def test_sparse_randomized_pca_inverse():
"""Test that RandomizedPCA is inversible on sparse data"""
rng = np.random.RandomState(0)
n, p = 50, 3
X = rng.randn(n, p) # spherical data
X[:, 1] *= 0.00001 # make middle component relatively small
# no large means because the sparse version of randomized pca does not do
# centering to avoid breaking the sparsity
X = csr_matrix(X)
# same check that we can find the original data from the transformed signal
# (since the data is almost of rank n_components)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always", DeprecationWarning)
pca = RandomizedPCA(n_components=2, random_state=0).fit(X)
assert_equal(len(w), 1)
assert_equal(w[0].category, DeprecationWarning)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
assert_almost_equal(X.todense(), Y_inverse, decimal=2)
# same as above with whitening (approximate reconstruction)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always", DeprecationWarning)
pca = RandomizedPCA(n_components=2, whiten=True, random_state=0).fit(X)
assert_equal(len(w), 1)
assert_equal(w[0].category, DeprecationWarning)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
relative_max_delta = (np.abs(X.todense() - Y_inverse) / np.abs(X).mean()).max()
# XXX: this does not seam to work as expected:
assert_almost_equal(relative_max_delta, 0.91, decimal=2)
def test_sparse_randomized_pca_inverse():
"""Test that RandomizedPCA is inversible on sparse data"""
rng = np.random.RandomState(0)
n, p = 50, 3
X = rng.randn(n, p) # spherical data
X[:, 1] *= .00001 # make middle component relatively small
# no large means because the sparse version of randomized pca does not do
# centering to avoid breaking the sparsity
X = csr_matrix(X)
# same check that we can find the original data from the transformed signal
# (since the data is almost of rank n_components)
pca = RandomizedPCA(n_components=2, random_state=0)
assert_warns(DeprecationWarning, pca.fit, X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
assert_almost_equal(X.toarray(), Y_inverse, decimal=2)
# same as above with whitening (approximate reconstruction)
pca = assert_warns(
DeprecationWarning,
RandomizedPCA(n_components=2, whiten=True, random_state=0).fit, X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
relative_max_delta = (np.abs(X.toarray() - Y_inverse) /
np.abs(X.toarray()).mean()).max()
# XXX: this does not seam to work as expected:
assert_almost_equal(relative_max_delta, 0.91, decimal=2)
def open_img():
x = filedialog.askopenfilenames(
parent=root,
initialdir='/',
initialfile='tmp',
filetypes=[
("All files", "*")])
img = Image.open(x[0])
img = img.resize((250, 250), Image.ANTIALIAS)
img = ImageTk.PhotoImage(img)
panel = tk.Label(root, image=img)
panel.image = img
panel.grid(row=70, column=1)
image = cv2.imread(x[0])
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
cv2.imwrite("grey.jpeg", gray)
gray.shape
img = mpimg.imread("grey.jpeg")
f=compo()
ipca = RandomizedPCA(f)
ipca.fit(img)
img_c = ipca.transform(img)
print(img_c.shape)
temp = ipca.inverse_transform(img_c)
print(temp.shape)
cv2.imwrite("pca1.jpg", temp)
print(np.sum(ipca.explained_variance_ratio_))
plt.plot(np.cumsum(ipca.explained_variance_ratio_))
plt.xlabel('number of components')
plt.ylabel('cumulative explained variance');
plt.savefig("graph.jpg")
def test_randomized_pca_inverse():
"""Test that RandomizedPCA is inversible on dense data"""
rng = np.random.RandomState(0)
n, p = 50, 3
X = rng.randn(n, p) # spherical data
X[:, 1] *= 0.00001 # make middle component relatively small
X += [5, 4, 3] # make a large mean
