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Implement Distributed Alternating Least Squares Algorithm for Matrix Completion Varun Gandhi (vg292) Computer Laboratory Netflix Problem V: mn matrix complete the matrix W: mr (row-factor matrix) H: r*n

Implement Distributed Alternating Least Squares Algorithm for Matrix Completion Varun Gandhi (vg292) Computer Laboratory
Netflix Problem • V: m*n matrix • complete the matrix � � � • W: m*r (row-factor matrix) • H: r*n (column-factor matrix) • W*H approx V • Loss function (V ij - WH ij ) 2 2
Motivation Large applications involve matrices with • millions of rows x columns; • billions of entries To achieve high-performance • parallel & distributed factorisation • keep the loss to minimum � 3
Algorithm Sequential Computation • Initial point W 0 and H 0 • ALS solved for every row & column � � � Parallel Computation • Parallelise computation for rows and columns respectively 4
Algorithm Distributed Computation • Partition (block) the matrix with m b *n b matrices • every node updates a matrix block � Why Spark? • In-memory algorithm • Matrix versions cached in memory 5
Progress • Revising all linear algebra concepts • Getting familiar with Scala and Spark • Trying examples in Python 6

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