BDW16 London - Harry Powell & Raffael Strassnig, Barclays UK - Graph-Based Recommendations

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A recommendation approach is developed based on the full customer relationship graph, and a similarity metric, the Expected Degrees of Separation between nodes. Scalability issues are discussed and a methodology for estimating EDS in big data sets is presented, along with empirical results based on anonymised Barclays customer transaction data.

Graph Recommendations
Harry Powell & Raffael Strassnig

Transactions imply customer preferences over
business values
Tesco

Price
Quality
Boots

Health
? Price ?
? Quality ?
Asda

Price

The data: Customer transactions
Timestam
p
Customer Business Amount (£)
… Bob Smith Tesco, Bristol …
… Mary
Jones
Tesco, Bristol …
… Bob Smith Asda, Bath …
… John
Taylor
Bristol Angling Centre …

Transactional data can be seen as a bipartite
graph
Tesco
Asda BP
Boots
Timestam
p
CustomerI
D
MerchantName Amount (£)
… 1 Tesco …
… 1 Asda …
… 2 Boots …
… 2 BP …
… 3 Tesco …
… 3 Boots …
… 3 BP …
… 4 Asda …

We wanted a way of inferring latent preferences
accounting for n-degree separation
Tesco Boots Asda Lloyds
Pharmacy

Tesco
Asda
BP
Boots
Expected Degrees of Separation

Can factorise out to homogeneous graph
Tesco Asda BP BootsTesco
Asda BP
Boots
Tesco
Asda
BP
Boots

Absorbing transition matrix
Discrete phase type distribution
– Computes EDS for all sources to single distribution
– Gives exact results
𝑃 =
𝑇 𝑡
0 1
, 𝐸𝐷𝑆 = 𝐼 − 𝑇 −1
Has unacceptably high complexity due to inverting large matrix
– Complexity = 𝑂(𝑛4)
– Try partitioning with partition transitions?

Estimating EDS using path sampling
An alternative is a sampling approach which is fully distributable
– Complexity = 𝑂(𝑛 × 𝑘 × 𝑙)
– Converges to analytical solution
Cautions
– Random fluctuations for 𝑙 > 4
– Signal dilution (applies to exact solution too)

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