# same check that we can find the original data from the transformed signal
# (since the data is almost of rank n_components)
pca = RandomizedPCA(n_components=2, random_state=0).fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
assert_almost_equal(X, Y_inverse, decimal=2)
# same as above with whitening (approximate reconstruction)
pca = RandomizedPCA(n_components=2, whiten=True, random_state=0).fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
relative_max_delta = (np.abs(X - Y_inverse) / np.abs(X).mean()).max()
assert_almost_equal(relative_max_delta, 0.11, decimal=2)
def test_randomized_pca_inverse():
"""Test that RandomizedPCA is inversible on dense data"""
rng = np.random.RandomState(0)
n, p = 50, 3
X = rng.randn(n, p) # spherical data
X[:, 1] *= .00001 # make middle component relatively small
X += [5, 4, 3] # make a large mean
# same check that we can find the original data from the transformed signal
# (since the data is almost of rank n_components)
pca = RandomizedPCA(n_components=2, random_state=0).fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
assert_almost_equal(X, Y_inverse, decimal=2)
# same as above with whitening (approximate reconstruction)
pca = RandomizedPCA(n_components=2, whiten=True, random_state=0).fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
relative_max_delta = (np.abs(X - Y_inverse) / np.abs(X).mean()).max()
assert_almost_equal(relative_max_delta, 0.11, decimal=2)
def gap_statistic(x, random_datasets=64):
"""
Returns the gap statistic of the data set. Keeps increasing the number of clusters until the maximum gap statistic is more than double the current gap statistic.
http://blog.echen.me/2011/03/19/counting-clusters/
"""
assert isinstance(x, np.ndarray)
assert len(x.shape) == 2
if x.shape > SETTINGS.GAP_STATISTIC.RANDOMIZED_PCA_THRESHOLD:
pca = RandomizedPCA(SETTINGS.GAP_STATISTIC.RANDOMIZED_PCA_THRESHOLD)
else:
pca = PCA()
pca.fit(x)
transformed = pca.transform(x)
reference_datasets = [
pca.inverse_transform(generate_random_dataset(transformed))
for _ in range(random_datasets)
]
max_gap_statistic = -1
best_num_clusters = 1
for num_clusters in range(1, x.shape[0] + 1):
kmeans = MiniBatchKMeans(num_clusters)
kmeans.fit(x)
trained_dispersion = dispersion(kmeans, x)
random_dispersions = [
dispersion(kmeans, data) for data in reference_datasets
]
gap_statistic = np.log(sum(random_dispersions) /
random_datasets) - np.log(trained_dispersion)
if gap_statistic > max_gap_statistic:
max_gap_statistic = gap_statistic
best_num_clusters = num_clusters
if gap_statistic < max_gap_statistic * SETTINGS.GAP_STATISTIC.MAXIMUM_DECLINE:
break
if num_clusters > best_num_clusters + SETTINGS.GAP_STATISTIC.NUM_CLUSTERS_WITHOUT_IMPROVEMENT:
break
return best_num_clusters
def callRandomizedPCA(X, n, type):
# type = 1 for Energy data to avoid 1D plot, 2 for others
rpca = RandomizedPCA(n_components=n)
rpca.fit(X)
transformed = rpca.transform(X)
print("original shape: ", X.shape)
print("transformed shape after Randomized PCA:", transformed.shape)
X_recons = rpca.inverse_transform(transformed)
print("reconstruct shape after Randomized PCA:", X_recons.shape)
if type == 2: # Gstore data
myplot(transformed[:, 0:2], np.transpose(rpca.components_[0:2, :]))
plt.show()
myplot(X_recons[:, 0:2], np.transpose(rpca.components_[0:2, :]))
plt.show()
return transformed
def gap_statistic(x, random_datasets=64):
"""
Returns the gap statistic of the data set. Keeps increasing the number of clusters until the maximum gap statistic is more than double the current gap statistic.
