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convex_hc_denoising.py
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convex_hc_denoising.py
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"""
Code for the dual FISTA algorithm for hierarchical
convex clustering
"""
import copy
import math
import numpy as np
import scipy as sc
import time
from projections import *
from utils import *
TOL_PROJ = 1e-4
TOL_INC = 5
TOL = 1e-2
MAX_ITER_PROJ = 1e4
MAXITER_FISTA = 200
ALPHA = 0.5
def hcc_FISTA_denoise(K, B, pi_prev, lambd, alpha=ALPHA, maxiterFISTA=MAXITER_FISTA,
eta=1.0, tol=TOL, verbose=True, tol_projection=TOL_PROJ,
max_iter_projection=MAX_ITER_PROJ,
logger = None):
''' Hierarchical clustering algorithm based on FISTA (dual)
Input: similarity matrix K assumed to be from a Mercer kernel (or at least PSD)
Output: the regularized soft membership assignment matrix
--------------------------------------------------------------------------
INPUT:
-----------------------------------------------------------
K : the similarity matrix
pi_prev : initialization value for pi (warm start)
lambd : the level of regularization desired
alpha : parameter for the total variation mixed penalty
maxiterFISTA : max number of iterations for FISTA (updates in X)
tol : tolerance level for the stopping criterion,
as a fraction of the number of nodes
sparse : boolean: should the algorithm assume sparisty of K?
verbose : boolean: allow printing of various statistics
and intermediary parameters
OUTPUT:
-----------------------------------------------------------
X : the corresponding soft clustering assignment matrix
t : the time that the procedure took
delta_x : list of updates in x (for each iteration)
delta_p : list of updates in p (for each iteration)
delta_q : list of updates in q (for each iteration)
dual : dual updates
--------------------------------------------------------------------------
'''
# Initialization
x_k, x_km1, y_k = pi_prev, pi_prev, pi_prev
n_nodes, _ = pi_prev.shape
if type(K) == np.matrixlib.defmatrix.matrix:
mask = np.array(K).flatten().reshape([-1,]).nonzero()[0]
else:
indices = K.nonzero()
mask = []
for i in range(K.nnz):
mask += [indices[0][i]*n_nodes+indices[1][i]]
mask = np.array(mask)
I = sc.sparse.eye(n_nodes)
delta_k=sc.sparse.lil_matrix((n_nodes, n_nodes**2))
for ii in range(n_nodes):
ind =K[ii, :].nonzero()[1]
delta_k[ii, ii * n_nodes + ind] = K[ii, ind]
delta_k[ii, ii + ind * n_nodes] = -K[ii, ind]
delta_k[ii, ii + ii * n_nodes] = 0.0
delta_k = delta_k[:, mask]
delta_k = delta_k.todense()
lmax = np.linalg.norm(delta_k,'fro')**2
gamma = 16 * max([alpha**2,(1-alpha)**2])*lmax * lambd**2
if verbose: print("lmax",lmax, "gamma", gamma)
I = sc.sparse.eye(n_nodes)
update = (delta_k.T.dot(x_k.T)).T
#print("update.max(())", update.max())
q = np.zeros((n_nodes, len(mask)))
p = project_unit_ball(update,
is_sparse=False)
q[np.where(update != 0)]= project_unit_cube(update[np.where(update != 0)],
