype(int)
dist_thresh = 0
while True:
n, labels = connected_components(W, directed=False, return_labels=True)
tree_sizes = np.bincount(labels)
min_tree_size = tree_sizes.min()
if min_tree_size > embed_dim:
break
Dcenter, min_edge_idxs = inter_cluster_distance(X, n, labels)
pairs = min_k_indices(Dcenter, 2) # self + 1 == 2
ninds = pairs[tree_sizes == min_tree_size]
meta_edge_lengths = Dcenter[ninds[:,0],ninds[:,1]]
dist_thresh = max(dist_thresh, np.max(meta_edge_lengths))
if verbose:
print n, 'CCs. dist thresh:', dist_thresh
# modify W to connect edges between nearby CCs
assert _connect_meta_edges(X,W,None,labels,ninds,dist_thresh=dist_thresh)[0]
return W
def join_CCs(X, W, embed_dim, num_ccs=1, max_angle=0.3, verbose=False):
n, labels = connected_components(W, directed=False, return_labels=True)
# compute linear subspaces for each connected component (assumed to be local+linear)
CC_planes, _ = cluster_subspaces(X, embed_dim, n, labels)
CC_labels = labels # keep around the original labels that go with CC_planes
angle_thresh = 0.1
while n > num_ccs:
# compute the distance between all clusters
# (by finding the distance between the closest 2 member points)
Dcenter, min_edge_idxs = inter_cluster_distance(X, n, labels)
# Find "meta-edges" between clusters (k=1)
ninds = min_k_indices(Dcenter, 2) # self + 1 == 2
meta_edge_lengths = Dcenter[ninds[:,0],ninds[:,1]]
dist_thresh = np.median(meta_edge_lengths)
if verbose:
print n, 'CCs'
# convert ninds to CC_ninds (back to the CC_labels space, via W-space)
CC_ninds = CC_labels[min_edge_idxs[ninds[:,0],ninds[:,1]]]
# modify W to connect edges between nearby CCs
while True:
if verbose:
print 'DT:', dist_thresh, 'AT:', angle_thresh
done, minD, minF = _connect_meta_edges(X, W, CC_planes, CC_labels, CC_ninds,
dist_thresh=dist_thresh,
angle_thresh=angle_thresh)
if done:
break
elif angle_thresh < minF <= max_angle:
angle_thresh = minF
elif dist_thresh < minD:
if np.isinf(minD):
max_angle += 0.1 # TODO: configure the step-up amount
angle_thresh = min(minF, max_angle)
if verbose:
print 'increasing max_angle to', max_angle
else:
dist_thresh = minD
else:
assert False, "Impossible state: can't increase dist_thresh enough to make a connection"
# recalc CCs and repeat (keeping the original CC_planes!) until there's only one left.
n, labels = connected_components(W, directed=False, return_labels=True)
return CC_labels, angle_thresh
