# Sparse Coding

### From Ufldl

(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 ...") |
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Assuming <math>\nu</math> is Gaussian white noise with variance <math>\sigma^2</math>, we have that | Assuming <math>\nu</math> is Gaussian white noise with variance <math>\sigma^2</math>, we have that | ||

:<math>\begin{align} | :<math>\begin{align} | ||

- | P(\mathbf{x} \mid \mathbf{a}, \mathbf{\phi}) = \frac | + | 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}</math> | \end{align}</math> | ||

In order to define the distribution <math>P(\mathbf{x}\mid\mathbf{\phi})</math>, we must first specify a prior distribution over the amplitudes <math>a_i</math> | In order to define the distribution <math>P(\mathbf{x}\mid\mathbf{\phi})</math>, we must first specify a prior distribution over the amplitudes <math>a_i</math> |