http://blog.echen.me/2011/03/19/counting-clusters/
"""
assert isinstance(x, np.ndarray)
assert len(x.shape) == 2
if x.shape > GAP_STATISTIC.RANDOMIZED_PCA_THRESHOLD:
pca = RandomizedPCA(GAP_STATISTIC.RANDOMIZED_PCA_THRESHOLD)
else:
pca = PCA()
pca.fit(x)
transformed = pca.transform(x)
reference_datasets = [pca.inverse_transform(generate_random_dataset(transformed)) for _ in range(random_datasets)]
max_gap_statistic = -1
best_num_clusters = 1
for num_clusters in range(1, x.shape[0] + 1):
kmeans = MiniBatchKMeans(num_clusters)
kmeans.fit(x)
trained_dispersion = dispersion(kmeans, x)
random_dispersions = [dispersion(kmeans, data) for data in reference_datasets]
gap_statistic = np.log(sum(random_dispersions) / random_datasets) - np.log(trained_dispersion)
if gap_statistic > max_gap_statistic:
max_gap_statistic = gap_statistic
best_num_clusters = num_clusters
if gap_statistic < max_gap_statistic * GAP_STATISTIC.MAXIMUM_DECLINE:
break
if num_clusters > best_num_clusters + GAP_STATISTIC.NUM_CLUSTERS_WITHOUT_IMPROVEMENT:
break
return best_num_clusters
def PCA():
img = mpimg.imread('imagep.png')
print("Real Image Shape:", img.shape)
a = img.shape[0]
b = img.shape[1]
c = img.shape[2]
img_r = np.reshape(img, (a, b * c))
print("Reshaped Image Shape:", img_r.shape)
ipca = RandomizedPCA(1000).fit(img_r)
img_c = ipca.transform(img_r)
print(img_c.shape)
print(np.sum(ipca.explained_variance_ratio_))
temp = ipca.inverse_transform(img_c)
temp = np.reshape(temp, (a, b, c))
print(temp.shape, a, b, c)
plt.axis('off')
plt.imshow(temp)
#plt.imshow(temp)
plt.show()
kmeans = KMeans(k=49, n_init=1)
if not os.path.exists(MODEL_NAME):
print "Training on ", train_set_x.shape
print "Fitting PCA"
X_tr = pca.fit_transform(X_tr)
X_tst = pca.transform(X_tst)
print "Fitted PCA"
# Train KMeans on whitened data
print "Transforming data"
X_tr_white = pca.fit_transform(X_tr)
print "Fitting KMEANS"
kmeans.fit(X_tr_white)
filters_kmeans = pca.inverse_transform(kmeans.cluster_centers_)
else:
pca, kmeans = cPickle.load(open(MODEL_NAME, "r"))
import matplotlib.pylab as plt
if Visualise:
for i, f in enumerate(F):
plt.subplot(7, 7, i + 1)
plt.imshow(f.reshape(ImageSideFinal, ImageSideFinal), cmap="gray")
plt.axis("off")
plt.show()
N=min(1000, test_set_x.shape[0])
x_plt, y_plt, clr_plt = [0]*int(N), [0]*int(N), [0]*int(N)
# range(2,74) means its goes from col 2 to col 73 df_input_data = df_input[list(range(2, 74))] df_input_target = df_input[list(range(0, 1))] colors = numpy.random.rand(len(df_input_target)) # Randomized PCA from sklearn.decomposition import RandomizedPCA pca = RandomizedPCA(n_components=6) #from optimal pca components chart n_components=6 proj1 = pca.fit_transform(df_input_data) # Relative weights on features print pca.explained_variance_ratio_ print pca.components_ # Plotting mpyplot.figure(1) p1 = mpyplot.scatter(proj1[:, 0], proj1[:, 1], c=colors) mpyplot.colorbar(p1) mpyplot.show(p1) # Randomized PCA using inverse transform - to make it linear proj2 = pca.inverse_transform(proj1) # Plotting mpyplot.figure(2) # p1 = mpyplot.scatter(proj1[:, 0], proj1[:, 1], c=colors, alpha=0.2) p2 = mpyplot.scatter(proj2[:, 0], proj2[:, 1], c=colors, alpha=0.8) mpyplot.colorbar(p1) mpyplot.show(p2)
print('reshaping image into 2 dimensions for PCA')
img_r = np.reshape(img, (img.shape[0],img.shape[1]*img.shape[2] ))
print(img_r.shape)
number_of_components = 64
print('transofming image with'+str(number_of_components)+'number of components')
ipca = RandomizedPCA(number_of_components).fit(img_r)
img_c = ipca.transform(img_r)
print('new shape of image after transformation')
print(img_c.shape)
print('Randomized PCA with 64 components:')
print(np.sum(ipca.explained_variance_ratio_))
print('inversing the transformation back to image')
temp = ipca.inverse_transform(img_c)
print('reshaping back to three dimension')
temp = np.reshape(temp, (img.shape[0],img.shape[1],img.shape[2]))
print(temp.shape)
m = interp1d([temp.min(),temp.max()],[0,1])
print('rescaling image this may take some time....')
