From 7fc1274a02de18710febd4a1f7d89ba7eaea6192 Mon Sep 17 00:00:00 2001
From: Neil Smith <neil.git@njae.me.uk>
Date: Mon, 10 Mar 2014 18:41:38 -0400
Subject: [PATCH] Finished for the day

---
 slides/aims.html            |   2 +-
 slides/caesar-break.html    | 105 +++++++++++++++++++++++++++++++++++-
 slides/caesar-encipher.html |  45 +++++++++++++++-
 3 files changed, 148 insertions(+), 4 deletions(-)

diff --git a/slides/aims.html b/slides/aims.html
index e830227..fcf0c70 100644
--- a/slides/aims.html
+++ b/slides/aims.html
@@ -70,7 +70,7 @@ This course will cover four things, in increasing order of importance.
     <script src="http://gnab.github.io/remark/downloads/remark-0.6.0.min.js" type="text/javascript">
     </script>
     <script type="text/javascript">
-      var slideshow = remark.create();
+      var slideshow = remark.create({ ratio: "16:9" });
     </script>
   </body>
 </html>
\ No newline at end of file
diff --git a/slides/caesar-break.html b/slides/caesar-break.html
index 5c95fc2..d552209 100644
--- a/slides/caesar-break.html
+++ b/slides/caesar-break.html
@@ -71,12 +71,113 @@ What does English look like?
 
 How do we define "closeness"?
 
+---
+
+# What does English look like?
+
+## Abstraction: frequency of letter counts
+
+Letter | Count
+-------|------
+a | 489107
+b | 92647
+c | 140497
+d | 267381
+e | 756288
+. | .
+. | .
+. | .
+z | 3575
+
+One way of thinking about this is a 26-dimensional vector. 
+
+Create a vector of our text, and one of idealised English. 
+
+The distance between the vectors is how far from English the text is.
+
+---
+
+# Vector distances
+
+
+## FIXME! Diagram of vector subtraction here
+
+Several different distance measures (__metrics__, also called __norms__):
+
+* L<sub>2</sub> norm (Euclidean distance):  `\(|\mathbf{x} - \mathbf{y}| = \sqrt{\sum_i (\mathbf{x}_i - \mathbf{y}_i)^2} \)`
+
+* L<sub>1</sub> norm (Manhattan distance, taxicab distance):  `\(|\mathbf{x} - \mathbf{y}| = \sum_i |\mathbf{x}_i - \mathbf{y}_i| \)`
+
+* L<sub>3</sub> norm:  `\(|\mathbf{x} - \mathbf{y}| = \sqrt[3]{\sum_i |\mathbf{x}_i - \mathbf{y}_i|^3} \)`
+
+The higher the power used, the more weight is given to the largest differences in components.
+
+(Extends out to:
+
+* L<sub>0</sub> norm (Hamming distance):  `\(|\mathbf{x} - \mathbf{y}| = \sum_i \left\{\begin{matrix} 1 &amp;\mbox{if}\ \mathbf{x}_i \neq \mathbf{y}_i , \\ 0 &amp;\mbox{if}\ \mathbf{x}_i = \mathbf{y}_i \end{matrix} \right| \)`
+
+* L<sub>&infin;</sub> norm:  `\(|\mathbf{x} - \mathbf{y}| = \max_i{(\mathbf{x}_i - \mathbf{y}_i)} \)`
+
+neither of which will be that useful.)
+---
+
+# Normalisation of vectors
+
+Frequency distributions drawn from different sources will have different lengths. For a fair comparison we need to scale them. 
+
+* Eucliean scaling (vector with unit length): `\( \hat{\mathbf{x}} = \frac{\mathbf{x}}{\| \mathbf{x} \|} = \frac{\mathbf{x}}{ \sqrt{\mathbf{x}_1^2 + \mathbf{x}_2^2 + \mathbf{x}_3^2 + \dots } }\)`
+
+* Normalisation (components of vector sum to 1): `\( \hat{\mathbf{x}} = \frac{\mathbf{x}}{\| \mathbf{x} \|} = \frac{\mathbf{x}}{ \mathbf{x}_1 + \mathbf{x}_2 + \mathbf{x}_3 + \dots }\)`
+
+---
+
+# Angle, not distance
+
+Rather than looking at the distance between the vectors, look at the angle between them.
+
+Vector dot product shows how much of one vector lies in the direction of another: 
+`\( \mathbf{A} \bullet \mathbf{B} = 
+\| \mathbf{A} \| \cdot \| \mathbf{B} \| \cos{\theta} \)`
+
+But, 
+`\( \mathbf{A} \bullet \mathbf{B} = \sum_i \mathbf{A}_i \cdot \mathbf{B}_i \)`
+and `\( \| \mathbf{A} \| = \sum_i \mathbf{A}_i^2 \)`
+
+A bit of rearranging give the cosine simiarity:
+`\( \cos{\theta} = \frac{ \mathbf{A} \bullet \mathbf{B} }{ \| \mathbf{A} \| \cdot \| \mathbf{B} \| } = 
+\frac{\sum_i \mathbf{A}_i \cdot \mathbf{B}_i}{\sum_i \mathbf{A}_i^2 \times \sum_i \mathbf{B}_i^2} \)`
+
+This is independent of vector lengths!
+
+Cosine similarity is 1 if in same direction, 0 if at 90⁰, -1 if antiparallel.
+
+## FIXME! Cosine distance bug: frequencies2 length not squared.
+
+
+## FIXME! Diagram of vector dot product
 
