Slides for the presentation I gave at the Dublin Data Science Meetup on 2018-03-15.

1. Matrix Factorisation for Recommender Systems

2. Contents
● Refresher about matrices
● SVD
● NMF
● ALS
● Recommender Metrics

3. Matrix Multiplication

4. Matrix Multiplication

5. Matrix Multiplication
In
→ identity matrix size n
∀ Am ⨉ n
, ∃ In
,Im
: AIn
= Im
A = A

6. Least Squares
BA A’
bij

7. The Problem

8. The Problem
★★★☆☆
★★★★★ ★☆☆☆☆
★★★★☆★★★☆☆
N/A
N/A N/A N/A
N/AN/A
N/AN/A
N/A
N/A

9. SVD
A
(m ⨉ n)
U
(m ⨉ m)
or
(m ⨉ k)
Σ
(m ⨉ n)
or
(k ⨉ k)
VT
(n ⨉ n)
or
(k ⨉ n)

10. SVD
https://github.com/mehese/svd_als_presentation/blob/master/SVD.ipynb

11. Everything should be made as simple as possible, but not simpler.
Albert Einstein

12. It can scarcely be denied that the supreme goal of all theory is to make the irreducible
basic elements as simple and as few as possible without having to surrender the
adequate representation of a single datum of experience.
Albert Einstein
"On the Method of Theoretical Physics" The Herbert Spencer Lecture, delivered at Oxford (10 June
1933); also published in Philosophy of Science, Vol. 1, No. 2 (April 1934), pp. 163-169., p. 165
(but I got it from Wikipedia and never double-checked…)

13. NMF
A
(m ⨉ n)
U
(m ⨉ k)
Σ
(k ⨉ k)
VT
(k ⨉ n)

14. NMF
A
(m ⨉ n)
X
(m ⨉ k)
YT
(k ⨉ n)

15. ALS
Y Koren et al, 2009Y Hu et al, 2008

16. ALS
X
YT
rui

17. ALS

18. ALS

19. ALS
X
Y
https://github.com/mehese/svd_als_presentation/blob/master/ALS.ipynb

20. ALS
How to get even more speedup
Small number of non-zero elements

21. ALS
But what about implicit feedback?
rui
= ★★☆☆☆ ?!?

22. Metrics
General
● Precision
● Root Mean Square Error
Rank aware
● Mean Average Precision
● Normalised Discounted Cumulative Gain
Others
● Reach
● Serendipity

23. Resources
● https://github.com/fastai/numerical-linear-algebra/blob/master/README.md
● http://ieeexplore.ieee.org/document/4781121/
● http://ieeexplore.ieee.org/abstract/document/5197422/
● https://www.cs.cmu.edu/~venkatg/teaching/CStheory-infoage/book-chapter-4.
pdf
● https://www.youtube.com/watch?v=mBcLRGuAFUk
● https://fenix.tecnico.ulisboa.pt/downloadFile/3779576344458/singular-value-d
ecomposition-fast-track-tutorial.pdf

24. Thank you
Eric Mehes
@meHessian
https://www.linkedin.com/in/eric-mehes/