This is a small notebook intended to play around with the Olivetti dataset

In [1]:

```
from sklearn.datasets import fetch_olivetti_faces
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
%matplotlib inline
```

In [2]:

```
faces = fetch_olivetti_faces()
print(faces.DESCR)
```

In [3]:

```
# Here are the first ten guys of the dataset
fig = plt.figure(figsize=(10, 10))
for i in range(10):
ax = plt.subplot2grid((1, 10), (0, i))
ax.imshow(faces.data[i * 10].reshape(64, 64), cmap=plt.cm.gray)
ax.axis('off')
```

In [4]:

```
# Let's compute the PCA
pca = PCA()
pca.fit(faces.data)
```

Out[4]:

In [5]:

```
# Now, the creepy guys are in the components_ attribute.
# Here are the first ten ones:
fig = plt.figure(figsize=(10, 10))
for i in range(10):
ax = plt.subplot2grid((1, 10), (0, i))
ax.imshow(pca.components_[i].reshape(64, 64), cmap=plt.cm.gray)
ax.axis('off')
```

In [7]:

```
# Reconstruction process
from skimage.io import imsave
face = faces.data[0] # we will reconstruct the first face
# During the reconstruction process we are actually computing, at the kth frame,
# a rank k approximation of the face. To get a rank k approximation of a face,
# we need to first transform it into the 'latent space', and then
# transform it back to the original space
# Step 1: transform the face into the latent space.
# It's now a vector with 400 components. The kth component gives the importance
# of the kth creepy guy
trans = pca.transform(face.reshape(1, -1)) # Reshape for scikit learn
# Step 2: reconstruction. To build the kth frame, we use all the creepy guys
# up until the kth one.
# Warning: this will save 400 png images.
for k in range(400):
rank_k_approx = trans[:, :k].dot(pca.components_[:k]) + pca.mean_
imsave('{:>03}'.format(str(k)) + '.jpg', rank_k_approx.reshape(64, 64))
```