def _polar_rotate_shrink(X, gamma=0.1):
# Algorithm 1 from the paper
U, _, _ = selectSVD(X, n_components=X.shape[1], algorithm="full")
# U = _polar(X)
# R, _ = orthogonal_procrustes(U_old, U)
# print(np.linalg.norm(U_old @ R - U))
U_rot = _varimax(U)
U_thresh = soft_threshold(U_rot, gamma)
return U_thresh
def _initialize(self, X):
"""[summary]
Parameters
----------
X : [type]
[description]
Returns
-------
[type]
[description]
"""
U, D, Vt = selectSVD(X, n_components=self.n_components)
score = np.linalg.norm(D)
return U, Vt.T, score
def sparse_component_analysis(X,
n_components=2,
gamma=None,
max_iter=10,
reorder_components=True):
X = X.copy()
U, D, Vt = selectSVD(X, n_components=n_components)
if gamma is None:
gamma = np.sqrt(U.shape[1] * X.shape[1])
Z_hat = U
Y_hat = Vt.T
i = 0
while i < max_iter:
Y_hat = _polar_rotate_shrink(X.T @ Z_hat, gamma=gamma)
Z_hat = _polar(X @ Y_hat)
i += 1
if reorder_components:
Z_hat, Y_hat = _reorder_components(X, Z_hat, Y_hat)
return Z_hat, Y_hat
def _polar(X):
# REF: https://en.wikipedia.org/wiki/Polar_decomposition#Relation_to_the_SVD
U, D, Vt = selectSVD(X, n_components=X.shape[1], algorithm="full")
return U @ Vt
def _polar_rotate_shrink(X, gamma=0.1):
U, D, Vt = selectSVD(X, n_components=X.shape[1], algorithm="full")
U_rot = _varimax(U)
U_thresh = _soft_threshold(U_rot, gamma)
return U_thresh
def _initialize(X):
U, D, Vt = selectSVD(X, n_components=n_components)
return U, Vt.T
va="center",
fontsize="xx-small",
)
ax.axis("off")
# ax.axis("off")
ax.set(xticks=[], yticks=[], ylabel="", xlabel="")
n_iter = 1
n_show = 5
fig, axs = plt.subplots(n_iter * n_show, 3 * n_show, figsize=(15, 5))
colors = sns.color_palette("deep", 3)
for i in range(n_iter):
A = X.T @ Z_hat
U, _, _ = selectSVD(A, n_components=A.shape[1], algorithm="full")
plot_components(U, axs[i * n_show : (i + 1) * n_show, :n_show], color=colors[0])
# pairplot(U, alpha=0.2)
U_rot = _varimax(U)
plot_components(
U_rot, axs[i * n_show : (i + 1) * n_show, n_show : 2 * n_show], color=colors[1]
)
# pairplot(U_rot, alpha=0.2)
U_thresh = soft_threshold(U_rot, gamma=5 * n_components)
plot_components(
U_thresh,
axs[i * n_show : (i + 1) * n_show, 2 * n_show : 3 * n_show],
color=colors[2],
)
#%% sns.histplot(lr_score) #%% adj = mg.sum.adj.copy() adj = remove_loops(adj) H = adj - adj.T # is it indeed skew symmetric? print((H == -H.T).all()) from graspologic.embed import selectSVD U, S, V = selectSVD(H, n_components=2) #%% n = len(adj) e = np.full(n, 1 / np.sqrt(n)) P = U @ U.T # project ones vector onto span of the first two components e_proj = P @ e e_proj = e_proj / np.linalg.norm(e_proj) # need to find the intersection of the orthogonal complement of e_proj and the span of U P_e_proj = np.outer(e_proj, e_proj) # get random vector in the span of U u_rand = P @ np.random.normal(size=n) # get vector orthogonal to e_proj svd_score = (np.eye(n) - P_e_proj) @ u_rand
X = ase.fit_transform(A)
Q = ortho_group.rvs(X.shape[1])
X = X @ Q
Xs.append(X)
sns.scatterplot(x=X[:, 0],
y=X[:, 1],
hue=labels,
ax=axs[i],
legend=False)
# ax.set(xticks=[], yticks=[])
plt.tight_layout()
Z = np.concatenate(Xs, axis=1)
# ase = AdjacencySpectralEmbed(n_components=2)
# V = ase.fit_transform(Z)
V, D, W = selectSVD(Z, n_components=2)
Vs.append(V)
#%%
from graspologic.align import OrthogonalProcrustes
fig, axs = plt.subplots(2, 5, figsize=(20, 8))
axs = axs.flat
for i, V in enumerate(Vs):
V_rot = OrthogonalProcrustes().fit_transform(V, Vs[0])
# V_rot = V
ax = axs[i]
sns.scatterplot(x=V_rot[:, 0],
y=V_rot[:, 1],
hue=labels,
ax=ax,
