def eccentricity(data, exponent=1., metricpar={}, callback=None):
if data.ndim==1:
assert metricpar=={}, 'No optional parameter is allowed for a dissimilarity matrix.'
ds = squareform(data, force='tomatrix')
if exponent in (np.inf, 'Inf', 'inf'):
return ds.max(axis=0)
elif exponent==1.:
ds = np.power(ds, exponent)
return ds.sum(axis=0)/float(np.alen(ds))
else:
ds = np.power(ds, exponent)
return np.power(ds.sum(axis=0)/float(np.alen(ds)), 1./exponent)
else:
progress = progressreporter(callback)
N = np.alen(data)
ecc = np.empty(N)
if exponent in (np.inf, 'Inf', 'inf'):
for i in range(N):
ecc[i] = cdist(data[(i,),:], data, **metricpar).max()
progress((i+1)*100//N)
elif exponent==1.:
for i in range(N):
ecc[i] = cdist(data[(i,),:], data, **metricpar).sum()/float(N)
progress((i+1)*100//N)
else:
for i in range(N):
dsum = np.power(cdist(data[(i,),:], data, **metricpar),
exponent).sum()
ecc[i] = np.power(dsum/float(N), 1./exponent)
progress((i+1)*100//N)
return ecc
def eccentricity(data, exponent=1., metricpar={}, callback=None):
if data.ndim==1:
assert metricpar=={}, 'No optional parameter is allowed for a dissimilarity matrix.'
ds = squareform(data, force='tomatrix')
if exponent in (np.inf, 'Inf', 'inf'):
return ds.max(axis=0)
elif exponent==1.:
ds = np.power(ds, exponent)
return ds.sum(axis=0)/float(np.alen(ds))
else:
ds = np.power(ds, exponent)
return np.power(ds.sum(axis=0)/float(np.alen(ds)), 1./exponent)
else:
progress = progressreporter(callback)
N = np.alen(data)
ecc = np.empty(N)
if exponent in (np.inf, 'Inf', 'inf'):
for i in range(N):
ecc[i] = cdist(data[(i,),:], data, **metricpar).max()
progress((i+1)*100//N)
elif exponent==1.:
for i in range(N):
ecc[i] = cdist(data[(i,),:], data, **metricpar).sum()/float(N)
progress((i+1)*100//N)
else:
for i in range(N):
dsum = np.power(cdist(data[(i,),:], data, **metricpar),
exponent).sum()
ecc[i] = np.power(dsum/float(N), 1./exponent)
progress((i+1)*100//N)
return ecc
def nearest_neighbors_from_dm(X, k, callback=None):
''' This is inefficient. To be done:
(1) Do not fully sort every row of the distance matrix but find the
first k=lo elements.
(2) Use the compressed distance matrix, not the square form.
Both improvements are realized in cmappertools 1.0.5.
'''
progress = progressreporter(callback)
D = squareform(X, force='tomatrix')
N = np.alen(D)
j = np.empty((N,k), dtype=np.intp)
d = np.empty((N,k))
for i, row in enumerate(D):
j[i] = np.argsort(row)[:k]
d[i] = D[i,j[i]]
progress((i+1)*100//N)
return d, j
def nearest_neighbors_from_dm(X, k, callback=None):
''' This is inefficient. To be done:
(1) Do not fully sort every row of the distance matrix but find the
first k=lo elements.
(2) Use the compressed distance matrix, not the square form.
Both improvements are realized in cmappertools 1.0.5.
