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transform.py
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transform.py
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"""
transform.py: Defines various tree transform matrices and their application to data
"""
import numpy as np
import scipy.stats
def bitree_partiton(row_tree,col_tree,row_part,col_part):
nrows = row_tree.size
ncols = col_tree.size
row_part = np.add(row_tree.level_partition(row_part),1)
col_part = np.add(col_tree.level_partition(col_part),1)
row_part_inds = np.tile(row_part[np.newaxis].T, (1,ncols)).flatten()
col_part_inds = np.tile(col_part, (nrows,1)).flatten()
partiton_mat = np.zeros(nrows*ncols)
k = 0
for i in np.unique(row_part):
for j in np.unique(col_part):
inds = np.logical_and((row_part_inds == i) ,(col_part_inds == j))
partiton_mat[inds] = k
k = k+1
return partiton_mat.reshape((nrows,ncols))
def calc_1demd_transform(data,row_tree, alpha=1.0, beta=0.0,
exc_sing=False, exc_raw=False):
"""
Calculates 2D EMD transform 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 = np.shape(data)
assert nrows == row_tree.size, "Tree size must match # rows in data."
row_folder_fraction = np.array([((node.size*1.0/nrows)**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:
row_folder_fraction[node.idx] = 0.0
coefs = averaging(data,row_tree)
avgs = np.diag(row_folder_fraction).dot(coefs)
if exc_raw:
row_singletons_start = row_tree.tree_size - nrows
avgs = avgs[:row_singletons_start,:]
return avgs
def calc_2demd_transform(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 transform 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 = 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)
coefs = joint_averaging(data,row_tree,col_tree)
avgs = folder_frac * coefs
if exc_raw:
m,n = np.shape(data)
col_singletons_start = col_tree.tree_size - n
row_singletons_start = row_tree.tree_size - m
avgs = avgs[:row_singletons_start,:col_singletons_start]
return avgs
def tree_sums_mat(row_tree,return_nodes=False):
node_ids = np.zeros(row_tree.tree_size,np.int)
node_ids[0] = -1
mat = np.zeros((row_tree.tree_size,row_tree.size))
for node in row_tree.traverse():
for i in node.elements:
mat[node.idx,i] = 1
node_ids[node.idx] = node.idx
if return_nodes:
return mat, node_ids
else:
return mat
def tree_averages_mat(row_tree,return_nodes=False):
mat, node_ids = tree_sums_mat(row_tree,return_nodes=True)
for node in row_tree.traverse():
mat[node.idx,:] /= node.size
if return_nodes:
return mat, node_ids
else:
return mat
def tree_differences_mat(row_tree,return_nodes=False):
node_ids = np.zeros(row_tree.tree_size,np.int)
node_ids[0] = -1
mat_avg = tree_averages_mat(row_tree)
mat = np.zeros(np.shape(mat_avg))
for node in row_tree.traverse():
if node.parent is None:
mat[node.idx,:] = mat_avg[node.idx,:]
else:
mat[node.idx,:] = mat_avg[node.idx,:] - mat_avg[node.parent.idx,:]
node_ids[node.idx] = node.idx
if return_nodes:
return mat, node_ids
else:
return mat
def entropy(data,row_tree,col_tree):
coefs = joint_difference(data,row_tree,col_tree)
return np.sum(np.absolute(coefs))
def averaging(data,tree):
nrows,ncols = np.shape(data)
if nrows == tree.size:
row_avg_mat = tree_averages_mat(tree)
coefs = row_avg_mat.dot(data)
elif ncols == tree.size:
col_avg_mat = tree_averages_mat(tree)
coefs = data.dot(col_avg_mat.T)
return coefs
def difference(data,tree):
nrows,ncols = np.shape(data)
if nrows == tree.size:
row_diff_mat = tree_differences_mat(tree)
coefs = row_diff_mat.dot(data)
elif ncols == tree.size:
col_diff_mat = tree_differences_mat(tree)
coefs = data.dot(col_diff_mat.T)
return coefs
def joint_averaging(data,row_tree,col_tree):
nrows,ncols = 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_avg_mat = tree_averages_mat(row_tree)
coefs = row_avg_mat.dot(data)
col_avg_mat = tree_averages_mat(col_tree)
coefs = coefs.dot(col_avg_mat.T)
return coefs
def joint_difference(data,row_tree,col_tree):
nrows,ncols = 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_diff_mat = tree_differences_mat(row_tree)
coefs = row_diff_mat.dot(data)
col_diff_mat = tree_differences_mat(col_tree)
coefs = coefs.dot(col_diff_mat.T)
return coefs