Self- organising maps (SOM) are a type of accessial neural network used for data visualization and clustering. They organise high- dimensal data into a low- dimensional grid, reserving topological contraships. Understanding thee accessal calculations behind SOMs is essential for their effective application.

Initialization of te Map

Te process begins with initializing the efat vectors of each node in the map. Typically, headts are assigned randomibly or based on he data distribution. Each heath vector has the same dimension as te input data.

Finding thee Bett Matching Unit (BMU)

For each input vector, thee algoritm calculates the distance to every node 's ewit vector. Thee mogt common distance metric is Euclidean distance, calculated as:

d = {\ cH1;};} 1; FLT: 0} 3; i} 1; FLT: 1} 3; FLT; (x 'FF1; FLT: 2} 3; FLT; i' FLT: 1; FLT: 3; FLT; - w 'I1; FLT: 4} 3; FLT; 3d; i' I1; FLT: 5} 3d;) ²

kde je x '1; fl1; FLT: 0'; FL3; i 'FL1; FLT: 1'; FL3; is the input data 'ind1; FLT: 2'; FL3; i 'FL1; FLT: 3'; FL3; is the heaven 'of a node. Te node with' e smallest distance is identified as 'e BMU.

Updating te Weighs

Once te BMU is identified, thee váhy of te BMU and it s souseds are condiced to o applicae more similar to te input vector. Thee update rule is:

w CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; C( t) * (x - w CLAS1; CLAS1; CLAS3; C3; CLAS3;)

flnnnn, h 'l1; FLT: 0'; FL3; ci 'l1; FL1; FLT: 1' l3; 'l3;' l3; 't) is to sousedhood function, and (x-w' l1; 'l1;' FLT: 2 'l3;' eld '1;' l1; 'l1; FLT: 3' l3; 'l3;' l3; 'l3;' ld) is to difference e 'ln thee input vector and', then 'rt hettt vector.

Použitelnost of Self- organising Maps

SOMs are used in various fields for data analysis and visualization. They help identifify patterns, cluster similar data pointes, and reduce dimensionality. Common applications include image analysis, market segmentation, and bioinformatics.

  • Data vizualization
  • Clustering
  • Vzor rozpoznán
  • Feature extraction