'''
progress = progressreporter(callback)
D = squareform(X, force='tomatrix')
N = np.alen(D)
j = np.empty((N,k), dtype=np.intp)
d = np.empty((N,k))
for i, row in enumerate(D):
j[i] = np.argsort(row)[:k]
d[i] = D[i,j[i]]
progress((i+1)*100//N)
return d, j
def Gauss_density(data, sigma, metricpar={}, callback=None):
denom = -2.*sigma*sigma
if data.ndim==1:
assert metricpar=={}, ('No optional parameter is allowed for a '
'dissimilarity matrix.')
ds = squareform(data, force='tomatrix')
dd = np.exp(ds*ds/denom)
# no normalization since the dimensionality is not known
#dd = 1/(N*(sqrt(2*pi)*sigma)^n)*exp(-ds*ds/(2*sigma*sigma)),
# where N=#samples, n=dimensionality
dens = dd.sum(axis=0)
else:
progress = progressreporter(callback)
N = np.alen(data)
dens = np.empty(N)
for i in range(N):
d = cdist(data[(i,),:], data, **metricpar)
dens[i] = np.exp(d*d/denom).sum()
progress(((i+1)*100//N))
dens /= N*np.power(np.sqrt(2*np.pi)*sigma,data.shape[1])
return dens
def Gauss_density(data, sigma, metricpar={}, callback=None):
denom = -2.*sigma*sigma
if data.ndim==1:
assert metricpar=={}, ('No optional parameter is allowed for a '
'dissimilarity matrix.')
ds = squareform(data, force='tomatrix')
dd = np.exp(ds*ds/denom)
# no normalization since the dimensionality is not known
#dd = 1/(N*(sqrt(2*pi)*sigma)^n)*exp(-ds*ds/(2*sigma*sigma)),
# where N=#samples, n=dimensionality
dens = dd.sum(axis=0)
else:
progress = progressreporter(callback)
N = np.alen(data)
dens = np.empty(N)
for i in range(N):
d = cdist(data[(i,),:], data, **metricpar)
dens[i] = np.exp(d*d/denom).sum()
progress(((i+1)*100//N))
dens /= N*np.power(np.sqrt(2*np.pi)*sigma,data.shape[1])
return dens
def do_scale_graph(M, weighting='inverse', exponent=0., maxcluster=None,
expand_intervals=False, verbose=True, callback=None):
'''
Compute the scale graph from a Mapper output.
'''
M.add_info(cutoff="Scale graph algorithm ({0}, '{1}', {2})".\
format(exponent, expand_intervals, maxcluster))
sgd = M.scale_graph_data
sgd.maxcluster = maxcluster
sgd.expand_intervals = expand_intervals
dendrogram = sgd.dendrogram
diameter = sgd.diameter
layers = len(dendrogram)
# Add edges
if verbose:
sys.stdout.write('Add edges:')
sys.stdout.flush()
N2, LB2, UB2, diam2 = sgd.layerdata(0)
Dijkstra = Layered_Dijkstra(weighting=weighting)
Dijkstra.start(N2)
progress = progressreporter(callback)
for i in range(1,layers):
N1, LB1, UB1, diam1 = N2, LB2, UB2, diam2
N2, LB2, UB2, diam2 = sgd.layerdata(i)
Dijkstra.next_layer(N2)
Dijkstra.add_edge(0,0)
for j in takewhile(lambda j: LB1[j]>=diam2, range(N1)):
Dijkstra.add_edge(j+1,0)
for j in takewhile(lambda j: LB2[j]>=diam1, range(N2)):
Dijkstra.add_edge(0,j+1)
if N1 and N2:
s0 = ( N1 if maxcluster is None else min(N1,maxcluster) ) + 1
t0 = ( N2 if maxcluster is None else min(N2,maxcluster) ) + 1
startk = 1
for j in range(1, s0):
a = LB1[j]
b = UB1[j-1]
for k in range(startk, t0):
c = LB2[k]
d = UB2[k-1]
if c>b:
startk += 1
continue
if d<a: break
maxac = max(a,c)
overlap = min(b,d)-maxac
assert overlap>=0.
if maxac>0:
Dijkstra.add_edge(j, k,
overlap, np.power(maxac, exponent))
progress(i*100//(layers-1))
if verbose:
print(' {0} edges in total.'.format(Dijkstra.num_edges()))
sgd.path, sgd.infmin = Dijkstra.shortest_path()
if verbose:
print('Scale graph path:\n{0}'.format(sgd.path))
sgd.edges = Dijkstra.edges
