5b - PCA-classification-DF.py

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# # 5b - PCA classification: Dark Field data
# Here, we will use Principal Component Analysis to reduce the dimensionality of the measured dark field spectra, to visualize the spectra and to cluster the data, automatically assigning labels to different areas. 
# This notebook is nominally the same as 5a, but applied to the dark field data and resulting in the dark field figures of the paper.
#
# First some preliminaries:

# +
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import dask.array as da
from dask_ml.decomposition import PCA
from dask_ml.preprocessing import StandardScaler
from sklearn.cluster import KMeans
from sklearn.preprocessing import Normalizer
from sklearn.pipeline import Pipeline, make_pipeline
from dask.distributed import Client
import time
import os
import xarray as xr

from matplotlib.colors import LinearSegmentedColormap, ListedColormap

def to_niceRGB(image):
    """Use basis colors as suggested by P. Kovesi http://arxiv.org/abs/1509.03700"""
    A = np.array([[0.90, 0.17, 0.00],
                 [0.00, 0.50, 0.00],
                 [0.10, 0.33, 1.00]])
    return np.dot(image,A)

bRed = LinearSegmentedColormap.from_list('bRed', ['black', to_niceRGB([1,0,0])], N=256)
bBlue = LinearSegmentedColormap.from_list('bBlue', ['black', to_niceRGB([0,0,1])], N=256)
bGreen = LinearSegmentedColormap.from_list('bGreen', ['black', to_niceRGB([0,1,0])], N=256)
cmaps = [bRed, bGreen, bBlue]*2
colors = [to_niceRGB([1,0,0]), to_niceRGB([0,1,0]), to_niceRGB([0,0,1])]*2

SAVEFIG=True

client = Client()
client


# -

"""Do a principle component analysis on a stack of images and use this for clustering, both using Dask"""
dimensions = 6
coarsen = 1

# +
folder = './data'
name = '20171120_215555_3.5um_583.1_IVhdr_DF2'

# Clip out anything before mirror mode and a bit more because of image distortion
Erange = slice(100, 410)
x_slice = slice(442, 1380)
y_slice = slice(92, 960)
xdata = xr.open_dataset(os.path.join(folder, name +'_driftcorrected.nc'), 
                        chunks={'x': 10 * coarsen, 'y': 10 * coarsen})
dset = xdata.Intensity.data

IVs = dset[Erange, x_slice, y_slice].rechunk(chunks=(-1, 10 * coarsen, 10 * coarsen))
fullIVs = dset[:, x_slice, y_slice].rechunk(chunks=(-1, 10 * coarsen, 10 * coarsen))
coarseIVs = IVs[:,::coarsen, ::coarsen].reshape((IVs.shape[0],-1)).T.persist()
IVs
# -

# Get metadata from netCDF file for plotting
EGY = xdata.Energy_set
multiplier = xdata.multiplier
plt.plot(EGY, multiplier)

# ## Principal Component Analysis
# To reduce the data to a reasonable number of dimensions, we use a pipeline of a standardscaler and PCA:

pca = PCA(n_components=dimensions, whiten=True, random_state=4)
pipe = make_pipeline(StandardScaler(), pca)
pipe_names = '_'.join(pipe.named_steps.keys())
pipe.fit(coarseIVs) # Fit the standard scaler and PCA vectors to the coarsened data

plt.figure(figsize=[3.5 ,3.5])
scree = np.concatenate([[0], pipe.named_steps['pca'].explained_variance_ratio_])
plt.scatter(np.arange(dimensions)+1, scree[1:], label='relative', facecolors='none', edgecolors=colors, linewidth=2)
plt.scatter(np.arange(dimensions+1), np.cumsum(scree), marker='+', label='cumulative', color='black', linewidth=2)
plt.ylabel('Explained variance')
plt.xlabel('Number of PCA components')
plt.axhline(0, color='black', alpha=0.5)
plt.legend(fontsize='large', scatterpoints=3)
plt.tight_layout()
plt.ylim([None,1])
if SAVEFIG:
    plt.savefig(f'scree_plot_DF_{pipe_names}.pdf')
f"{dimensions} PCA components explain {scree.sum():.4f} of the total variance"

