Part.25_Multiclass_Classification-Neural_Network(ML_Andrew.Ng.)
# Multiclass Classification
Tags: #MachineLearning #NeuralNetwork
We can define our set of resulting classes as y: $$ y^{(i)}=\left[\begin{array}{l} 1 \\ 0 \\ 0 \\ 0 \end{array}\right],\left[\begin{array}{l} 0 \\ 1 \\ 0 \\ 0 \end{array}\right],\left[\begin{array}{l} 0 \\ 0 \\ 1 \\ 0 \end{array}\right],\left[\begin{array}{l} 0 \\ 0 \\ 0 \\ 1 \end{array}\right] $$ 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: $$ \left[\begin{array}{c} x_{0} \\ x_{1} \\ x_{2} \\ \cdots \\ x_{n} \end{array}\right] \rightarrow\left[\begin{array}{c} a_{0}^{(2)} \\ a_{1}^{(2)} \\ a_{2}^{(2)} \\ \ldots \end{array}\right] \rightarrow\left[\begin{array}{c} a_{0}^{(3)} \\ a_{1}^{(3)} \\ a_{2}^{(3)} \\ \cdots \end{array}\right] \rightarrow \ldots \rightarrow\left[\begin{array}{l} h_{\Theta}(x){1} \\ h{\Theta}(x){2} \\ h{\Theta}(x){3} \\ h{\Theta}(x)_{4} \end{array}\right] $$