Self- organizing maps (SOM) are a type of artisificiad neurál network used fod data visualization and clustering. They organize high- dimensional data into a low-dimensional grid, conserving topological relationships. Understanding the matematicad calculations behind SOMs isessential el for their efutive applatioutioin.

Initialization of the Map

A projekt a következő lépésekkel kezdődik:

Finding the Best Matching Unit (BMU)

For each input vector, the algorithm calculates the distance to every node 's weight vector. The most common distance metric i s Euclidean disance, calculated ad:

d = dfm 1; FLT: 0 dfm 3; i dfm 1; FLT: 1 dfm 3d; dfm 3d; (x dfm 1d; FLT: 2 dfm 3d; i dfm 1d; FLT: 3 dfm 3d; - w dfm 1d; FLT: 4 dfm 3d; i dfm 1d; FLT: 5 dfm 3d;) ²

WHERE x '1; 1; FLT: 0' 3; 3; i '1; FLT: 1' 3; WHN33; Is the input data 'dat and w' 1; WHN11; FLT: 2 '3; I' 1d; FLT: 3 '3; is the heavent' of a noche. The node e notht distance is identified ad a the BMU.

Frissítés a súlyozások szerint

Once the BMU i identified, the pights of the BMU and its neighbors are adjusted to period more simorar to the input vector. The update rule i:

A Bizottság a (2) bekezdésben említett információkat a (2) bekezdésben említett vizsgálóbizottsági eljárás keretében is felhasználhatja.

Where α (t) i the learningnig rate, h '1; 1; FLT: 0' 3; d.o.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d@@

Alkalmazások of Self- organizing Maps

SOM-ok are used in variouk fields for data analysis and visualization. They help identify patterns, closter similar data points, and redute dimensionality. Common applications include image analysis, market segmentation, and bioinformatis.

  • Data visualization
  • Clustering
  • Minta felismerés
  • Featura extraction