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 _calc_affinity(self,data,affinity_type,**kwargs):
if affinity_type == run_quest.INIT_AFF_COS_SIM: #cosine similarity
affinity_matrix = affinity.mutual_cosine_similarity(data,**kwargs)
elif affinity_type == run_quest.DUAL_EMD: #EMD
emd = dual_affinity.calc_emd(data,**kwargs)
affinity_matrix = dual_affinity.emd_dual_aff(emd)
return affinity_matrix
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
def pyquest_newtree(data,tree_constant=0.25,row_alpha=0.5,col_alpha=0.5,beta=1.0,n_iters=3):
init_row_aff = affinity.mutual_cosine_similarity(data.T,False,0,threshold=0.1)
#Compute diffusion embedding of initial affinities
init_row_vecs,init_row_vals = markov.markov_eigs(init_row_aff, 12)
init_row_vals[np.isnan(init_row_vals)] = 0.0
row_embedding = init_row_vecs.dot(np.diag(init_row_vals))
row_distances = spsp.distance.squareform(spsp.distance.pdist(row_embedding))
row_affinity = np.max(row_distances) - row_distances
#Generate initial tree
#print "call1 tree_constant:{}".format(tree_constant)
init_row_tree = tree_building.make_tree_embedding(row_affinity,tree_constant)
dual_col_trees = []
dual_row_trees = [init_row_tree]
for _ in xrange(n_iters):
#print "Beginning iteration {}".format(i)
col_emd = dual_affinity.calc_emd(data,dual_row_trees[-1],alpha=col_alpha,beta=beta)
col_aff = dual_affinity.emd_dual_aff(col_emd)
#print "call2 tree_constant:{}".format(tree_constant)
dual_col_trees.append(tree_building.make_tree_embedding(col_aff,tree_constant))
row_emd = dual_affinity.calc_emd(data.T,dual_col_trees[-1],alpha=row_alpha,beta=beta)
row_aff = dual_affinity.emd_dual_aff(row_emd)
#print "call3 tree_constant:{}".format(tree_constant)
dual_row_trees.append(tree_building.make_tree_embedding(row_aff,tree_constant))
col_tree = dual_col_trees[-1]
row_tree = dual_row_trees[-1]
col_emd = dual_affinity.calc_emd(data,row_tree,alpha=col_alpha,beta=beta)
row_emd = dual_affinity.calc_emd(data.T,col_tree,alpha=row_alpha,beta=beta)
row_aff = dual_affinity.emd_dual_aff(row_emd)
col_aff = dual_affinity.emd_dual_aff(col_emd)
row_vecs,row_vals = markov.markov_eigs(row_aff, 12)
col_vecs,col_vals = markov.markov_eigs(col_aff, 12)
return row_tree,col_tree,row_vecs,col_vecs,row_vals,col_vals
def pyquest_bintree(data,row_alpha=0.5,col_alpha=0.5,beta=1.0,bal_constant=1.0,n_iters=3):
"""
runs what is momentarily the standard questionnaire algorithm:
initial affinity = mutual cosine similarity
initial tree based on median of successive eigenvectors
dual affinities based on earth mover distance.
