/
bintree_construct.py
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/
bintree_construct.py
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import tree
import dual_affinity
import markov
import numpy as np
def median_tree(eigvecs,eigvals,max_levels=0):
"""
Crude tree construction method (suitable for initial affinity)
Split at level n is determined by the taking the median of the nth
non-trivial eigenvector from the original embedding.
"""
#check to see if the all ones vector has been removed yet.
if np.std(eigvecs[:,0]) == 0.0:
eigvecs = eigvecs[:,1:]
eigvals = eigvals[1:]
d,n = np.shape(eigvecs)
#default max_levels
if max_levels == 0:
max_levels = min(n,np.floor(np.log(d/5.0)/np.log(2.0))+2)
vecs = eigvecs.dot(np.diag(eigvals))
root = tree.ClusterTreeNode(range(d))
queue = [root]
while max([x.size for x in queue]) > 1:
#work on one level at a time to match how the matlab trees are created
new_queue = []
for node in queue:
if node.size >= 4 and node.level + 1 < max_levels:
#cut it
cut = median_cut(node,vecs)
node.create_subclusters(cut)
else:
#make the singletons
node.create_subclusters(np.arange(node.size))
new_queue.extend(node.children)
queue = new_queue
root.make_index()
return root
def median_cut(node,vec):
"""
node is a tree node. vec is an entire eigenvector.
takes vec on just the node elements, and returns the partition resulting
from cutting at the median of the subvector.
"""
cut_data = vec[node.elements,node.level-1]
cut_loc = np.median(cut_data)
labels = np.ones(len(node.elements))*(cut_data > cut_loc)
return labels
def old_eigen_tree(data,row_tree,alpha=1.0,beta=0.0,noise=0.0,min_folder_size=4.0):
"""
Constructs binary tree on columns of data with respect to dual affinity
on row_tree by cutting at the median the first nontrivial eigenvector at
each node (reconstructing the eigenvector for only the rows at that node).
Returns a tree.
"""
col_emd = dual_affinity.calc_emd(data,row_tree,alpha,beta)
_,n = data.shape
#default max levels
max_levels = np.floor(np.log(n)/np.log(2.0))
root = tree.ClusterTreeNode(range(n))
queue = [root]
while max([x.size for x in queue]) > 1:
new_queue = []
for node in queue:
if node.size >= min_folder_size and node.level < max_levels:
#cut it
cut = eigen_cut(node,col_emd,noise)
node.create_subclusters(cut)
else:
#make the singletons
node.create_subclusters(np.arange(node.size))
new_queue.extend(node.children)
queue = new_queue
root.make_index()
return root
def eigen_cut(node,emd,noise,eps=1.0):
affinity = dual_affinity.emd_dual_aff(emd[node.elements,:][:,node.elements]
,eps)
try:
vecs,_ = markov.markov_eigs(affinity,2)
except:
print affinity
print emd
print node.elements
raise
eig = vecs[:,1]
eig_sorted = np.sort(eig)
n = len(eig_sorted)
rnoise = np.random.uniform(-noise,noise)
if noise < 1e-8:
labels = np.zeros(n)
labels[np.argsort(eig)[0:int(n/2)]] = 1
else:
cut_loc = eig_sorted[int((n/2)+(rnoise*n))]
labels = np.ones(n)*(eig > cut_loc)
return labels
def bal_eigen_cut(node,emd,bal_constant=1.0,eps=1.0):
affinity = dual_affinity.emd_dual_aff(emd[node.elements,:][:,node.elements]
,eps)
try:
vecs,_ = markov.markov_eigs(affinity,2)
except:
print affinity
print emd
print node.elements
raise
eig = vecs[:,1]
eig_sorted = np.argsort(eig)
n = len(eig)
l,r = bal_cut(n,bal_constant)
cut_loc = np.random.randint(l,r+1)
labels = np.zeros(n,np.int)
labels[eig_sorted[0:cut_loc]] = 1
return labels
def eigen_cut_zero(node,emd,eps=1.0):
affinity = dual_affinity.emd_dual_aff(emd[node.elements,:][:,node.elements]
,eps)
try:
vecs,_ = markov.markov_eigs(affinity,2)
except:
print affinity
print emd
print node.elements
raise
eig = vecs[:,1]
n = len(eig)
labels = np.ones(n)
labels *= (eig > 0.0)
return labels
def eigen_tree(data,row_tree,alpha=1.0,beta=0.0,bal_constant=1.0):
"""
Constructs binary tree on columns of data with respect to dual affinity
on row_tree by cutting at the median the first nontrivial eigenvector at
each node (reconstructing the eigenvector for only the rows at that node).
Returns a tree.
"""
col_emd = dual_affinity.calc_emd(data,row_tree,alpha,beta)
_,n = data.shape
root = tree.ClusterTreeNode(range(n))
queue = [root]
while max([x.size for x in queue]) > 1:
new_queue = []
for node in queue:
if node.size > 2:
#cut it
cut = bal_eigen_cut(node,col_emd,bal_constant)
node.create_subclusters(cut)
else:
#make the singletons
node.create_subclusters(np.arange(node.size))
new_queue.extend(node.children)
queue = new_queue
root.make_index()
return root
def bal_cut(n,balance_constant):
if n==1:
return 0,1
left = int(np.ceil((1.0/(1.0+balance_constant))*n))
right = int(np.floor((balance_constant/(1.0+balance_constant))*n))
if left > right and n % 2 == 1:
left = int(np.floor(n/2.0))
right = int(np.ceil(n/2.0))
elif left > right:
left = right
return left,right
def eigen_tree_zero(data,row_tree,alpha=1.0,beta=0.0):
"""
Constructs binary tree on columns of data with respect to dual affinity
on row_tree by cutting at the median the first nontrivial eigenvector at
each node (reconstructing the eigenvector for only the rows at that node).
Returns a tree.
"""
col_emd = dual_affinity.calc_emd(data,row_tree,alpha,beta)
_,n = data.shape
root = tree.ClusterTreeNode(range(n))
queue = [root]
while max([x.size for x in queue]) > 1:
new_queue = []
for node in queue:
if node.size > 2:
#cut it
cut = eigen_cut_zero(node,col_emd)
node.create_subclusters(cut)
else:
#make the singletons
node.create_subclusters(np.arange(node.size))
new_queue.extend(node.children)
queue = new_queue
root.make_index()
return root