# The sign of the PCA vectors has a degeneracy dependent on the random initialization: minus a PCA vector explains as much variance as plus the vector, as we take a linear span.
#
# To make the visualization reproducible, the degeneracy of the sign of the PCA components needs to be lifted. Here, we align the signs such that positive vector corresponds to being brighter in the majority of the images.
# After this we can transform all original data to the reduced number of dimensions

pipe_diffs = pipe.inverse_transform(np.eye(dimensions)).compute()
signs = np.sign(np.nanmean((np.log(pipe_diffs) - 
                            np.log(pipe.named_steps['standardscaler'].mean_)),
                           axis=1))
pipe.named_steps['pca'].components_ *= signs[:,np.newaxis]
signs

rIVs = pipe.transform(IVs.reshape(IVs.shape[0], -1).T).persist()

# To visualize the dimension reduction, we calculate the spectra corresponding to the extrema of the components, as well as the spectra _occuring in the dataset_ with the extreme values of the components:

# +
argextrema = da.concatenate([rIVs[rIVs.argmin(axis=0), :], 
                             rIVs[rIVs.argmax(axis=0), :]])
argextrema = pipe.inverse_transform(argextrema) / multiplier[Erange]
argextrema = argextrema.reshape((2, 6, -1))

extrema = da.concatenate([da.diag(rIVs.min(axis=0)), 
                          da.diag(rIVs.max(axis=0))])
extrema = pipe.inverse_transform(extrema) / multiplier[Erange]
extrema = extrema.reshape((2, 6, -1))

argextrema, extrema = da.compute(argextrema, extrema)
# -

fig,axs = plt.subplots(2, dimensions, figsize=[10, 3.5],
                      sharex='row', sharey='row',
                      constrained_layout=True)
E = EGY[Erange]
for i in range(dimensions):
    axs[0,i].imshow(rIVs[:,i].reshape(IVs.shape[1:]).T, interpolation='none', cmap=cmaps[i])
    axs[0,i].set_title('PCA component {}'.format(i+1), fontsize='small')
    axs[1,i].plot(E, argextrema[1][i], color=cmaps[i](1.0), linestyle=':')
    axs[1,i].plot(E, argextrema[0][i], color=cmaps[i](0.0), linestyle=':')
    axs[1,i].plot(E, extrema[1][i], color=cmaps[i](1.0), alpha=0.6)
    axs[1,i].plot(E, extrema[0][i], color=cmaps[i](0.0), alpha=0.6)
    axs[1,i].set_yscale('log')
    axs[1,i].set_xlabel('$E_0$ (eV)')
    axs[1,i].margins(x=0)
axs[1,0].set_ylabel('Intensity')
if SAVEFIG:
    plt.savefig(f'DF_PCAcomponents_{pipe_names}.pdf')

# ## Visualization
#
# To visualize the dataset, we combine the PCA components in groups of three, and use these as RGB images in real space:

# +
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=[6, 3], constrained_layout=True)
img = rIVs[:, :3].reshape(IVs.shape[1:] + (3,)).swapaxes(0, 1)
img = img - img.min(axis=(0, 1), keepdims=True)
img = img / img.max(axis=(0, 1), keepdims=True)
ax1.imshow(to_niceRGB(img), interpolation='none')
ax1.set_title('DF PCA component 1 to 3')

img = rIVs[:, 3:6].reshape(IVs.shape[1:] + (3,)).swapaxes(0, 1)
img = img - img.min(axis=(0, 1), keepdims=True)
img = img / img.max(axis=(0, 1), keepdims=True)
ax2.imshow(to_niceRGB(img), interpolation='none')
ax2.set_title('DF PCA component 4 to 6')
if SAVEFIG:
    plt.savefig(f'DF_visualization_{pipe_names}.pdf')
# -

