# Sparse Coding

 Revision as of 11:18, 21 March 2011 (view source)Zhenghao (Talk | contribs) (Created page with "== Background and Motivation == Sparse coding is a class of unsupervised methods for learning sets of over-complete bases to represent data efficiently. The aim of sparse coding ...")← Older edit Revision as of 11:20, 21 March 2011 (view source)Zhenghao (Talk | contribs) Newer edit → Line 37: Line 37: Assuming $\nu$ is Gaussian white noise with variance $\sigma^2$, we have that Assuming $\nu$ is Gaussian white noise with variance $\sigma^2$, we have that :\begin{align} :[itex]\begin{align} - P(\mathbf{x} \mid \mathbf{a}, \mathbf{\phi}) = \frac^{1}_{Z} \exp(- \frac^{1}_{2\sigma^2}) + P(\mathbf{x} \mid \mathbf{a}, \mathbf{\phi}) = \frac{1}{Z} \exp(- \frac{\mathbf{x}-\sum^{k}_{i=1} a_i \mathbf{\phi}_{i} }{2\sigma^2}) \end{align} \end{align}[/itex] In order to define the distribution $P(\mathbf{x}\mid\mathbf{\phi})$, we must first specify a prior distribution over the amplitudes $a_i$ In order to define the distribution $P(\mathbf{x}\mid\mathbf{\phi})$, we must first specify a prior distribution over the amplitudes $a_i$