dual trees based on eigen_cut method
"""
#Generate initial affinity
init_row_aff = affinity.mutual_cosine_similarity(data.T,False,0,threshold=0.1)
#Compute diffusion embedding of initial affinities
init_row_vecs,init_row_vals = markov.markov_eigs(init_row_aff, 12)
#Generate median trees
init_row_tree = bintree_construct.median_tree(init_row_vecs,init_row_vals,max_levels=12)
dual_col_trees = []
dual_row_trees = [init_row_tree]
for _ in xrange(n_iters):
dual_col_trees.append(bintree_construct.old_eigen_tree(data,dual_row_trees[-1],alpha=col_alpha,beta=beta,noise=0.0))
dual_row_trees.append(bintree_construct.old_eigen_tree(data.T,dual_col_trees[-1],alpha=row_alpha,beta=beta,noise=0.0))
# dual_col_trees.append(bintree_construct.eigen_tree(data,dual_row_trees[-1],alpha=col_alpha,beta=beta,bal_constant=bal_constant))
# dual_row_trees.append(bintree_construct.eigen_tree(data.T,dual_col_trees[-1],alpha=row_alpha,beta=beta,bal_constant=bal_constant))
col_tree = dual_col_trees[-1]
row_tree = dual_row_trees[-1]
col_emd = dual_affinity.calc_emd(data,row_tree,alpha=0.5,beta=1.0)
row_emd = dual_affinity.calc_emd(data.T,col_tree,alpha=0.5,beta=1.0)
row_aff = dual_affinity.emd_dual_aff(row_emd)
col_aff = dual_affinity.emd_dual_aff(col_emd)
row_vecs,row_vals = markov.markov_eigs(row_aff, 12)
col_vecs,col_vals = markov.markov_eigs(col_aff, 12)
return row_tree,col_tree,row_vecs,col_vecs,row_vals,col_vals
def break_node(train_data,
col_tree_node,
row_tree,
regressors=None,
k=5,
alpha=0.0,
beta=1.0,
col_emd=None):
"""
First calculates the EMD on the columns of train_data
in col_tree_node.elements using row_tree. Converts that to an affinity.
Calculates the second eigenvector of the markov matrix based on that
affinity.
Then fits a linear model using the rows in regressors (all if it's None)
and uses the LASSO path to identify the best k rows.
Splits the node using the predicted eigenvector values.
"""
import sklearn.linear_model as sklm
col_indices = col_tree_node.elements
node_data = train_data[:, col_indices].astype(np.float64)
if col_emd is None:
col_emd = dual_affinity.calc_emd(node_data, row_tree, alpha, beta)
col_aff = dual_affinity.emd_dual_aff(col_emd)
else:
col_aff = dual_affinity.emd_dual_aff(
col_emd[:, col_indices][col_tree_node.elements, :])
vecs, _ = markov.markov_eigs(col_aff, 2)
eig = vecs[:, 1]
if regressors is None:
regressors = range(row_tree.size)
_, active, _ = sklm.lars_path(node_data[regressors, :].T, eig, max_iter=50)
regr_indices = active[0:k]
lm = sklm.LinearRegression()
lm.fit(node_data[regr_indices, :].T, eig)
pred_eigs = lm.predict(node_data[regr_indices, :].T)
labels = pred_eigs > 0.0
partition = labels * np.ones(labels.shape[0])
col_tree_node.create_subclusters(partition)
return np.array([regressors[x] for x in regr_indices]), lm
def mtree(train_data,row_tree,regressors=None):
"""
Generates the question tree on the training data.
"""
root = tree.ClusterTreeNode(range(train_data.shape[1]))
node_list = []
node_list.append(root)
if regressors is None:
regressors = range(row_tree.size)
col_emd = dual_affinity.calc_emd(train_data,row_tree,alpha=0.0,beta=1.0)
while node_list:
process_node(train_data,row_tree,node_list,regressors,col_emd)
fix_leaves(root)
root.make_index()
return root
def mtree(train_data, row_tree, regressors=None):
"""
Generates the question tree on the training data.
"""
root = tree.ClusterTreeNode(range(train_data.shape[1]))
node_list = []
node_list.append(root)
if regressors is None:
regressors = range(row_tree.size)
col_emd = dual_affinity.calc_emd(train_data, row_tree, alpha=0.0, beta=1.0)
while node_list:
process_node(train_data, row_tree, node_list, regressors, col_emd)
fix_leaves(root)
root.make_index()
return root
def break_node(train_data,col_tree_node,row_tree,regressors=None,
k=5,alpha=0.0,beta=1.0,col_emd=None):
"""
First calculates the EMD on the columns of train_data
in col_tree_node.elements using row_tree. Converts that to an affinity.