is_sparse=False)
index_rev = [jj*n_nodes + ii for ii in range(n_nodes) for jj in range(n_nodes)]
#print("init p", p.max(), q.max(), q.min())
t_k, it = 1, 1
converged = False
t_k, it = 1, 1
converged = False
tic0 = time.time()
delta_x = []
delta_p = []
delta_q = []
dual = []
it = 0
eps_reg =1e-5
p_old = copy.deepcopy(p)
q_old = copy.deepcopy(q)
r = copy.deepcopy(p)
s = copy.deepcopy(q)
inc = 0
vpos = np.vectorize(lambda x: x if x>0 else 0)
while not converged:
belly = (alpha * r + (1-alpha) * s).dot(delta_k.T)
proj = project_DS2(vpos(B-lambd * belly), max_it=max_iter_projection, eps = tol_projection)
x_k = proj
L_x = proj.dot(delta_k)
#print("update.max(())", L_x.max())
update_p = p + 2.0 * alpha *lambd / gamma * L_x
p = project_unit_ball(update_p,
is_sparse=False)
update_q = q+ 2.0 * (1-alpha) / gamma * L_x
inv_update_q = copy.deepcopy(update_q)
inv_update_q[np.where(update_q!=0)] = 1.0/np.abs(update_q[np.where(inv_update_q!=0)])
q = np.multiply(inv_update_q, update_q)
if verbose: print("max q, p",q.max(), q.min(), p.max(), p.min())
#### Check convergence
delta_x.append(np.linalg.norm( x_k - x_km1, 'fro')/np.linalg.norm(x_km1,'fro'))
delta_p.append(np.linalg.norm(p - p_old, 'fro'))
delta_q.append(np.linalg.norm(q - q_old, 'fro'))
if delta_x[-1] < TOL:
inc += 1
else:
inc = 0
converged = (math.sqrt((alpha**2 * np.linalg.norm(p-p_old,'fro')**2
+ (1 - alpha)**2 * np.linalg.norm(q-q_old,'fro')**2))
/ np.max([0, math.sqrt((alpha**2 * np.linalg.norm(p_old,'fro')**2
+ (1 - alpha)**2 * np.linalg.norm(q_old,'fro')**2))])
< tol)\
or (delta_x[-1] < tol and it >= 2)\
or (it > maxiterFISTA)
if verbose:
if logger is not None: logger.info("norm dual= %f"%(math.sqrt((alpha**2 * np.linalg.norm(p-p_old,'fro')**2
+ (1 - alpha)**2 * np.linalg.norm(q - q_old, 'fro')**2))
/ np.max([0, math.sqrt((alpha**2 * np.linalg.norm(p_old, 'fro')**2
+ (1 - alpha)**2 * np.linalg.norm(q_old, 'fro')**2))])))
else: print("norm", math.sqrt((alpha**2 * np.linalg.norm(p - p_old, 'fro')**2
+ (1 - alpha)**2 * np.linalg.norm(q - q_old, 'fro')**2))
/ np.max([0, math.sqrt((alpha**2 * np.linalg.norm(p_old, 'fro')**2
+ (1 - alpha)**2 * np.linalg.norm(q_old, 'fro')**2))]))
t_kp1 = 0.5 * (1 + np.sqrt(1 + 4 * t_k**2))
r = p + (t_k - 1.0) / t_kp1 * (p - p_old)
s = q + (t_k - 1.0) / t_kp1 * (q - q_old)
t_k = t_kp1
x_km1 = x_k
p_old, q_old = copy.deepcopy(p), copy.deepcopy(q)
it += 1
if verbose:
try: eff_rank = efficient_rank(x_k)
except: eff_rank = np.nan
if logger is not None:
logger.info('inner loop %i: efficient rank x_k: %f, delta_x: %f'%(it, eff_rank, delta_x[-1])
)
else:
print('inner loop %i: efficient rank x_k: %f, delta_x: %f'%(it, eff_rank, delta_x[-1]))
toc0 = time.time()
if verbose: print("time:",time.time() - tic0)
belly = (alpha * p+ (1.0 - alpha) * q).dot(delta_k.T)
x_k = project_DS2(B - lambd * belly, max_it=max_iter_projection, eps = tol_projection)
val = np.trace(x_k.T.dot(K.todense().dot(x_k))
