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Good Day to everyone. I have spent quite some time now, introducing myself to neural networks. Therefore i am also looking into SOM's. Of course also on this site, as far as i have potentially "duplicate questions". The Statement: "...finding a corresponding point between a representative of the input space and a representative from a lower dimensional space." But what does this actually mean? I can see the concept to adjust weights to move in the high dim. space. How does the movement in an m - dimensional space affect the representation in an n-m dimensional space? In other words: how can the initialization of a vector with n (n <=3 seems intuitive) dimensions be interpreted(mapped, assigned,...) meaningfully in i.e. 2D? (without ideas like: cut away everything but the first two data-rows). I can see the concept of using RGB colors, but is there a more general approach?

Thank you for your time and answers (or links that might contain an answer)

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Let's look at example of handwritten digits mapping in SOM. picture from kaggle handwritten digits competition

You have your input space, 28*28 pixels -> 784 dimensions. 3 dimensions in case of RGB colors. SOM is learning mapping from those 284 dimensional space, to 2D space of it's own grid, in a way that similar inputs are located close together, which is done during your training. Every point in the grid, is one specific 'neuron' which is tuned to react most strongly to a specific input. And neighboring neurons are tuned to react to similar, but different inputs. As you can see from the picture, there is a meaningful mapping from 784D to 2D space based on inputs similarities.

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  • $\begingroup$ Thank you for your answer and example. I can perfectly "imagine" how those points move in a 784D grid. That is not a problem. I simply don't see the corresponding movement in 2D. How does that work? $\endgroup$
    – SOMnus
    Nov 10 '15 at 10:31
  • $\begingroup$ Nothing moves in the 2D layout. It defines neighbors and neighborhoods in the high-D space. $\endgroup$
    – Wayne
    Nov 29 '15 at 18:28
  • $\begingroup$ Thanks you two. Because of wayne's comment i could resolve the knot in my head :) $\endgroup$
    – SOMnus
    Dec 18 '15 at 7:27
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The 784 dimension represents each point in the 784-dimensional input space, where as the 2D weights or in this case Neurons represent the point in another 2-Dimensional Space. Data dimension is different from the lattice dimension (lattice is where you can see the data clustered)

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