Clustering and Factorization using Apache SystemML by Prithviraj Sen
Click here to load reader
-
Upload
arvind-surve -
Category
Education
-
view
17 -
download
0
Transcript of Clustering and Factorization using Apache SystemML by Prithviraj Sen
![Page 1: Clustering and Factorization using Apache SystemML by Prithviraj Sen](https://reader037.fdocuments.in/reader037/viewer/2022100802/588003501a28ab421b8b461f/html5/thumbnails/1.jpg)
MatrixFactorizationAlgorithmsinApacheSystemML
PrithvirajSen
![Page 2: Clustering and Factorization using Apache SystemML by Prithviraj Sen](https://reader037.fdocuments.in/reader037/viewer/2022100802/588003501a28ab421b8b461f/html5/thumbnails/2.jpg)
ApplicationsofMatrixFactorization
• NetflixPrize• Givenratingsdatapredictwhatmoviesuserswillwatch
1 3 4 ? ? ?
? 3 5 ? ? 5
? ? 4 5 ? 5
? ? 3 ? ? ?
? ? 3 ? ? ?
2 ? ? 2 ? 2
? ? ? ? 5 ?
? 2 1 ? ? 1
? 3 ? ? 3 ?
1 ? ? ? ? ?
17,700 movies
480,000users
![Page 3: Clustering and Factorization using Apache SystemML by Prithviraj Sen](https://reader037.fdocuments.in/reader037/viewer/2022100802/588003501a28ab421b8b461f/html5/thumbnails/3.jpg)
Applications:PartsBasedDecomposition
![Page 4: Clustering and Factorization using Apache SystemML by Prithviraj Sen](https://reader037.fdocuments.in/reader037/viewer/2022100802/588003501a28ab421b8b461f/html5/thumbnails/4.jpg)
LeastSquaresMatrixFactorization
• ApproximateVusingLRmin∑ (𝑣$%−𝑙$′𝑟%)2($,%)
• Leadstotheverywellknownalternatingleastsquaresalgorithm• Onlyrequiressolvingleastsquares• Embarassingly parallel
V L
Rf
f
~~x
![Page 5: Clustering and Factorization using Apache SystemML by Prithviraj Sen](https://reader037.fdocuments.in/reader037/viewer/2022100802/588003501a28ab421b8b461f/html5/thumbnails/5.jpg)
ALSinDML
parfor
parfor
Directsolvingleastsquares
Directsolvingleastsquares
![Page 6: Clustering and Factorization using Apache SystemML by Prithviraj Sen](https://reader037.fdocuments.in/reader037/viewer/2022100802/588003501a28ab421b8b461f/html5/thumbnails/6.jpg)
PoissonMatrixFactorization(NMF)
• Suitableifyouarelookingfornon-negativefactors𝑣 = 𝑒/01𝑙𝑟𝑛/𝑛!
• LeadstothewellknownGeneralizedKL-Divergencemax∑ (𝑛𝑖𝑗log𝑙𝑖′𝑟𝑗 − 𝑙𝑖′𝑟𝑗)$%
• Wellknownupdateequationsexist*
*“Generalized NonnegativeMatrixApproximationswithBregman Divergences” byDhillon andSra inNIPS2005.* “DistributedNonnegativeMatrixFactorizationforWeb-ScaleDyadicDataAnalysisonMapReduce”byLiuetalinWWW2010.
![Page 7: Clustering and Factorization using Apache SystemML by Prithviraj Sen](https://reader037.fdocuments.in/reader037/viewer/2022100802/588003501a28ab421b8b461f/html5/thumbnails/7.jpg)
PNMFinDML
• Veryefficientupdatesusingonlylinearalgebra• UsesApacheSystemML’s wdivmm operator
wdivmm operator