April 2017
Intermediate to advanced
532 pages
12h 39m
English
book
Machine Learning with Spark - Second Edition
by Rajdeep Dua, Brian O'Neill, Stephen Boesch, Manpreet Singh Ghotra, Nick Pentreath
Content preview from Machine Learning with Spark - Second Edition
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Singular value decomposition
Singular value decomposition of a matrix M: m x n (real or complex) is a factorization with the form UΣV*, where U is an m x R matrix. Σ is an R x R rectangular diagonal matrix with non-negative real numbers on the diagonal, and V is an n x r unitary matrix. r is equal to the rank of the matrix M.
The diagonal entries Σii of Sigma are known as the singular values of M. The columns of U and the columns of V are called the left-singular vectors and right-singular vectors of M respectively.
The following is an example of an SVD in Apache Spark:
package linalg.svd import org.apache.spark.{SparkConf, SparkContext} import org.apache.spark.mllib.linalg.distributed.RowMatrix import org.apache.spark.mllib.linalg.{Matrix, ...Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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