non-negative matrix factorization for analysing high ... · experts in numerical software and high...
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Experts in numerical software and High Performance Computing
Non-negative matrix factorization for
analysing high-dimensional datasets
The 3rd Machine Learning & AI in Quantitative Finance Conference
22nd March 2019
Edvin Hopkins
Technical Consultant
2 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
3 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
4 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
5 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
6 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
7 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
8 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
9 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
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Ale
x
Bo
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y
Ch
arlie
Dan
a
English 58.1 19.5 66.3 48.3
Math(s) 84.2 85.1 90.7 81.4
History 96.1 61.2 85.6 52.1
Geography 45.3 97.8 75.0 81.2
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58.1 19.5 66.3 48.3
84.2 85.1 90.7 81.4
96.1 61.2 85.6 52.1
45.3 97.8 75.0 81.2
columns = observations
rows =
variables
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Observations Variables
People Exam grades
Medical test scores
Companies Share prices
Pixels/voxels Concentration of chemicals
Spectroscopy data
Light intensities
News articles Word frequencies
Plants or animals Anatomical lengths
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17 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
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X X X X X X X X X X
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≈
X X X
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X X X
X X X
X X X
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X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
×
𝑚 × 𝑛 𝑚 × 𝑘 𝑘 × 𝑛
19 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
≈
X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
×
𝑚 × 𝑛 𝑚 × 𝑘 𝑘 × 𝑛
A H W
Data matrix All elements are non-negative
You choose 𝑘 ≪ min(𝑚, 𝑛)
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≈ × A H W
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X X X X X X
X X X X X X X X
X X X X X X X X
21 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
≈ × A H W
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X X X X X X
X X X X X X X X
X X X X X X X X
22 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
23 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
24 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
25 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
26 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
27 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
28 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
29 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
30 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
Category 1 Category 2
deal trump
brexit president
extension women
vote nielsen
could border
parliament mccain
government security
europe senator
delay class
referendum administration
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Category 1 Category 2
deal trump
brexit president
extension women
vote nielsen
could border
parliament mccain
government security
europe senator
delay class
referendum administration
32 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
33 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
Brexit delay: How can Article 50 be extended?
Kirstjen Nielsen: Walking a tightrope working for Trump
Trump homes plan at Menie being recommended for approval
Theresa May at her worst during Brexit speech - Mark Drakeford
President Trump shows map of 'IS defeat'
Brexit: What happens now?
Trump spooks markets with China trade tariffs warning
A tale of two Trumps: Jair Bolsonaro goes to Washington
Brexit: Theresa May to formally ask for delay
Corbyn calls for compromise to avoid no-deal Brexit
Trump: I didn't get a thank you for McCain funeral
Brexit: EU draft plans propose Brexit delay until May
Trump: Time to recognise Golan Heights as Israeli territory
Brexit: MPs urged not to travel home alone as tensions rise
'Cancel Brexit' petition passes 1m signatures on Parliament site
34 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
Brexit delay: How can Article 50 be extended?
Kirstjen Nielsen: Walking a tightrope working for Trump
Trump homes plan at Menie being recommended for approval
Theresa May at her worst during Brexit speech - Mark Drakeford
President Trump shows map of 'IS defeat'
Brexit: What happens now?
Trump spooks markets with China trade tariffs warning
A tale of two Trumps: Jair Bolsonaro goes to Washington
Brexit: Theresa May to formally ask for delay
Corbyn calls for compromise to avoid no-deal Brexit
Trump: I didn't get a thank you for McCain funeral
Brexit: EU draft plans propose Brexit delay until May
Trump: Time to recognise Golan Heights as Israeli territory
Brexit: MPs urged not to travel home alone as tensions rise
'Cancel Brexit' petition passes 1m signatures on Parliament site
35 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
36 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
37 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com
Category 1 Category 2
GlaxoSmithKline BTG
Grainger Dechra
Helical Bar Derwent London
Segro Genus
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