left_dim=d,
right_dim=d,
nb_factors=nb_factors,
sparsity_factor=sparsity_factor,
residual_on_right=True,
fast_unstable_proj=False,
constant_first=False)
logger.info(
"Description of projection operators for each iteration of hierarchical_palm: \n{}"
.format(pprint.pformat(lst_proj_op_by_fac_step_desc)))
print(np.__version__)
# Call the algorithm
final_lambda, final_factors, final_X, _, _ = hierarchical_palm4msa(
arr_X_target=H,
lst_S_init=lst_factors,
lst_dct_projection_function=lst_proj_op_by_fac_step,
f_lambda_init=_lambda,
nb_iter=nb_iter,
update_right_to_left=True,
residual_on_right=True)
# Vizualization utility
visual_evaluation_palm4msa(H, lst_factors, final_factors, final_X)
vec = np.random.rand(d)
h_vec = H @ vec
r_vec = final_X @ vec
logger.info("Distance matrice to random vector (true vs fake):{}".format(
norm(h_vec - r_vec) / np.linalg.norm(r_vec)))
def qmeans(X_data: np.ndarray,
K_nb_cluster: int,
nb_iter: int,
nb_factors: int,
params_palm4msa: dict,
initialization: np.ndarray,
hierarchical_inside=False,
graphical_display=False):
"""
:param X_data: The data matrix of n examples in dimensions d in shape (n, d).
:param K_nb_cluster: The number of clusters to look for.
:param nb_iter: The maximum number of iteration.
:param nb_factors: The number of factors for the decomposition.
:param initialization: The initial matrix of centroids not yet factorized.
:param params_palm4msa: The dictionnary of parameters for the palm4msa algorithm.
:param hierarchical_inside: Tell the algorithm if the hierarchical version of palm4msa should be used.
:param graphical_display: Tell the algorithm to display the results.
:return:
"""
assert K_nb_cluster == initialization.shape[0]
X_data_norms = get_squared_froebenius_norm_line_wise(X_data)
init_lambda = params_palm4msa["init_lambda"]
nb_iter_palm = params_palm4msa["nb_iter"]
lst_proj_op_by_fac_step = params_palm4msa["lst_constraint_sets"]
residual_on_right = params_palm4msa["residual_on_right"]
X_centroids_hat = copy.deepcopy(initialization)
min_K_d = min(X_centroids_hat.shape)
lst_factors = [np.eye(min_K_d) for _ in range(nb_factors)]
eye_norm = np.sqrt(K_nb_cluster)
lst_factors[0] = np.eye(K_nb_cluster) / eye_norm
lst_factors[1] = np.eye(K_nb_cluster, min_K_d)
lst_factors[-1] = np.zeros((min_K_d, X_centroids_hat.shape[1]))
if graphical_display:
lst_factors_init = copy.deepcopy(lst_factors)
_lambda_tmp, lst_factors, U_centroids, nb_iter_by_factor, objective_palm = hierarchical_palm4msa(
arr_X_target=np.eye(K_nb_cluster) @ X_centroids_hat,
lst_S_init=lst_factors,
lst_dct_projection_function=lst_proj_op_by_fac_step,
f_lambda_init=init_lambda * eye_norm,
nb_iter=nb_iter_palm,
update_right_to_left=True,
residual_on_right=residual_on_right,
graphical_display=False)
_lambda = _lambda_tmp / eye_norm
if graphical_display:
if hierarchical_inside:
plt.figure()
plt.yscale("log")
plt.scatter(np.arange(len(objective_palm) * 3, step=3),
objective_palm[:, 0],
marker="x",
label="before split")
plt.scatter(np.arange(len(objective_palm) * 3, step=3) + 1,
objective_palm[:, 1],
marker="x",
label="between")
plt.scatter(np.arange(len(objective_palm) * 3, step=3) + 2,
objective_palm[:, 2],
marker="x",
label="after finetune")
plt.plot(np.arange(len(objective_palm) * 3),
objective_palm.flatten(),
color="k")
plt.legend()
plt.show()
visual_evaluation_palm4msa(
np.eye(K_nb_cluster) @ X_centroids_hat, lst_factors_init,
lst_factors, _lambda * multi_dot(lst_factors))
objective_function = np.empty((nb_iter, 2))
# Loop for the maximum number of iterations
i_iter = 0
delta_objective_error_threshold = 1e-6
delta_objective_error = np.inf
while (i_iter <= 1) or (
(i_iter < nb_iter) and
(delta_objective_error > delta_objective_error_threshold)):
logger.info("Iteration Qmeans {}".format(i_iter))
