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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:

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    About the transpose: note that $\mathbf u^T \mathbf v$ is the dot-product of the column-vectors $\mathbf u$ and $\mathbf v$. – 2017-01-26
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    All I can say from the context is that $\phi(\mathbf x_n)$ is some kind of vector, which is to say that $\phi$ is a function that takes vectors and produces vectors – 2017-01-26
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    [Possible Use?](http://math.stackexchange.com/questions/1104964/machine-learning-linear-regression-models?rq=1) – 2017-01-26

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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.