# ## Clustering: $k$-means
# To assign labels to different spectra, we cluster using a standard unsupervised machine learning algorithm: $k$-means:

rIVs = rIVs.compute()
kmeans_d = 4

from sklearn.metrics import silhouette_samples, silhouette_score
scores = []
klabels = np.arange(3,12)
for n in klabels:
    clusterer = KMeans(n_clusters=n, random_state=10)
    cl_labels = clusterer.fit_predict(rIVs[::20,:kmeans_d])
    print(n, "fit_predicted")
    scores.append(silhouette_score(rIVs[::20,:kmeans_d], cl_labels))
    print(f"{n} clusters, score = {scores[-1]}")
plt.plot(klabels, scores)
plt.ylabel('Silhoutte score')
plt.xlabel('$n_{clusters}$')

print('Performing clustering via KMeans', rIVs[:,:kmeans_d].shape)
kmeans = KMeans(n_clusters=8, random_state=10, n_jobs=-1).fit(rIVs[:,:kmeans_d])
clustering = kmeans.predict(rIVs[:,:kmeans_d])

# For visualization of curves corresponding to clusters, we grab the full spectra, filter out points where the spectrum was not measured due to drift and calculate the mean per image per spectrum.

validIVs = da.where(fullIVs == 0, np.nan, fullIVs).reshape((fullIVs.shape[0],-1))
meanIVs = [da.nanmean(validIVs[:,clustering == index], axis=1) 
           for index in range(kmeans.n_clusters)]

# +
tstart = time.time()
print('plotting clustering data')


fig2,axs = plt.subplots(2,4, figsize=[11,5], dpi=600)
#In case of 1 out of 1 columns figure
axs = np.transpose(axs)

coarse_2d = 3*coarsen
color = rIVs[::coarse_2d,:3]
center_colors = kmeans.cluster_centers_[:,:3] - color.min(axis=0)
color = color - color.min(axis=0, keepdims=True)
center_colors = center_colors / color.max(axis=0)
center_colors = to_niceRGB(center_colors)
color = color / color.max(axis=0,keepdims=True)
color = to_niceRGB(color)

newcmap = ListedColormap(center_colors)

colorargs = {'cmap': newcmap, 'vmin': 0, 'vmax': 8}
axs[0,0].scatter(rIVs[::coarse_2d, 0], 
                 rIVs[::coarse_2d, 1], 
                 c=color, s=0.2, alpha=0.2,
                 **colorargs, rasterized=True,
                 )
axs[0,1].scatter(rIVs[::coarse_2d, 0], 
                 rIVs[::coarse_2d, 2], 
                 c=color, s=0.2, alpha=0.2,
                 **colorargs, rasterized=True,
                 )

for i in [0,1,2]:
    axs[i,0].set_ylabel("Pca dim 1", color=colors[1], fontweight=700)
    axs[i,0].set_xlabel("Pca dim 0", color=colors[0], fontweight=700)
    axs[i,1].set_ylabel("Pca dim 2", color=colors[2], fontweight=700)
    axs[i,1].set_xlabel("Pca dim 0", color=colors[0], fontweight=700)

hist, edges = np.histogramdd(rIVs[:,:3], bins=200,
                             range=[axs[0,0].get_xlim(), 
                                    axs[0,0].get_ylim(), 
                                    axs[0,1].get_ylim()])
edges = np.array(edges)
#xedges, yedges, zedges = edges[0], edges[1], edges[2]

axs[1,0].imshow(hist.sum(axis=-1)[:,::-1].T,
                extent=[edges[0,0], edges[0,-1], 
                        edges[1,0], edges[1,-1]],
                aspect='auto',
                cmap='gray_r')

axs[1,1].imshow(hist.sum(axis=1)[:,::-1].T, 
                extent=[edges[0,0], edges[0,-1],
                        edges[2,0], edges[2,-1]], 
                aspect='auto',
                cmap='gray_r')
colorargs['cmap'] = 'tab10'
colorargs['vmax'] = 10

