### Stacked combining

By stacked combining, sets of mappings are combined that operate from the same input space into different output spaces. The resulting mapping concatenates these output spaces. The combining operator is the horizontal concatenation. So if we have three mappings `W1`

, `W2`

and `W3`

, they are combined by

W = [W1 W2 W3];

which means that if a dataset `A`

is mapped by `W`

it results in the concatenation of resulting datasets:

B = A*W;
B = [A*W1 A*W2 A*W3];

Example_1

Stacked combining can also be applied to untrained mappings. In that case a set of untrained base mappings `U1`

, `U2`

, `...` are trained separately, resulting in `W1`

, `W2`

, `...`. These constitute a new, now trained, combined mapping.

U = [U1 U2 U3]; % concatenation of untrained mappings
W = A*U; % training, results in W = [A*U1 A*U2 A*U3] = [W1 W2 W3]

Example_2

### Links

operations: basic, datasets, datafiles, mappings, classifiers, stacked, parallel, sequential, dyadic

commands: datasets, representation , classifiers, evaluation, clustering and regression, examples, support