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# PolynomialExpansion 

### Companion class PolynomialExpansion

#### object PolynomialExpansion extends DefaultParamsReadable[PolynomialExpansion] with Serializable

The expansion is done via recursion. Given n features and degree d, the size after expansion is (n + d choose d) (including 1 and first-order values). For example, let f([a, b, c], 3) be the function that expands [a, b, c] to their monomials of degree 3. We have the following recursion:

\$\$ f([a, b, c], 3) &= f([a, b], 3) ++ f([a, b], 2) * c ++ f([a, b], 1) * c^2 ++ [c^3] \$\$

To handle sparsity, if c is zero, we can skip all monomials that contain it. We remember the current index and increment it properly for sparse input.

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