Calculates the second eigenvector of the markov matrix based on that
affinity.
Then fits a linear model using the rows in regressors (all if it's None)
and uses the LASSO path to identify the best k rows.
Splits the node using the predicted eigenvector values.
"""
import sklearn.linear_model as sklm
col_indices = col_tree_node.elements
node_data = train_data[:,col_indices].astype(np.float64)
if col_emd is None:
col_emd = dual_affinity.calc_emd(node_data,row_tree,alpha,beta)
col_aff = dual_affinity.emd_dual_aff(col_emd)
else:
col_aff = dual_affinity.emd_dual_aff(col_emd[:,col_indices][col_tree_node.elements,:])
vecs,_ = markov.markov_eigs(col_aff,2)
eig = vecs[:,1]
if regressors is None:
regressors = range(row_tree.size)
_,active,_ = sklm.lars_path(node_data[regressors,:].T,eig,max_iter=50)
regr_indices = active[0:k]
lm = sklm.LinearRegression()
lm.fit(node_data[regr_indices,:].T,eig)
pred_eigs = lm.predict(node_data[regr_indices,:].T)
labels = pred_eigs > 0.0
partition = labels*np.ones(labels.shape[0])
col_tree_node.create_subclusters(partition)
return np.array([regressors[x] for x in regr_indices]),lm
def pyquest(data,params):
"""
Runs the questionnaire on data with params.
params is a PyQuestParams object.
"""
if params.init_aff_type == INIT_AFF_COS_SIM:
init_row_aff = affinity.mutual_cosine_similarity(
data.T,False,0,threshold=params.init_aff_threshold)
elif params.init_aff_type == INIT_AFF_GAUSSIAN:
init_row_aff = affinity.gaussian_euclidean(
data.T, params.init_aff_knn, params.init_aff_epsilon)
#Initial row tree
if params.tree_type == TREE_TYPE_BINARY:
init_row_tree = bin_tree_build.bin_tree_build(init_row_aff,'r_dyadic',
params.tree_bal_constant)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
init_row_tree = flex_tree_build.flex_tree_diffusion(init_row_aff,
params.tree_constant)
dual_col_trees = []
dual_row_trees = [init_row_tree]
row_tree_descs = ["Initial tree"]
col_tree_descs = []
for i in xrange(params.n_iters):
message = "Iteration {}: calculating column affinity...".format(i)
#print "Beginning iteration {}".format(i)
if params.col_affinity_type == DUAL_EMD:
col_emd = dual_affinity.calc_emd(data,dual_row_trees[-1],
params.col_alpha,params.col_beta)
col_aff = dual_affinity.emd_dual_aff(col_emd)
elif params.col_affinity_type == DUAL_GAUSSIAN:
print "Gaussian dual affinity not supported at the moment."
return None
message = "Iteration {}: calculating column tree...".format(i)
if params.tree_type == TREE_TYPE_BINARY:
col_tree = bin_tree_build.bin_tree_build(col_aff,'r_dyadic',
params.tree_bal_constant)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
col_tree = flex_tree_build.flex_tree_diffusion(col_aff,
params.tree_constant)
dual_col_trees.append(col_tree)
col_tree_descs.append("Iteration {}".format(i))
message = "Iteration {}: calculating row affinity...".format(i)
if params.row_affinity_type == DUAL_EMD:
row_emd = dual_affinity.calc_emd(data.T,dual_col_trees[-1],
params.row_alpha,params.row_beta)
row_aff = dual_affinity.emd_dual_aff(row_emd)
elif params.row_affinity_type == DUAL_GAUSSIAN:
print "Gaussian dual affinity not supported at the moment."
return None
message = "Iteration {}: calculating row tree...".format(i)
if params.tree_type == TREE_TYPE_BINARY:
row_tree = bin_tree_build.bin_tree_build(row_aff,'r_dyadic',
params.tree_bal_constant)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
row_tree = flex_tree_build.flex_tree_diffusion(row_aff,
params.tree_constant)
dual_row_trees.append(row_tree)
row_tree_descs.append("Iteration {}".format(i))
quest_run_desc = "{}".format(datetime.datetime.now())
return PyQuestRun(quest_run_desc,dual_row_trees,dual_col_trees,
row_tree_descs,col_tree_descs,params)
def pyquest(data, params):
"""
Runs the questionnaire on data with params. params is a PyQuestParams object.
