def barycenter_density(data, grid, upper, lower, vmin, dens = 0e0):
''' Recursively search for the initial seed on the densest regions of the sample.
Uses numpy.histogramdd to divide multidimensional samples on regions. '''
rng = range(data.shape[1])
# Number of division on each variable
nbin = map(int,array([grid]*data.shape[1]))
# Define the number of points (hist) and the limits (edges) on each region.
hist, edges = histogramdd(data,bins=nbin,range=tuple(zip(lower, upper)))
# Transform the limits into a paired list.
limits = array([list(pairwise(edges[i])) for i in rng])
# Find the indexes of the region limits that contains the max number of points.
ind = unravel_index(argmax(hist), hist.shape)
# Define the zone containing the maximum number of points.
zone = array([limits[i,j] for i, j in izip(rng, ind)])
# Calculate density:
density = amax(hist) / volume(zone)
# Elements inside the zone:
inside = filter(lambda x: x != None, \
imap(lambda i, y: boolist(i,y,zone), xrange(data.shape[0]), data))
# If density keep growing and vmin not reached, the function works recursively.
# Stops when any of thoses conditions are not satisfied anymore.
if density > dens and aall(mad(data[inside]) > diagonal(vmin)):
zone = zone.T
return barycenter_density(data, grid, zone[1], zone[0], vmin, density)
else:
return inside
def G(N, f, X, ct, iS):
''' G parameter --> Transforms a X2 estimator to a Gaussian estimator '''
#z2 = iR * asum( ( (X - ct) / (iS + TINY) )**2 ) # Z2 estimator
# Mahalanobis distance estimator:
X = X - ct
z2 = asum( fabs( X * ravel( dot(iS, X ) ) ) )
# G transformation:
if aall(N*f > 100e0):
return sqrt(2e0*z2) - sqrt(2e0*f - 1e0)
elif aall(N*f >= 30e0) and aall(N*f <= 100e0):
return ((z2/f)**(1e0/3) - (1e0 - (2e0/9)*f))/sqrt((2e0/9)*f)
elif aall(N*f < 30e0):
return 9e9
def pearson_r2(X):
r2 = corrcoef(zip(*X))**2
if aall(isnan(r2)) :
r2 = eye(X.shape[1])
else:
whereNaN = isnan(r2)
r2[whereNaN] = 1e0
return matrix(r2)
def Robust_r2(X, ct, dev):
''' Shevlyakov 1997 - On a Robust Estimation of Correlation Coeficient'''
warnings.simplefilter("ignore")
X = (X - ct)/(dev + TINY)
r2 = deque()
for i in xrange(X.shape[1]):
u = median(fabs(X.T + X[:,i]), axis=1)**2
v = median(fabs(X.T - X[:,i]), axis=1)**2
ri = (u - v)/(u + v)
r2.append(ri**2)
r2 = matrix(r2)
if aall(isnan(r2)) :
r2 = matrix(eye(X.shape[1]))
else:
whereNaN = isnan(r2)
r2[whereNaN] = 1e0
return r2
def hyp_test(N, q1, f, key, x, ct, iS):
''' G hypothesis testing'''
if aall(G(N, f, x, ct, iS) <= q1):
#print(G(N, f, x, ct, iS))
return key
