Backpropagation Algorithm

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Finally, we can also re-write the algorithm using matrix-vectorial notation. We will use "<math>\textstyle \bullet</math>" to denote the element-wise product operator (denoted "<tt>.*</tt>" in Matlab or Octave, and also called the Hadamard product), so that if <math>\textstyle a = b \bullet c</math>, then <math>\textstyle a_i = b_ic_i</math>. Similar to how we extended the definition of <math>\textstyle f(\cdot)</math> to apply element-wise to vectors, we also do the same for <math>\textstyle f'(\cdot)</math> (so that <math>\textstyle f'([z_1, z_2, z_3]) =
Finally, we can also re-write the algorithm using matrix-vectorial notation. We will use "<math>\textstyle \bullet</math>" to denote the element-wise product operator (denoted "<tt>.*</tt>" in Matlab or Octave, and also called the Hadamard product), so that if <math>\textstyle a = b \bullet c</math>, then <math>\textstyle a_i = b_ic_i</math>. Similar to how we extended the definition of <math>\textstyle f(\cdot)</math> to apply element-wise to vectors, we also do the same for <math>\textstyle f'(\cdot)</math> (so that <math>\textstyle f'([z_1, z_2, z_3]) =
-
[\frac{\partial}{\partial z_1} f(z_1),
+
[f'(z_1),
-
\frac{\partial}{\partial z_2} f(z_2),
+
f'(z_2),
-
\frac{\partial}{\partial z_3} f(z_3)]</math>).
+
f'(z_3)]</math>).
The algorithm can then be written:
The algorithm can then be written:

Revision as of 05:23, 11 May 2011

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