Coursera ML(6)-Neural Networks Representation
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Coursera ML(6)-Neural Networks Representation

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Neural Networks Model

A single neuron model: logistic unit

$$\begin{bmatrix}x_0 \newline x_1 \newline x_2 \newline \end{bmatrix}\rightarrow\begin{bmatrix}\ \ \ \newline \end{bmatrix}\rightarrow h_\theta(x)$$

Neural Networks

$$\begin{bmatrix}x_0 \newline x_1 \newline x_2 \newline x_3\end{bmatrix}\rightarrow\begin{bmatrix}a_1^{(2)} \newline a_2^{(2)} \newline a_3^{(2)} \newline \end{bmatrix}\rightarrow h_\theta(x)$$

$$\begin{align*}& a_i^{(j)} = \text{"activation" of unit $i$ in layer $j$} \newline& \Theta^{(j)} = \text{matrix of weights controlling function mapping from layer $j$ to layer $j+1$}\end{align*}$$

Calculation from one layer to the next

In the picture above, we have the networks from layer j to layer j+1, in which layer j has 3(+1) units while layer j+1 has 3 layers. Let $s_j=3$, $s_j+1=3$

Multiclass Classification


Each $y^{(i)}$ represents a different image corresponding to either a car, pedestrian, truck, or motorcycle. The inner layers, each provide us with some new information which leads to our final hypothesis function. The setup looks like:


Example: layer 1 has 2 input nodes and layer 2 has 4 activation nodes. Dimension of $\Theta^{(1)}$ is going to be 4×3 where $s_j = 2$ and $s_{j+1} = 4$, so $s_{j+1} \times (s_j + 1) = 4 \times 3$$



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