Starts by constructing the initial affinity on the rows of the matrix (default).
"""
# construct row affinity
if params.init_aff_type == INIT_AFF_COS_SIM:
init_row_aff = affinity.mutual_cosine_similarity(
data.T, False, 0, threshold=params.init_aff_threshold)
elif params.init_aff_type == INIT_AFF_GAUSSIAN:
init_row_aff = affinity.gaussian_euclidean(data.T, params.init_aff_knn,
params.init_aff_epsilon)
#Initial row tree
if params.row_tree_type == TREE_TYPE_BINARY:
init_row_tree = bin_tree_build.bin_tree_build(
init_row_aff, 'r_dyadic', params.row_tree_bal_constant)
elif params.row_tree_type == TREE_TYPE_FLEXIBLE:
init_row_tree = flex_tree_build.flex_tree_diffusion(
init_row_aff, params.row_tree_constant)
# data structure for trees. All trees calculated in the process are exported
dual_row_trees = [init_row_tree]
dual_col_trees = []
row_tree_descs = ["Initial tree"]
col_tree_descs = []
# iterate over the questionnaire starting with columns and then rows in each iteration
for i in xrange(params.n_iters):
message = "Iteration {}: calculating column affinity...".format(i)
print message
# calculating column affinity based on row tree
#print "Beginning iteration {}".format(i)
if params.col_affinity_type == DUAL_EMD:
if params.col_weighted == True:
print "weighted emd"
row_coefs = tree_util.tree_transform_mat(
dual_row_trees[-1]).dot(data)
row_weights = np.sqrt(np.sum(row_coefs**2, axis=1))
col_emd = dual_affinity.calc_emd(data,
dual_row_trees[-1],
alpha=0,
beta=0,
weights=row_weights)
else:
col_emd = dual_affinity.calc_emd(data, dual_row_trees[-1],
params.col_alpha,
params.col_beta)
col_aff = dual_affinity.emd_dual_aff(col_emd)
elif params.col_affinity_type == DUAL_GAUSSIAN:
print "Gaussian dual affinity not supported at the moment."
return None
message = "Iteration {}: calculating column tree...".format(i)
print message
# constructing column tree
if params.col_tree_type == TREE_TYPE_BINARY:
col_tree = bin_tree_build.bin_tree_build(
col_aff, 'r_dyadic', params.col_tree_bal_constant)
elif params.col_tree_type == TREE_TYPE_FLEXIBLE:
col_tree = flex_tree_build.flex_tree_diffusion(
col_aff, params.col_tree_constant)
dual_col_trees.append(col_tree)
col_tree_descs.append("Iteration {}".format(i))
# column tree finished, now starting with rows
message = "Iteration {}: calculating row affinity...".format(i)
print message
# calculate row affinity based on column tree
if params.row_affinity_type == DUAL_EMD:
if params.row_weighted == True:
print "weighted emd"
col_coefs = tree_util.tree_transform_mat(
dual_col_trees[-1]).dot(data.T)
col_weights = np.sqrt(np.sum(col_coefs**2, axis=1))
row_emd = dual_affinity.calc_emd(data.T,
dual_col_trees[-1],
alpha=0,
beta=0,
weights=col_weights)
else:
row_emd = dual_affinity.calc_emd(data.T, dual_col_trees[-1],
params.row_alpha,
params.row_beta)
row_aff = dual_affinity.emd_dual_aff(row_emd)
elif params.row_affinity_type == DUAL_GAUSSIAN:
print "Gaussian dual affinity not supported at the moment."
