In order to restore compressed data you need use the Grossberg's layer connecting to Kohonen's layer output. Usually for compression use the Counter Рropagation Network (Kohonen and Grossberg layers).

Dear Alexander,

Thank you so much for your great comment. I could finally reconstruct the compressed image.

I would also be thankful if you could help me with the following questions:

I appreciate it once again for the time you've spent on my question.

Regards,

Amirmohammad

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from my understanding of the Kohonen / Grossberg architecture, the training of both layers are independent :

- first, train the Kohonen layer (with no Grossberg layer) until convergence using the standard algorithm

- second, "freeze" the Kohonen layer and use its output to train the (supervised) Grossberg layer which performs reconstruction using backpropagation

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note that you might use more complex architectures in your "Grossberg layer" (adding one hidden layer, for instance)

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whether you perform the training of the complete architecture at the same time or not did not seem to have such an influence on the result as, with a simple no hidden layer Grossberg architecture, the training of the reconstruction layer is much faster than the training of the quantization layer and the former "follows" the later

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in this way, you keep the unsupervised character of the Kohonen representation (quantization) and add an output layer similar to the output layer of an autoencoder (except that the compressed representation is frozen in the Kohonen layer)

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whether you are better off with a classical autoencoder or with this Kohonen / Grossberg architecture will depend on your application

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attached is a very old paper describing this architecture

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Dear Amirmohammad. I will glad to help you if I can.

Dear Fabrice.

1. Compression ratio is depends from: 1) number of inputs - size of input block of image, witch you feed to Kohonen layer; 2) number of Kohonen neurons. Thus, relation of this parameters determines the compression level. 

Additionally you need to save the Grossberg layer synapses in order to 'draw' compressed image. But the parameters of Grossberg layer is determined from size of input block of image and number of Kohonen neurons. Thus, the quality of training of Grossberg layer effects only on loss in the compressed image, but not on compressed level.

Also you can try to correct Grossberg layer synapses in adaptive manner: you don't need to save them - the compression ratio will improve, but  the loss in compressed image will grow. 

2. Training of Kohonen layer is unsupervised. The training of Grossberg layer is supervised, but the target outputs of Grossbers neurons is the inputs of Kohonen layer (block of image). In result the training of all network is unsupervised, because you don't feed any additional target outputs to network.

3. As wrote Fabrice you can train Gorssberg neurons after training Kohonen neurons or simultaneously with them. The Grossberg and Kohonen synapses after training represent a averaged snapshot of input image block. 

We need the Grossberg layer because the Kohonen neuron used normalized synapses vectors. Thus we can't to 'draw' the image using such normalized (deformed) snapshot of input blocks.

In order to solve the compression only in one layer you need to eliminate the normalization (deformation) of synapses. As an alternative of Kohonen layer it possible to implement it's clustering on Voronoi diagrams. The Kohonen neurons performs the function of vector's (X and W) scalar multiplication. Thus if the vectors are similar you have the Max of this function and this neuron will be a champion. In alternative variant (Voronoi diagrams) the neuron will measure the Euclidean distance between them. Now the criterion of neuron-champion will be the Min of distance.

As the disadvantage of Voronoi diagrams it is the nonstandard activation function of neurons.

The normalization useful if the inputs have different nature. The of image block can be separate to clusters without normalization.