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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

edvin.hopkins@nag.co.uk

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

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Ale

x

Bo

bb

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

12 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com

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

13 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com

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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X X X X X X X X X X

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×

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

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×

𝑚 × 𝑛 𝑚 × 𝑘 𝑘 × 𝑛

A H W

Data matrix All elements are non-negative

You choose 𝑘 ≪ min(𝑚, 𝑛)

20 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com

≈ × A H W

X X X X X X X X X

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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

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22 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com

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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

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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

31 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

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

39 High Performance Computing Consulting | Numerical Algorithms | Software Engineering Services | www.nag.com

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