def smatrix_from_nd_idx(idx, nn=0):
"""Create a sparse adjacency matrix from nd index system
Parameters
----------
idx:array of shape (n_samples, dim), type int
indexes of certain positions in a nd space
nn: int, optional
nd neighboring system, unused at the moment
Returns
-------
coo_mat: a sparse coo matrix,
adjacency of the neighboring system
"""
n = idx.shape[0]
dim = idx.shape[1]
nidx = idx - idx.min(0)
eA = []
eB = []
# compute the edges in each possible direction
for d in range(dim):
mi = nidx.max(0) + 2
a = np.hstack((1, np.cumprod(mi[:dim - 1])))
v1 = np.dot(nidx, a)
assert(np.size(v1) == np.size(np.unique(v1)))
o1 = np.argsort(v1)
sv1 = v1[o1]
nz = np.squeeze(np.nonzero(sv1[:n - 1] - sv1[1:] == - 1))
nz = np.reshape(nz, np.size(nz))
eA.append(o1[nz])
eB.append(o1[nz + 1])
nidx = np.roll(nidx, 1, 1)
eA = np.concatenate(eA)
eB = np.concatenate(eB)
E = 2 * np.size(eA)
# create a graph structure
if E == 0:
return sp.coo_matrix((n, n))
edges = np.vstack((np.hstack((eA, eB)), np.hstack((eB, eA)))).T
weights = np.ones(E)
G = WeightedGraph(n, edges, weights)
return G.to_coo_matrix()
def smatrix_from_nd_idx(idx, nn=0):
"""Create a sparse adjacency matrix from nd index system
Parameters
----------
idx:array of shape (n_samples, dim), type int
indexes of certain positions in a nd space
nn: int, optional
nd neighboring system, unused at the moment
Returns
-------
coo_mat: a sparse coo matrix,
adjacency of the neighboring system
"""
n = idx.shape[0]
dim = idx.shape[1]
nidx = idx - idx.min(0)
eA = []
eB = []
# compute the edges in each possible direction
for d in range(dim):
mi = nidx.max(0) + 2
a = np.hstack((1, np.cumprod(mi[:dim - 1])))
v1 = np.dot(nidx, a)
assert (np.size(v1) == np.size(np.unique(v1)))
o1 = np.argsort(v1)
sv1 = v1[o1]
nz = np.squeeze(np.nonzero(sv1[:n - 1] - sv1[1:] == -1))
nz = np.reshape(nz, np.size(nz))
eA.append(o1[nz])
eB.append(o1[nz + 1])
nidx = np.roll(nidx, 1, 1)
eA = np.concatenate(eA)
eB = np.concatenate(eB)
E = 2 * np.size(eA)
# create a graph structure
if E == 0:
return sp.coo_matrix((n, n))
edges = np.vstack((np.hstack((eA, eB)), np.hstack((eB, eA)))).T
weights = np.ones(E)
G = WeightedGraph(n, edges, weights)
return G.to_coo_matrix()
def topology(self):
"""returns a sparse matrix that represents the connectivity in self
"""
E = len(self.triangles)
edges = np.zeros((3 * E, 2))
weights = np.zeros(3 * E)
for i in range(E):
sa, sb, sc = self.triangles[i]
edges[3 * i] = np.array([sa, sb])
edges[3 * i + 1] = np.array([sa, sc])
edges[3 * i + 2] = np.array([sb, sc])
G = WeightedGraph(self.V, edges, weights)
# symmeterize the graph
G.symmeterize()
# remove redundant edges
G = G.cut_redundancies()
# make it a metric graph
G.set_euclidian(self.coord)
return G.to_coo_matrix()
def topology(self):
"""Returns a sparse matrix that represents the connectivity in self
"""
E = len(self.triangles)
edges = np.zeros((3 * E, 2))
weights = np.ones(3 * E)
for i in range(E):
sa, sb, sc = self.triangles[i]
edges[3 * i] = np.array([sa, sb])
edges[3 * i + 1] = np.array([sa, sc])
edges[3 * i + 2] = np.array([sb, sc])
G = WeightedGraph(self.V, edges, weights)
# symmeterize the graph
G = G.symmeterize()
# remove redundant edges
G = G.cut_redundancies()
# make it a metric graph
G.set_euclidian(self.coord)
return G.to_coo_matrix()
import numpy as np
from numpy.random import randn, rand
import matplotlib.pylab as mp
from nipy.algorithms.graph import WeightedGraph
from nipy.algorithms.clustering.hierarchical_clustering import ward
# n = number of points, k = number of nearest neighbours
n = 100
k = 5
verbose = 0
X = randn(n, 2)
X[:np.ceil(n / 3)] += 3
G = WeightedGraph(n)
G.knn(X, 5)
tree = ward(G, X, verbose)
threshold = .5 * n
u = tree.partition(threshold)
mp.figure(figsize=(12, 6))
mp.subplot(1, 3, 1)
for i in range(u.max()+1):
mp.plot(X[u == i, 0], X[u == i, 1], 'o', color=(rand(), rand(), rand()))
mp.axis('tight')
mp.axis('off')
mp.title('clustering into clusters \n of inertia < %g' % threshold)