for i in range(temp.shape[0]):
for j in range(temp.shape[1]):
for k in range(temp.shape[2]):
temp[i][j][k] = float(m(temp[i][j][k]))
fig = plt.figure()
plt.axis('off')
plt.imshow(temp)
plotImageGrid(X[sample_patches_ind, ...],
image_size=(patch_size, patch_size, 3), nrow=6, ncol=6)
#plt.savefig('patches16.png')
plt.show()
#perform whitening
# 590 components = 99% explained varience
pca = RandomizedPCA(n_components=590, whiten=True, random_state=seed)
w_X = pca.fit_transform(X)
print("==== PCA fitted =====")
print("variance explained:")
print(pca.explained_variance_ratio_)
#plot whitened patches after inverse transform
orig_X = pca.inverse_transform(w_X[sample_patches_ind, ...])
plotImageGrid(orig_X, image_size=(patch_size, patch_size, 3), nrow=6, ncol=6)
#plt.savefig('patches_whitened16.png')
plt.show()
###KMEANS
k_means = cluster.KMeans(n_clusters=50, n_jobs=3)
k_means.fit(X)
print("==== K-Means fitted ====")
# get centroids and transform them to original space
#tmp = pca.inverse_transform(k_means.cluster_centers_.copy())
tmp = k_means.cluster_centers_.copy()
plotImageGrid(tmp, image_size=(16, 16, 3), nrow=5, ncol=10 )
plt.savefig('centroids_nw.png')
cmap='bone')
plt.show()
# In image above, you should could check, that at first the principal components are the base face structure, then we moved to recognize face features like nose, eyes, mouth, etc
# Let's find out the cumulative some of the variance to determine how much PCs suitable for our case
plt.plot(np.cumsum(pca.explained_variance_ratio_))
plt.xlabel('Number of components: ')
plt.ylabel('Cumulative explained variance: ')
plt.show()
# From the plot above, we can safely assume that using 150 PCs alreaed retrieve ~90% of our variances
# Let's see it by comparing the original image with image using only 150PCs
pca = RandomizedPCA(150).fit(faces.data)
components = pca.transform(faces.data)
pca_faces = pca.inverse_transform(components)
# Plot the results
fig, ax = plt.subplots(2,
10,
figsize=(10, 2.5),
subplot_kw={
'xticks': [],
'yticks': []
},
gridspec_kw=dict(hspace=0.1, wspace=0.1))
for i in range(10):
dimensionH = faces.images.shape[1]
dimensionW = faces.images.shape[2]
ax[0, i].imshow(faces.data[i].reshape(dimensionH, dimensionW),
for i, ax in enumerate(axes.flat):
ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')
plt.show()
plt.plot(np.cumsum(pca.explained_variance_ratio_))
plt.xlabel('number of components')
plt.ylabel('cumulative explained variance')
plt.show()
# compute the components and projected faces
pca = RandomizedPCA(150).fit(faces.data)
components = pca.transform(faces.data)
projected = pca.inverse_transform(components)
