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dual_affinity.py
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"""
dual_affinity.py: Functions for calculating dual affinity based on Earth
Mover's Distance.
"""
import numpy as np
import tree_util
import scipy.spatial as spsp
import collections
import transform
def emd_dual_aff(emd,eps=1.0):
"""
Calculates the EMD affinity from a distance matrix
by normalizing by the median EMD and taking exp^(-EMD)
without thresholding.
"""
epall = eps*np.median(emd)
if epall == 0.0:
epall = 1.0
return np.exp(-emd/epall)
def calc_emd(data,row_tree,alpha=1.0,beta=0.0,exc_sing=False,weights=None):
"""
Calculates the EMD on the *columns* from data and a tree on the rows.
each level is weighted by 2**((1-level)*alpha)
each folder size (fraction) is raised to the beta power for weighting.
"""
rows,_ = np.shape(data)
assert rows == row_tree.size, "Tree size must match # rows in data."
folder_fraction = np.array([((node.size*1.0/rows)**beta)*
(2.0**((1.0-node.level)*alpha))
for node in row_tree])
if weights is not None:
folder_fraction = folder_fraction*weights
if exc_sing:
for node in row_tree:
if node.size == 1:
folder_fraction[node.idx] = 0.0
coefs = tree_util.tree_averages(data,row_tree)
ext_vecs = np.diag(folder_fraction).dot(coefs)
pds = spsp.distance.pdist(ext_vecs.T,"cityblock")
distances = spsp.distance.squareform(pds)
return distances
def calc_emd_multi_tree(data,row_trees,alpha=1.0,beta=0.0,exc_sing=False):
rows,cols = np.shape(data)
ext_vecs = np.array([]).reshape(0,cols)
n_trees = len(row_trees)
for i in range(ntrees):
row_tree = row_trees[i]
assert rows == row_tree.size, "Tree size must match # rows in data."
folder_fraction = np.array([((node.size*1.0/rows)**beta)*
(2.0**((1.0-node.level)*alpha))
for node in row_tree])
if exc_sing:
for node in row_tree:
if node.size == 1:
folder_fraction[node.idx] = 0.0
coefs = transform.averaging(data,row_tree)
ext_vecs = np.vstack([ext_vecs, np.diag(folder_fraction).dot(coefs)])
pds = spsp.distance.pdist(ext_vecs.T,"cityblock")
distances = spsp.distance.squareform(pds)
return distances / float(n_trees)
def calc_emd_multi_tree_ref(ref_data,data,row_trees,alpha=1.0,beta=0.0,exc_sing=False):
rows,cols = np.shape(data)
ref_rows,ref_cols = np.shape(ref_data)
emd = np.zeros([ref_cols,cols])
ntrees = len(row_trees)
for i in range(ntrees):
row_tree = row_trees[i]
emd += calc_emd_ref(ref_data,data,row_tree,alpha=alpha,beta=beta)
return emd/ float(ntrees)
def calc_emd_ref(ref_data,data,row_tree,alpha=1.0,beta=0.0):
"""
Calculates the EMD from a set of points to a reference set of points
The columns of ref_data are each a reference set point.
The columns of data are each a point outside the reference set.
"""
ref_rows,ref_cols = np.shape(ref_data)
rows,cols = np.shape(data)
assert rows == row_tree.size, "Tree size must match # rows in data."
assert ref_rows == rows, "Mismatched row #: reference and sample sets."
emd = np.zeros([ref_cols,cols])
ref_coefs = tree_util.tree_averages(ref_data, row_tree)
coefs = tree_util.tree_averages(data, row_tree)
level_elements = collections.defaultdict(list)
level_sizes = collections.defaultdict(int)
for node in row_tree:
level_elements[node.level].append(node.idx)
level_sizes[node.level] += node.size
folder_fraction = np.array([node.size for node in row_tree],np.float)
for level in xrange(1,row_tree.tree_depth+1):
fsize = np.sum(folder_fraction[level_elements[level]])
folder_fraction[level_elements[level]] /= fsize
folder_fraction = folder_fraction**beta
coefs = np.diag(folder_fraction).dot(coefs)
ref_coefs = np.diag(folder_fraction).dot(ref_coefs)
for level in xrange(1,row_tree.tree_depth+1):
distances = spsp.distance.cdist(coefs[level_elements[level],:].T,
ref_coefs[level_elements[level],:].T,
"cityblock").T
emd += (2**((1.0-level)*alpha))*distances
return emd
def calc_emd_ref2(ref_data,data,row_tree,alpha=1.0,beta=0.0,weights=None):
"""
Calculates the EMD from a set of points to a reference set of points
The columns of ref_data are each a reference set point.
The columns of data are each a point outside the reference set.