return None
message = "Iteration {}: calculating row tree...".format(i)
print message
# constructing row tree
if params.row_tree_type == TREE_TYPE_BINARY:
row_tree = bin_tree_build.bin_tree_build(
row_aff, 'r_dyadic', params.row_tree_bal_constant)
elif params.row_tree_type == TREE_TYPE_FLEXIBLE:
row_tree = flex_tree_build.flex_tree_diffusion(
row_aff, params.row_tree_constant)
dual_row_trees.append(row_tree)
row_tree_descs.append("Iteration {}".format(i))
quest_run_desc = "{}".format(datetime.datetime.now())
# iterations have finished, outputting structures of the tree,
# parameters
return PyQuestRun(quest_run_desc, dual_row_trees, dual_col_trees,
row_tree_descs, col_tree_descs, params)
def pyquest(data,params):
#params should be a PyQuestParams object
Publisher.sendMessage("status.bar", "Calculating initial affinity...")
if params.init_aff_type == INIT_AFF_COS_SIM:
init_row_aff = affinity.mutual_cosine_similarity(
data.T,False,0,threshold=params.init_aff_threshold)
elif params.init_aff_type == INIT_AFF_GAUSSIAN:
#add KNN to the page
init_row_aff = affinity.gaussian_euclidean(
data.T, 5, params.init_aff_epsilon)
#Compute diffusion embedding of initial affinities
init_row_vecs,init_row_vals = markov.markov_eigs(init_row_aff, 12)
init_row_vals[np.isnan(init_row_vals)] = 0.0
row_embedding = init_row_vecs.dot(np.diag(init_row_vals))
row_distances = spsp.distance.squareform(spsp.distance.pdist(row_embedding))
row_affinity = np.max(row_distances) - row_distances
#Generate initial tree
#print "call1 tree_constant:{}".format(tree_constant)
Publisher.sendMessage("status.bar", "Calculating initial row tree...")
if params.tree_type == TREE_TYPE_BINARY:
init_row_tree = bintree_construct.median_tree(
init_row_vecs,init_row_vals,max_levels=12)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
# init_row_tree = tree_building.make_tree_embedding(
# row_affinity,params.tree_constant)
init_row_tree = tree_building.make_tree_embedding(
row_affinity,params.tree_constant)
dual_col_trees = []
dual_row_trees = [init_row_tree]
row_tree_descs = ["Initial tree"]
col_tree_descs = []
for i in xrange(params.n_iters):
message = "Iteration {}: calculating column affinity...".format(i)
Publisher.sendMessage("status.bar", message)
#print "Beginning iteration {}".format(i)
if params.col_affinity_type == DUAL_EMD:
col_emd = dual_affinity.calc_emd(data,dual_row_trees[-1],
params.col_alpha,params.col_beta)
col_aff = dual_affinity.emd_dual_aff(col_emd)
elif params.col_affinity_type == DUAL_GAUSSIAN:
print "Gaussian dual affinity not supported at the moment."
return None
message = "Iteration {}: calculating column tree...".format(i)
Publisher.sendMessage("status.bar", message)
if params.tree_type == TREE_TYPE_BINARY:
col_tree = bintree_construct.eigen_tree(data,dual_row_trees[-1],
params.col_alpha,params.col_beta,params.tree_bal_constant)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
col_tree = tree_building.make_tree_embedding(col_aff,
params.tree_constant)
dual_col_trees.append(col_tree)
col_tree_descs.append("Iteration {}".format(i))
message = "Iteration {}: calculating row affinity...".format(i)
Publisher.sendMessage("status.bar", message)
if params.row_affinity_type == DUAL_EMD:
row_emd = dual_affinity.calc_emd(data.T,dual_col_trees[-1],
params.row_alpha,params.row_beta)
row_aff = dual_affinity.emd_dual_aff(row_emd)
elif params.row_affinity_type == DUAL_GAUSSIAN:
print "Gaussian dual affinity not supported at the moment."
