[SPARK-23946] Fix 2.3.0 ScalaDocs are linked to the wrong source code
[spark-website.git] / site / docs / 2.3.0 / api / scala / org / apache / spark / ml / feature / PolynomialExpansion$.html
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33 <h1><a href="PolynomialExpansion.html" title="See companion class">PolynomialExpansion</a></h1><h3><span class="morelinks"><div>
34 Related Docs:
35 <a href="PolynomialExpansion.html" title="See companion class">class PolynomialExpansion</a>
36 | <a href="package.html" class="extype" name="org.apache.spark.ml.feature">package feature</a>
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53
54 <div id="comment" class="fullcommenttop"><div class="comment cmt"><p>The expansion is done via recursion. Given n features and degree d, the size after expansion is
55 (n + d choose d) (including 1 and first-order values). For example, let f([a, b, c], 3) be the
56 function that expands [a, b, c] to their monomials of degree 3. We have the following recursion:</p><p><blockquote>
57 $$
58 f([a, b, c], 3) &= f([a, b], 3) ++ f([a, b], 2) * c ++ f([a, b], 1) * c^2 ++ [c^3]
59 $$
60 </blockquote></p><p>To handle sparsity, if c is zero, we can skip all monomials that contain it. We remember the
61 current index and increment it properly for sparse input.
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