I was reading Pattern Recognition and Machine Learning and I ran into this equation, and I can't figure out what phi(xn) is referring to. I am aware that it is representing regularized regression, but not sure what phi symbolizes or why you need to transpose w:
I think $\phi(x_n)$ is a feature representation of $x_n$, i.e. it is the original data point $x_n$ lifted to a higher-dimensional feature space $\phi(x_n)$. The inner product $w^{T}\phi(x_n)$ is a weighted combination of feature vectors and is an example of a generalized linear model.