"""
ref_rows,ref_cols = np.shape(ref_data)
rows,cols = np.shape(data)
assert rows == row_tree.size, "Tree size must match # rows in data."
assert ref_rows == rows, "Mismatched row #: reference and sample sets."
emd = np.zeros([ref_cols,cols])
averages_mat = transform.tree_averages_mat(row_tree)
ref_coefs = averages_mat.dot(ref_data)
coefs = averages_mat.dot(data)
folder_fraction = np.array([((node.size*1.0/rows)**beta)*
(2.0**((1.0-node.level)*alpha))
for node in row_tree])
if weights is not None:
folder_fraction = folder_fraction*weights
coefs = np.diag(folder_fraction).dot(coefs)
ref_coefs = np.diag(folder_fraction).dot(ref_coefs)
emd = spsp.distance.cdist(ref_coefs.T,coefs.T,"cityblock")
return emd
def calc_2demd(data,row_tree, col_tree, row_alpha=1.0, row_beta=0.0,
col_alpha=1.0, col_beta=0.0, exc_sing=False, exc_raw=False):
"""
Calculates 2D EMD on database of data using a tree on the rows and columns.
each level is weighted by 2**((1-level)*alpha)
each folder size (fraction) is raised to the beta power for weighting.
"""
nrows,ncols,nchannels = np.shape(data)
assert nrows == row_tree.size, "Tree size must match # rows in data."
assert ncols == col_tree.size, "Tree size must match # cols in data."
row_folder_fraction = np.array([((node.size*1.0/nrows)**row_beta)*
(2.0**((1.0-node.level)*row_alpha))
for node in row_tree])
col_folder_fraction = np.array([((node.size*1.0/ncols)**col_beta)*
(2.0**((1.0-node.level)*col_alpha))
for node in col_tree])
if exc_sing:
for node in row_tree:
if node.size == 1:
row_folder_fraction[node.idx] = 0.0
for node in col_tree:
if node.size == 1:
col_folder_fraction[node.idx] = 0.0
folder_frac = np.outer(row_folder_fraction, col_folder_fraction)
avgs = tree_util.bitree_averages(data[:,:,0], row_tree, col_tree)
avgs = folder_frac * avgs
if exc_raw:
col_singletons_start = col_tree.tree_size - ncols
row_singletons_start = row_tree.tree_size - nrows
avgs = avgs[:row_singletons_start,:col_singletons_start]
sums3d = np.zeros((nchannels,np.size(avgs)))
sums3d[0,:] = np.reshape(avgs,(1,-1))
for t in range(1,nchannels):
avgs = tree_util.bitree_averages(data[:,:,t], row_tree, col_tree)
avgs = folder_frac * avgs
if exc_raw:
avgs = avgs[:row_singletons_start,:col_singletons_start]
sums3d[t,:] = np.reshape(avgs,(1,-1))
pds = spsp.distance.pdist(sums3d, "cityblock")
distances = spsp.distance.squareform(pds)
return distances
def calc_2demd_ref(ref_data,data,row_tree,col_tree, row_alpha=1.0, row_beta=0.0,
col_alpha=1.0, col_beta=0.0, exc_sing=False,exc_raw=False):
"""
Calculates the EMD from a set of points to a reference set of points
The columns of ref_data are each a reference set point.
The columns of data are each a point outside the reference set.
"""
if data.ndim == 2:
ref_rows,ref_cols = np.shape(ref_data)
rows,cols = np.shape(data)
else:
ref_rows,ref_cols,ref_chans = np.shape(ref_data)
rows,cols,chans = np.shape(data)
col_singletons_start = col_tree.tree_size - cols
row_singletons_start = row_tree.tree_size - rows
assert rows == row_tree.size, "Tree size must match # rows in data."
assert ref_rows == rows, "Mismatched row #: reference and sample sets."
assert cols == col_tree.size, "Tree size must match # cols in data."
assert ref_cols == cols, "Mismatched col #: reference and sample sets."
row_folder_fraction = np.array([((node.size*1.0/rows)**row_beta)*
(2.0**((1.0-node.level)*row_alpha))
for node in row_tree])
col_folder_fraction = np.array([((node.size*1.0/cols)**col_beta)*
(2.0**((1.0-node.level)*col_alpha))
for node in col_tree])
if exc_sing:
for node in row_tree:
if node.size == 1:
row_folder_fraction[node.idx] = 0.0
for node in col_tree:
if node.size == 1:
col_folder_fraction[node.idx] = 0.0
folder_frac = np.outer(row_folder_fraction, col_folder_fraction)
if data.ndim == 2:
ref_coefs = tree_util.bitree_averages(ref_data, row_tree, col_tree)
coefs = tree_util.bitree_averages(data, row_tree, col_tree)
coefs = folder_frac * coefs
ref_coefs = folder_frac * ref_coefs
if exc_raw:
avgs = avgs[:row_singletons_start,:col_singletons_start]
return spsp.distance.cityblock(coefs.flatten(),ref_coefs.flatten())
else:
if exc_raw:
folder_frac = folder_frac[:row_singletons_start,:col_singletons_start]
sums3d = np.zeros((chans,np.size(folder_frac)))
for t in range(0,chans):
avgs = tree_util.bitree_averages(data[:,:,t], row_tree, col_tree)
if exc_raw:
avgs = avgs[:row_singletons_start,:col_singletons_start]
avgs = folder_frac * avgs
sums3d[t,:] = np.reshape(avgs,(1,-1))
ref_sums3d = np.zeros((ref_chans,np.size(folder_frac)))
for t in range(0,ref_chans):
avgs = tree_util.bitree_averages(ref_data[:,:,t], row_tree, col_tree)
if exc_raw:
avgs = avgs[:row_singletons_start,:col_singletons_start]
avgs = folder_frac * avgs
ref_sums3d[t,:] = np.reshape(avgs,(1,-1))
return spsp.distance.cdist(sums3d,ref_sums3d, "cityblock")