# plot the results
fig,ax=plt.subplots(2,10,figsize=(10,2.5),subplot_kw={'xticks':[],'yticks':[]},\
gridspec_kw=dict(hspace=0.1,wspace=0.1))
for i in range(10):
ax[0, i].imshow(faces.data[i].reshape(62, 47), cmap='binary_r')
ax[1, i].imshow(projected[i].reshape(62, 47), cmap='binary_r')
ax[0, 0].set_ylabel('full-dim\ninput')
ax[1, 0].set_ylabel('150-dim\nreconstruction')
plt.show()
resolution = 50
alpha_X, beta_Y = np.meshgrid(
np.linspace(
np.min(path[:, 0]) - 1.0,
np.max(path[:, 0]) + 1.0, resolution),
np.linspace(
np.min(path[:, 1]) - 1.0,
np.max(path[:, 1]) + 1.0, resolution))
Esurface = np.zeros((resolution, resolution))
for alpha_idx in xrange(resolution):
for beta_idx in xrange(resolution):
alpha, beta = alpha_X[alpha_idx, beta_idx], beta_Y[alpha_idx, beta_idx]
sigma = pca.inverse_transform(np.asarray((alpha, beta)))
Esurface[alpha_idx, beta_idx] = run_net(net, sigma, ds,
gradient_postproc)
errors = [
run_net(net,
pca.inverse_transform(path[epoch]),
ds,
gradient_postproc,
learn=False) for epoch in xrange(epochs)
]
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(alpha_X,
beta_Y,
pfd_data = pfddata(os.path.join(input_dir, fn))
nbins = 64
data = pfd_data.getdata(subbands=nbins)
print("processing %s" % fn)
fig = plt.figure()
fig.set_size_inches(5, 5)
ax = plt.Axes(fig, [0., 0., 1., 1.])
ax = plt.gca()
ax.set_axis_off()
fig.add_axes(ax)
pca = PCA(n_components=24)
rd = data.reshape(nbins, int(data.shape[0] / nbins))
pca.fit(rd)
data = pca.inverse_transform(pca.transform(rd)).flatten()
data = data.reshape((nbins, data.shape[0] / nbins))
plt.imshow(data,
origin='lower',
interpolation='bilinear',
cmap=plt.cm.gray_r
) #aspect='auto'plt.cm.Greys) #interpolation='bilinear'
plt.savefig("%s_subbands.png" % os.path.join(output_dir, fn))
intervals_data = pfd_data.getdata(intervals=64)
fig = plt.figure()
fig.set_size_inches(5, 5)
ax = plt.Axes(fig, [0., 0., 1., 1.])
ax = plt.gca()
ax.set_axis_off()
betweenss[kIdx] / totss * 100,
marker='o',
markersize=12,
markeredgewidth=2,
markeredgecolor='r',
markerfacecolor='None')
ax.set_ylim((0, 100))
plt.grid(True)
plt.xlabel('Number of clusters')
plt.ylabel('Percentage of variance explained (%)')
plt.title('Elbow for KMeans clustering')
# show centroids for K=10 clusters
plt.figure()
for i in range(kIdx + 1):
img = pca.inverse_transform(centroids[kIdx][i]).reshape(8, 8)
ax = plt.subplot(3, 4, i + 1)
ax.set_xticks([])
ax.set_yticks([])
plt.imshow(img, cmap=cm.gray)
plt.title('Cluster %d' % i)
# compare K=10 clustering vs. actual digits (PCA projections)
fig = plt.figure()
ax = fig.add_subplot(121)
for i in range(10):
ind = (t == i)
ax.scatter(X[ind, 0],
X[ind, 1],
s=35,
c=clr[i],