def find_temporal_adjacency_matrix(min_abundance, phylo_column, full_svd):
"""
Find the adjacency matrix among clusters of bacteria from week to week,
assuming the interaction between clusters is changing.
:param min_abundance: ignore the bacteria if their abundance is always
below the min_abundance
:param phylo_column: the data is clustered based on the phylo_column
:param full_svd:the method of singular value decomposition. full SVD is
more accurate and slower than the reduced SVD
"""
# Default values
if min_abundance is None:
min_abundance = 0
if phylo_column is None:
phylo_column = 'family'
if full_svd is None:
full_svd = False
# snapshots of samples over 11 weeks
# todo: python reserves capital letters for classes.
snapshots = prepare_DMD_matrices(min_abundance, phylo_column, oxygen='all', debug=False)
linear_mappings = {}
nodes_list = {}
for descriptive_tuple in snapshots.keys():
df = snapshots[descriptive_tuple]
data = df.values
for time in range(10):
X = data[:, time:time+1]
Y = data[:, time+1:time+2]
# Preprocess the abundance data
X = normalize(X, axis=0)
Y = normalize(Y, axis=0)
U, s, V = np.linalg.svd(X, full_matrices=full_svd)
if full_svd is True: # slower
S = np.zeros((len(U), len(s)), dtype=complex)
S[:len(s), :len(s)] = np.diag(s)
pseu_inv_x = np.dot(np.linalg.inv(V),
np.dot(np.linalg.pinv(S), np.linalg.inv(U)))
else: # faster
S = np.diag(s)
pseu_inv_x = np.dot(np.linalg.inv(V),
np.dot(np.linalg.inv(S), np.linalg.pinv(U)))
# Adjacency matrix between clusters
A = np.dot(Y, pseu_inv_x)
# A = np.dot(Y, np.linalg.pinv(X)) # full SVD (slower)
key = descriptive_tuple + ('Week ' + str(time+1),)
linear_mappings[key] = A
nodes_list[key] = list(df.index)
return linear_mappings, nodes_list
def find_fixed_adjacency_matrix(min_abundance=0.0, phylo_column='order',
full_svd=True):
"""
This function find the adjacency matrix among clusters of bacteria over
the 11 weeks of sampling assuming the interaction between clusters is
fixed.
It creates a dictionary of descriptive tuples like ("High", 2) for
high-oxygen week 2, and corresponding dataframe values. These
dataframes have weeks as columns and taxa ("bacteria") as rows.
Unlike find_temporal_adjacency_matrix(), we get only one predictive
matrix that represents the 10 transitions between sampling points.
Since the dictionary has 8 tuple keys for High/Low oxygen and 4
replicates for each condition, 8 interaction ("A") matrices are created.
These are accessed by the dictionary linear_mappings, with the same
tuples as keys.
The names of each node can be accessed by nodes_list, the other output.
:param min_abundance: minimum abundance to loook for in original data
:param phylo_column: most detailed phylogenetic column to consider
:param full_svd: if True, runs the full svd algorithm. If False,
runs a faster version.
"""
# Default values
if min_abundance is None:
min_abundance = 0
if phylo_column is None:
phylo_column = 'order'
if full_svd is None:
full_svd = False
# snapshots of samples over 11 weeks
snapshots = prepare_DMD_matrices(min_abundance, phylo_column, oxygen='all',debug=False)
linear_mappings = {}
nodes_list = {}
for descriptive_tuple in snapshots.keys():
df = snapshots[descriptive_tuple]
data = df.values
X = data[:, 0:10]
Y = data[:, 1:11]
# Preprocess the abundance data
X = normalize(X, axis=0)
Y = normalize(Y, axis=0)
U, s, V = np.linalg.svd(X, full_matrices=full_svd)
if full_svd is True: # slower
S = np.zeros((len(U), len(s)), dtype=float)
S[:len(s), :len(s)] = np.diag(s)
pseu_inv_x = np.dot(np.linalg.inv(V),
np.dot(np.linalg.pinv(S), np.linalg.inv(U)))
else: # faster
S = np.diag(s)
pseu_inv_x = np.dot(np.linalg.inv(V),
np.dot(np.linalg.inv(S), np.linalg.pinv(U)))
# Adjacency matrix between clusters
A = np.dot(Y, pseu_inv_x)
# A = np.dot(Y, np.linalg.pinv(X)) # full SVD (slower)
linear_mappings[descriptive_tuple] = A
nodes_list[descriptive_tuple] = list(df.index)
return linear_mappings, nodes_list