axs[2,0].scatter(rIVs[::coarse_2d,0], rIVs[::coarse_2d,1], c=clustering[::coarse_2d], s=0.2, alpha=0.2,
                 **colorargs, rasterized=True,
                 )
axs[2,1].scatter(rIVs[::coarse_2d,0], rIVs[::coarse_2d,2], c=clustering[::coarse_2d], s=0.2, alpha=0.2,
                 **colorargs, rasterized=True,
                 )

clusteringimg = clustering.reshape((IVs.shape[1],IVs.shape[2]))
axs[3,0].imshow(clusteringimg.T,
                **colorargs
                )
for i,v in enumerate(kmeans.cluster_centers_):
    axs[1,0].scatter(v[0], v[1], s=20, color=center_colors[i])
    axs[1,1].scatter(v[0], v[2], s=20, color=center_colors[i])
print("Time elapsed: {}".format(time.time()-tstart))
meanIVs = da.compute(*meanIVs)
print("Time elapsed: {}".format(time.time()-tstart))
for i,meanIV in enumerate(meanIVs):
    axs[3,1].plot(xdata.Energy, (meanIV / multiplier),) # color=center_colors[i], alpha=0.75)

axs[3,1].set_yscale('log')
axs[3,1].set_xlabel('Energy (eV)')
axs[3,1].set_ylabel('Reflectivity ()')
axs[3,1].margins(x=0)
axs[3,0].set_xlabel(r'$x$ (pixels)')
axs[3,0].set_ylabel(r'$y$ (pixels)')

#In case of 1 out of two columns figure
#for ax in axs[:,1]:
    #ax.yaxis.set_label_position("right")
    #ax.tick_params(axis='y', labelright=True, labelleft=False)
    
plt.tight_layout()
print("Time elapsed: {}".format(time.time()-tstart))
if SAVEFIG:
    plt.savefig('clustering_DF_2_0_perp.pdf', dpi=600)
    print("Total time elapsed: {}".format(time.time()-tstart))

# +
tstart = time.time()
print('plotting clustering data')


fig2 = plt.figure(figsize=[2.8,5], dpi=600)
axs = np.array([fig2.add_subplot(211), fig2.add_subplot(212)])

coarse_2d = 3*coarsen
color = rIVs[::coarse_2d,:3]
center_colors = kmeans.cluster_centers_[:,:3] - color.min(axis=0)
color = color - color.min(axis=0, keepdims=True)
center_colors = center_colors / color.max(axis=0)
center_colors = to_niceRGB(center_colors)
color = color / color.max(axis=0,keepdims=True)
color = to_niceRGB(color)

newcmap = ListedColormap(center_colors)

colorargs = {'cmap': newcmap, 'vmin': 0, 'vmax': 8}


edges = np.array(edges)
#xedges, yedges, zedges = edges[0], edges[1], edges[2]

colorargs['cmap'] = 'tab10'
colorargs['vmax'] = 10

clusteringimg = clustering.reshape((IVs.shape[1],IVs.shape[2]))
axs[0].imshow(clusteringimg.T,
                **colorargs
                )

for i,meanIV in enumerate(meanIVs):
    axs[1].plot(xdata.Energy, (meanIV / multiplier),) # color=center_colors[i], alpha=0.75)

axs[1].set_yscale('log')
axs[1].set_xlabel('Energy (eV)')
axs[1].set_ylabel('Reflectivity')
axs[1].margins(x=0)
axs[0].set_xlabel(r'$x$ (pixels)')
axs[0].set_ylabel(r'$y$ (pixels)')

#In case of 1 out of two columns figure
#for ax in axs[:,1]:
    #ax.yaxis.set_label_position("right")
    #ax.tick_params(axis='y', labelright=True, labelleft=False)
    
plt.tight_layout()
print("Time elapsed: {}".format(time.time()-tstart))
if SAVEFIG:
    plt.savefig('clustering_DF_3_0.pdf', dpi=600)
print("Total time elapsed: {}".format(time.time()-tstart))

# -