Feature extraction using convolution

From Ufldl

Jump to: navigation, search
(Convolution)
(Convolution)
Line 9: Line 9:
[[File:Convolution_schematic.gif]]
[[File:Convolution_schematic.gif]]
-
Formally, given some large <math>r \times c</math> images <math>x_{large}</math>, we first train a sparse autoencoder on small <math>a \times b</math> patches <math>x_{small}</math> sampled from these images, learning <math>k</math> features <math>f = \sigma(W^{(1)}x_{small} + b^{(1)})</math> (where <math>\sigma</math> is the sigmoid function), given by the weights <math>W^{(1)}M</math> and biases <math>b^{(1)}</math> from the visible units to the hidden units. For every <math>a \times b</math> patch <math>x_s</math> in the large image, we compute <math>f_s = \sigma(W^{(1)}x_s + b^{(1)})</math>, giving us <math>f_{convolved}</math>, a <math>k \times (r - a + 1) \times (c - b + 1)</math> array of convolved features. These convolved features can then be [[#pooling | pooled]] for classification, as described below.
+
Formally, given some large <math>r \times c</math> images <math>x_{large}</math>, we first train a sparse autoencoder on small <math>a \times b</math> patches <math>x_{small}</math> sampled from these images, learning <math>k</math> features <math>f = \sigma(W^{(1)}x_{small} + b^{(1)})</math> (where <math>\sigma</math> is the sigmoid function), given by the weights <math>W^{(1)}</math> and biases <math>b^{(1)}</math> from the visible units to the hidden units. For every <math>a \times b</math> patch <math>x_s</math> in the large image, we compute <math>f_s = \sigma(W^{(1)}x_s + b^{(1)})</math>, giving us <math>f_{convolved}</math>, a <math>k \times (r - a + 1) \times (c - b + 1)</math> array of convolved features. These convolved features can then be [[#pooling | pooled]] for classification, as described below.

Revision as of 07:02, 20 May 2011

Personal tools