From da913f9a4dabab31698669b09b69a215d7947c4e Mon Sep 17 00:00:00 2001
From: Vasil Zlatanov <v@skozl.com>
Date: Sun, 10 Mar 2019 17:01:42 +0000
Subject: Add TSNE and fix PCA

---
 lenet.py        | 31 ++++++++++++++++++++-----------
 report/paper.md |  8 ++++++--
 2 files changed, 26 insertions(+), 13 deletions(-)

diff --git a/lenet.py b/lenet.py
index 3d388de..3d9ed20 100644
--- a/lenet.py
+++ b/lenet.py
@@ -16,6 +16,7 @@ from sklearn.model_selection import train_test_split
 from sklearn.decomposition import PCA
 from classifier_metrics_impl import classifier_score_from_logits
 from sklearn.utils import shuffle
+from sklearn.manifold import TSNE
 
 def import_mnist():
   from tensorflow.examples.tutorials.mnist import input_data
@@ -141,12 +142,12 @@ def train_classifier(x_train, y_train, x_val, y_val, batch_size=128, epochs=100,
   model.save_weights('./weights.h5')
   return model 
 
-def test_classifier(model, x_test, y_true, conf_mat=False, pca=False):
+def test_classifier(model, x_test, y_true, conf_mat=False, pca=False, tsne=False):
   x_test = np.pad(x_test, ((0,0),(2,2),(2,2),(0,0)), 'constant')
-  y_pred = model.predict(x_test)
-  logits = tf.convert_to_tensor(y_pred, dtype=tf.float32)
-  inception_score = tf.keras.backend.eval(classifier_score_from_logits(logits))
-  y_pred = np.argmax(y_pred, axis=1)
+  logits = model.predict(x_test)
+  tf_logits = tf.convert_to_tensor(logits, dtype=tf.float32)
+  inception_score = tf.keras.backend.eval(classifier_score_from_logits(tf_logits))
+  y_pred = np.argmax(logits, axis=1)
   y_true = np.argmax(y_true, axis=1)
   plot_example_errors(y_pred, y_true, x_test)
   cm = confusion_matrix(y_true, y_pred)
@@ -158,16 +159,24 @@ def test_classifier(model, x_test, y_true, conf_mat=False, pca=False):
     plt.show()
   if pca:
     set_pca = PCA(n_components=2)
-    pca_rep = np.reshape(x_test, (x_test.shape[0], x_test.shape[1]*x_test.shape[2]))
-    print(pca_rep.shape)
-    pca_rep = set_pca.fit_transform(pca_rep)
-    print(pca_rep.shape)
+    pca_rep = set_pca.fit_transform(logits)
     pca_rep, y_tmp = shuffle(pca_rep, y_true, random_state=0)
-    plt.scatter(pca_rep[:100, 0], pca_rep[:100, 1], c=y_true[:100], edgecolor='none', alpha=0.5, cmap=plt.cm.get_cmap('Paired', 10))
+    plt.scatter(pca_rep[:1000, 0], pca_rep[:1000, 1], c=y_true[:1000], edgecolor='none', alpha=0.5, cmap=plt.cm.get_cmap('Paired', 10))
     plt.xlabel('component 1')
     plt.ylabel('component 2')
     plt.colorbar();
     plt.show()
+  if tsne:
+    tsne = TSNE(n_components=2, random_state=0)
+    components = tsne.fit_transform(logits)
+    print(components.shape)
+    components, y_tmp = shuffle(components, y_true, random_state=0)
+    plt.scatter(components[:1000, 0], components[:1000, 1], c=y_true[:1000], edgecolor='none', alpha=0.5, cmap=plt.cm.get_cmap('Paired', 10))
+    plt.xlabel('component 1')
+    plt.ylabel('component 2')
+    plt.colorbar();
+    plt.show()
+
   
   return accuracy_score(y_true, y_pred), inception_score
 
@@ -202,4 +211,4 @@ if __name__ == '__main__':
   x_train, y_train, x_val, y_val, x_t, y_t = import_mnist()
   print(y_t.shape)
   model = train_classifier(x_train[:100], y_train[:100], x_val, y_val, epochs=3)
-  print(test_classifier(model, x_t, y_t, pca=True))
+  print(test_classifier(model, x_t, y_t, pca=False, tsne=True))
diff --git a/report/paper.md b/report/paper.md
index 53cdb3f..e053353 100644
--- a/report/paper.md
+++ b/report/paper.md
@@ -151,7 +151,7 @@ architectures in Q2.**
 We measure the performance of the considered GAN's using the Inecption score [-inception], as calculated
 with L2-Net logits.
 
-$$ \textrm{IS}(x) = \exp(\mathcal{E}_x \left( \textrm{KL} ( p(y\|x) \|\| p(y) ) \right) ) $$
+$$ \textrm{IS}(x) = \exp(\mathbb{E}_x \left( \textrm{KL} ( p(y\mid x) \| p(y) ) \right) ) $$
 
 ```
 \begin{table}[]
@@ -252,7 +252,11 @@ as most of the testing images that got misclassified (mainly nines and fours) sh
 
 # Bonus
 
-This is an open question. Do you have any other ideas to improve GANs or
+## Relation to PCA
+
+Similarly to GAN's, PCA can be used to formulate **generative** models of a system. While GAN's are trained neural networks, PCA is a definite statistical procedure which perform orthogonal transformations of the data. While both attempt to identify the most important or *variant* features of the data (which we may then use to generate new data), PCA by itself is only able to extract linearly related features. In a purely linear system, a GAN would be converging to PCA. In a more complicated system, we would ndeed to identify relevant kernels in order to extract relevant features with PCA, while a GAN is able to leverage dense and convolutional neural network layers which may be trained to perform relevant transformations.
+
+* This is an open question. Do you have any other ideas to improve GANs or
 have more insightful and comparative evaluations of GANs? Ideas are not limited. For instance,
 
 \begin{itemize}
-- 
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