     </textarea>
     <script src="http://gnab.github.io/remark/downloads/remark-0.6.0.min.js" type="text/javascript">
     </script>
+
+    <script type="text/javascript"
+      src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML&delayStartupUntil=configured"></script>
+
     <script type="text/javascript">
-      var slideshow = remark.create();
+      var slideshow = remark.create({ ratio: "16:9" });
+
+      // Setup MathJax
+      MathJax.Hub.Config({
+        tex2jax: {
+        skipTags: ['script', 'noscript', 'style', 'textarea', 'pre']
+        }
+      });
+      MathJax.Hub.Queue(function() {
+        $(MathJax.Hub.getAllJax()).map(function(index, elem) {
+            return(elem.SourceElement());
+        }).parent().addClass('has-jax');
+      });
+      MathJax.Hub.Configured();
     </script>
   </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/slides/caesar-encipher.html b/slides/caesar-encipher.html
index c4e8fb1..f45a166 100644
--- a/slides/caesar-encipher.html
+++ b/slides/caesar-encipher.html
@@ -120,6 +120,49 @@ if __name__ == "__main__":
 
 ---
 
+# Accents
+
+```python
+>>> caesar_encipher_letter('é', 1)
+```
+What does it produce?
+
+What should it produce?
+
+## Unicode, combining codepoints, and normal forms
+
+Text encodings will bite you when you least expect it.
+
+* urlencoding is the other pain point.
+
+---
+
+# Five minutes on StackOverflow later...
+
+```python
+def unaccent(text):
+    """Remove all accents from letters. 
+    It does this by converting the unicode string to decomposed compatibility
+    form, dropping all the combining accents, then re-encoding the bytes.
+
+    >>> unaccent('hello')
+    'hello'
+    >>> unaccent('HELLO')
+    'HELLO'
+    >>> unaccent('héllo')
+    'hello'
+    >>> unaccent('héllö')
+    'hello'
+    >>> unaccent('HÉLLÖ')
+    'HELLO'
+    """
+    return unicodedata.normalize('NFKD', text).\
+        encode('ascii', 'ignore').\
+        decode('utf-8')
+```
+
+---
+
 # Doing all the letters
 
 ## Test-first developement
@@ -186,7 +229,7 @@ ciphertext = [caesar_encipher_letter(p, key) for p in plaintext]
     <script src="http://gnab.github.io/remark/downloads/remark-0.6.0.min.js" type="text/javascript">
     </script>
     <script type="text/javascript">
-      var slideshow = remark.create();
+      var slideshow = remark.create({ ratio: "16:9" });
     </script>
   </body>
 </html>
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-- 
2.34.1