Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Rigorous Link Between Self-Organizing Maps and Gaussian Mixture Models   This work presents a mathematical treatment of the relation between
Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that
energy-based SOM models can be interpreted as performing gradient descent,
minimizing an approximation to the GMM log-likelihood that is particularly
valid for high data dimensionalities. The SOM-like decrease of the neighborhood
radius can be understood as an annealing procedure ensuring that gradient
descent does not get stuck in undesirable local minima. This link allows to
treat SOMs as generative probabilistic models, giving a formal justification
for using SOMs, e.g., to detect outliers, or for sampling.

12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph