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I have some high dimensional data and I want to reduce it to 2 dimensions for visualization. The goal is to color the points in this 2D space to see whether there is any clustering due to different features of my dataset. I'm not interested in doing any actual clustering, or making any predictions from this model, simply to visualize it to identify patterns.

I'm struggling to understand the difference between t-SNE and SOM (self organizing map). Clearly the calculations that go into each technique are different, but I'm wondering how the techniques differ, and what factors should go into deciding which technique to use

As I understand it, there seems to be a number of similarities:

  1. Both used for manifold learning, and should only be used if you expect your high dimensional data to conform to some lower dimensional manifold.

  2. Mapping from high to low dimensions is done using euclidean distance in both cases

  3. They both use some sort of neighborhood function to preserve the local structure of data. I believe global structure is also preserved in some sense as well

  4. They both seem to preserve the topology of the input. For example, a SOM produces a 2D representation of the input space, where data points that are close together in the higher dimensional input space are placed close together in the output SOM.

So, what are the key differences between these techniques, and when should you use one over the other?

More generally, how do you determine whether its even important to preserve the topology of your input, and to use these types of techniques over something like PCA?

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    $\begingroup$ +1. I don't know much about SOM so I don't think I can answer this question without further reading, but for t-SNE all 4 points are basically wrong :-) $\endgroup$ – amoeba Nov 23 '18 at 12:43
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    $\begingroup$ +1 to @amoeba 's comment. To be a bit more specific: $t$-SNE involves no manifold learning but rather a non-parametric mapping, the main metric used is the KL divergence and the global structure is seriously distorted. The 4th point is almost moot, as locally it holds true for almost any visualisation technique... CV has really nice threads under tnse you might want to explore further before revisiting this question. (I would assume that the comparison between SOM and (deep) auto-encoders would be more meaningful.) $\endgroup$ – usεr11852 Nov 24 '18 at 0:25

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