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Update SVD documentation to reflect roughly square
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docs/mllib-dimensionality-reduction.md

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@@ -11,7 +11,7 @@ displayTitle: <a href="mllib-guide.html">MLlib</a> - Dimensionality Reduction
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of reducing the number of variables under consideration.
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It can be used to extract latent features from raw and noisy features
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or compress data while maintaining the structure.
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MLlib provides support for dimensionality reduction on tall-and-skinny matrices.
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MLlib provides support for dimensionality reduction on the RowMatrix class.
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## Singular value decomposition (SVD)
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* `$\Sigma$`: `$k \times k$`,
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* `$V$`: `$n \times k$`.
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MLlib provides SVD functionality to row-oriented matrices that have only a few columns,
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say, less than $1000$, but many rows, i.e., *tall-and-skinny* matrices.
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MLlib provides SVD functionality to row-oriented matrices, provided in the RowMatrix class.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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possible, and each succeeding coordinate in turn has the largest variance possible. The columns of
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the rotation matrix are called principal components. PCA is used widely in dimensionality reduction.
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MLlib supports PCA for tall-and-skinny matrices stored in row-oriented format.
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MLlib supports PCA for matrices stored in row-oriented format.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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The following code demonstrates how to compute principal components on a tall-and-skinny `RowMatrix`
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The following code demonstrates how to compute principal components on a `RowMatrix`
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and use them to project the vectors into a low-dimensional space.
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The number of columns should be small, e.g, less than 1000.
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{% highlight scala %}
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import org.apache.spark.mllib.linalg.Matrix
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<div data-lang="java" markdown="1">
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The following code demonstrates how to compute principal components on a tall-and-skinny `RowMatrix`
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The following code demonstrates how to compute principal components on a `RowMatrix`
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and use them to project the vectors into a low-dimensional space.
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The number of columns should be small, e.g, less than 1000.
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