U_centroids = _lambda * multi_dot(lst_factors[1:])
if i_iter > 0:
objective_function[i_iter,
0] = compute_objective(X_data, U_centroids,
indicator_vector)
# Assign all points to the nearest centroid
# first get distance from all points to all centroids
distances = get_distances(X_data,
U_centroids,
precomputed_data_points_norm=X_data_norms)
# then, Determine class membership of each point
# by picking the closest centroid
indicator_vector = np.argmin(distances, axis=1)
objective_function[i_iter,
1] = compute_objective(X_data, U_centroids,
indicator_vector)
# Update centroid location using the newly
# assigned data point classes
for c in range(K_nb_cluster):
X_centroids_hat[c] = np.mean(X_data[indicator_vector == c], 0)
# get the number of observation in each cluster
cluster_names, counts = np.unique(indicator_vector, return_counts=True)
cluster_names_sorted = np.argsort(cluster_names)
if len(counts) < K_nb_cluster:
raise ValueError(
"Some clusters have no point. Aborting iteration {}".format(
i_iter))
diag_counts_sqrt = np.diag(np.sqrt(
counts[cluster_names_sorted])) # todo use sparse matrix object
diag_counts_sqrt_norm = np.linalg.norm(
diag_counts_sqrt
) # todo analytic sqrt(n) instead of cumputing it with norm
diag_counts_sqrt_normalized = diag_counts_sqrt / diag_counts_sqrt_norm
# set it as first factor
lst_factors[0] = diag_counts_sqrt_normalized
if graphical_display:
lst_factors_init = copy.deepcopy(lst_factors)
if hierarchical_inside:
_lambda_tmp, lst_factors, _, nb_iter_by_factor, objective_palm = hierarchical_palm4msa(
arr_X_target=diag_counts_sqrt @ X_centroids_hat,
lst_S_init=lst_factors,
lst_dct_projection_function=lst_proj_op_by_fac_step,
# f_lambda_init=_lambda,
f_lambda_init=_lambda * diag_counts_sqrt_norm,
nb_iter=nb_iter_palm,
update_right_to_left=True,
residual_on_right=residual_on_right,
graphical_display=False)
loss_palm_before = objective_palm[0, 0]
loss_palm_after = objective_palm[-1, -1]
else:
_lambda_tmp, lst_factors, _, objective_palm, nb_iter_palm = palm4msa(
arr_X_target=diag_counts_sqrt @ X_centroids_hat,
lst_S_init=lst_factors,
nb_factors=len(lst_factors),
lst_projection_functions=lst_proj_op_by_fac_step[-1]
["finetune"],
f_lambda_init=_lambda * diag_counts_sqrt_norm,
nb_iter=nb_iter_palm,
update_right_to_left=True,
graphical_display=False)
loss_palm_before = objective_palm[0, -1]
loss_palm_after = objective_palm[-1, -1]
logger.debug("Loss palm before: {}".format(loss_palm_before))
logger.debug("Loss palm after: {}".format(loss_palm_after))
if graphical_display:
if hierarchical_inside:
plt.figure()
plt.yscale("log")
plt.scatter(np.arange(len(objective_palm) * 3, step=3),
objective_palm[:, 0],
marker="x",
label="before split")
plt.scatter(np.arange(len(objective_palm) * 3, step=3) + 1,
objective_palm[:, 1],
marker="x",
label="between")
plt.scatter(np.arange(len(objective_palm) * 3, step=3) + 2,
objective_palm[:, 2],
marker="x",
label="after finetune")
plt.plot(np.arange(len(objective_palm) * 3),
objective_palm.flatten(),
color="k")
plt.legend()
plt.show()
visual_evaluation_palm4msa(diag_counts_sqrt @ X_centroids_hat,
lst_factors_init, lst_factors,
_lambda_tmp * multi_dot(lst_factors))
_lambda = _lambda_tmp / diag_counts_sqrt_norm
logger.debug("Returned loss (with diag) palm: {}".format(
objective_palm[-1, 0]))
if i_iter >= 2:
delta_objective_error = np.abs(
objective_function[i_iter, 0] -
objective_function[i_iter - 1, 0]
) / objective_function[
i_iter - 1,
0] # todo vérifier que l'erreur absolue est plus petite que le threshold plusieurs fois d'affilée
i_iter += 1
U_centroids = _lambda * multi_dot(lst_factors[1:])
distances = get_distances(X_data,
U_centroids,
precomputed_data_points_norm=X_data_norms)
indicator_vector = np.argmin(distances, axis=1)
return objective_function[:i_iter], U_centroids, indicator_vector