I have been studying back propagation using this UFDL For a network like this
Given the data points $\{ (x^{(1)}, y^{(1)}), \ldots, (x^{(m)}, y^{(m)}) \}$
is the cost function defined as such (according to them):
\begin{align} J(W,b; x,y) = \frac{1}{2} \left\| h_{W,b}(x) - y \right\|^2. \end{align}
and for $m$ data points
\begin{align} J(W,b) &= \left[ \frac{1}{m} \sum_{i=1}^m J(W,b;x^{(i)},y^{(i)}) \right] + \frac{\lambda}{2} \sum_{l=1}^{n_l-1} \; \sum_{i=1}^{s_l} \; \sum_{j=1}^{s_{l+1}} \left( W^{(l)}_{ji} \right)^2 \\ &= \left[ \frac{1}{m} \sum_{i=1}^m \left( \frac{1}{2} \left\| h_{W,b}(x^{(i)}) - y^{(i)} \right\|^2 \right) \right] + \frac{\lambda}{2} \sum_{l=1}^{n_l-1} \; \sum_{i=1}^{s_l} \; \sum_{j=1}^{s_{l+1}} \left( W^{(l)}_{ji} \right)^2 \end{align}
What I don't understand how the error function is defined as (actual - target), and not (target-actual)?..
Like it is done later in the text, when they define the error term..
\begin{align} \delta^{(n_l)}_i = \frac{\partial}{\partial z^{(n_l)}_i} \;\; \frac{1}{2} \left\|y - h_{W,b}(x)\right\|^2 = - (y_i - a^{(n_l)}_i) \cdot f'(z^{(n_l)}_i) \end{align}
Is this an error? Or is there something else I oversee?