return None
message = "Iteration {}: calculating row tree...".format(i)
Publisher.sendMessage("status.bar", message)
if params.tree_type == TREE_TYPE_BINARY:
row_tree = bintree_construct.eigen_tree(data.T,dual_col_trees[-1],
params.row_alpha,params.row_beta,params.tree_bal_constant)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
row_tree = tree_building.make_tree_embedding(row_aff,
params.tree_constant)
dual_row_trees.append(row_tree)
row_tree_descs.append("Iteration {}".format(i))
quest_run_desc = "{}".format(datetime.datetime.now())
return PyQuestRun(quest_run_desc,dual_row_trees,dual_col_trees,
row_tree_descs,col_tree_descs,params)
def pyquest(data, params):
"""
Runs the questionnaire on data with params.
params is a PyQuestParams object.
"""
if params.init_aff_type == INIT_AFF_COS_SIM:
init_row_aff = affinity.mutual_cosine_similarity(
data.T, False, 0, threshold=params.init_aff_threshold)
elif params.init_aff_type == INIT_AFF_GAUSSIAN:
init_row_aff = affinity.gaussian_euclidean(data.T, params.init_aff_knn,
params.init_aff_epsilon)
#Initial row tree
if params.tree_type == TREE_TYPE_BINARY:
init_row_tree = bin_tree_build.bin_tree_build(init_row_aff, 'r_dyadic',
params.tree_bal_constant)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
init_row_tree = flex_tree_build.flex_tree_diffusion(
init_row_aff, params.tree_constant)
dual_col_trees = []
dual_row_trees = [init_row_tree]
row_tree_descs = ["Initial tree"]
col_tree_descs = []
for i in xrange(params.n_iters):
message = "Iteration {}: calculating column affinity...".format(i)
#print "Beginning iteration {}".format(i)
if params.col_affinity_type == DUAL_EMD:
col_emd = dual_affinity.calc_emd(data, dual_row_trees[-1],
params.col_alpha, params.col_beta)
col_aff = dual_affinity.emd_dual_aff(col_emd)
elif params.col_affinity_type == DUAL_GAUSSIAN:
print "Gaussian dual affinity not supported at the moment."
return None
message = "Iteration {}: calculating column tree...".format(i)
if params.tree_type == TREE_TYPE_BINARY:
col_tree = bin_tree_build.bin_tree_build(col_aff, 'r_dyadic',
params.tree_bal_constant)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
col_tree = flex_tree_build.flex_tree_diffusion(
col_aff, params.tree_constant)
dual_col_trees.append(col_tree)
col_tree_descs.append("Iteration {}".format(i))
message = "Iteration {}: calculating row affinity...".format(i)
if params.row_affinity_type == DUAL_EMD:
row_emd = dual_affinity.calc_emd(data.T, dual_col_trees[-1],
params.row_alpha, params.row_beta)
row_aff = dual_affinity.emd_dual_aff(row_emd)
elif params.row_affinity_type == DUAL_GAUSSIAN:
print "Gaussian dual affinity not supported at the moment."
return None
message = "Iteration {}: calculating row tree...".format(i)
if params.tree_type == TREE_TYPE_BINARY:
row_tree = bin_tree_build.bin_tree_build(row_aff, 'r_dyadic',
params.tree_bal_constant)
elif params.tree_type == TREE_TYPE_FLEXIBLE:
row_tree = flex_tree_build.flex_tree_diffusion(
row_aff, params.tree_constant)
dual_row_trees.append(row_tree)
row_tree_descs.append("Iteration {}".format(i))
quest_run_desc = "{}".format(datetime.datetime.now())
return PyQuestRun(quest_run_desc, dual_row_trees, dual_col_trees,
row_tree_descs, col_tree_descs, params)