there will be shoes on different places.
all the neurons will try to learn not only shoes but also the place of the shoes in the images because it will not have the concept of 'local image patch' inside weights.
DBN makes sense if all your images are aligned by means of size, translation and rotation.
first you looked at 7x7 patches, and according to your example - as an example of 3 of your neurons in the first layer you can say that they learned shoes 'front', 'back-bottom' and 'back-upper' parts as these would look alike for a 7x7 patch through all shoes.
Normally the idea is to have multiple convolution layers one after another to learn
You can think of these 3 different things I told you as 3 different neurons. And such areas/neurons in your images will fire when there are shoes in some part of the image.
Pooling will protect your higher activations while sub-sampling your images and creating a lower-dimensional space to make things computationally easier and feasible.
So at last layer when you look at your 25X4x4, in other words 400 dimensional vector, if there is a shoe somewhere in the picture your 'shoe neuron(s)' will be active whereas non-shoe neurons will be close to zero.
And to understand which neurons are for shoes and which ones are not you will put that 400 dimensional vector to another supervised classifier(this can be anything like multi-class-SVM or as you said a soft-max-layer)
I will try to explain the situation through learning shoes.
If you use DBN to learn those images here is the bad thing that will happen in your learning algorithm
there will be shoes on different places.
all the neurons will try to learn not only shoes but also the place of the shoes in the images because it will not have the concept of 'local image patch' inside weights.
DBN makes sense if all your images are aligned by means of size, translation and rotation.
the idea of convolutional networks is that, there is a concept called weight sharing. If I try to extend this 'weight sharing' concept
first you looked at 7x7 patches, and according to your example - as an example of 3 of your neurons in the first layer you can say that they learned shoes 'front', 'back-bottom' and 'back-upper' parts as these would look alike for a 7x7 patch through all shoes.
Normally the idea is to have multiple convolution layers one after another to learn
You can think of these 3 different things I told you as 3 different neurons. And such areas/neurons in your images will fire when there are shoes in some part of the image.
Pooling will protect your higher activations while sub-sampling your images and creating a lower-dimensional space to make things computationally easier and feasible.
So at last layer when you look at your 25X4x4, in other words 400 dimensional vector, if there is a shoe somewhere in the picture your 'shoe neuron(s)' will be active whereas non-shoe neurons will be close to zero.
And to understand which neurons are for shoes and which ones are not you will put that 400 dimensional vector to another supervised classifier(this can be anything like multi-class-SVM or as you said a soft-max-layer)
I can advise you to have a glance at Fukushima 1980 paper to understand what I try to say about translation invariance and line -> arc -> semicircle -> shoe front -> shoe idea (http://www.cs.princeton.edu/courses/archive/spr08/cos598B/Readings/Fukushima1980.pdf). Even just looking at the images in the paper will give you some idea.