- 2*(K.todense() -lambd *(delta_k.dot(alpha * p.T + (1.0 - alpha) * q.T)).dot(x_k)))
if logger is not None:
logger.info('--------------------------------------------------------')
return x_k, toc0-tic0, delta_x, delta_p, delta_q, dual, val
def hcc_FISTA(K, pi_warm_start, lambd0, alpha=ALPHA,
maxiterFISTA=MAXITER_FISTA, tol=TOL, debug_mode=True,
lambda_spot=0, verbose=False, logger=None):
if debug_mode: verbose =True
Y, pi_prev, pi_prev_old = [pi_warm_start] * 3
evol_efficient_rank=[]
#L = 2 * sc.sparse.linalg.norm(K, 'fro')
L = 2*sc.sparse.linalg.norm(K.power(2), 'fro')
lambd = 2 * lambd0 / L
t_k = 1
tic = time.time()
delta_pi=[]
it = 0
converged = False
if verbose:
if logger is not None: logger.info("Beginning l=%f"%(lambd0))
else: print("Beginning l=%f"%(lambd0))
B = pi_prev
inc = 0
inc_rank = 0
n_nodes = K.shape[0]
indices = K.nonzero()
mask = []
for i in range(K.nnz):
mask += [indices[0][i]*n_nodes+indices[1][i]]
mask = np.array(mask)
delta_k=sc.sparse.lil_matrix((n_nodes, n_nodes**2))
for ii in range(n_nodes):
ind =K[ii, :].nonzero()[1]
delta_k[ii, ii * n_nodes + ind] = K[ii, ind]
delta_k[ii, ii + ind * n_nodes] = -K[ii, ind]
delta_k[ii, ii + ii * n_nodes] = 0.0
delta_k = delta_k[:, mask]
delta_k = delta_k.todense()
old_val = np.trace(pi_prev.T.dot(K.todense().dot(pi_prev))
- 2*(K.todense().dot(pi_prev)
-lambd * (ALPHA * np.sqrt(np.sum(np.square(delta_k.T.dot(pi_prev)),axis=-1)).sum()
+(1-ALPHA) * np.sum(np.abs(delta_k.T.dot(pi_prev))))))
delta_val= []
while not converged:
g_t = (K.todense().dot(B) - K.todense())
Z, time_taken, delta_x, _, _, dual, val = hcc_FISTA_denoise(K,
B - 2.0/L * g_t,
pi_prev,
lambd0,
alpha=alpha,
maxiterFISTA=maxiterFISTA,
eta=1.0,
tol=tol,
verbose=True,
tol_projection=TOL_PROJ,
logger=logger)
pi_prev = Z
if False: #old_val < val:
pi_prev = pi_prev_old
delta_val.append(0.0)
else:
delta_val.append(np.abs(val-old_val)/np.abs(old_val))
old_val = val
t_kp1 = 0.5 * (1 + np.sqrt(1 + 4 * t_k**2))
delta_pi.append(np.linalg.norm( pi_prev_old-pi_prev, 'fro')/np.linalg.norm( pi_prev_old, 'fro'))
if delta_val[-1]< tol:
inc+=1
else:
inc=0
print("inc = ", inc)
converged = (inc > TOL_INC) or (it > maxiterFISTA)
try: eff_rank = efficient_rank(pi_prev)
except: eff_rank = np.nan
evol_efficient_rank += [eff_rank]
B = pi_prev + t_k / t_kp1 * (Z - pi_prev) +\
(t_k - 1) / t_kp1 * (pi_prev - pi_prev_old)
pi_prev_old = pi_prev
t_k = t_kp1
it+=1
if verbose:
if logger is not None:
logger.info("it:%i, convergence value:%f, convergence pi:%f, rk: %f)"%(it,
delta_val[-1],
delta_pi[-1],
evol_efficient_rank[-1]))
else:
print("it:%i, convergence value:%f, convergence pi:%f, rk: %f)"%(it,
delta_val[-1],
delta_pi[-1],
evol_efficient_rank[-1]))
print('-----------------------------------')
if logger is not None:
logger.info("**********************************")
logger.info("**********************************")
logger.info("**********************************")
toc = time.time()
return pi_prev, toc-tic, evol_efficient_rank, delta_pi