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Made by: Csernenszky András (OTP)Kovács Gyula (Sixtep)Krész Miklós (University of Szeged)Pluhár András (University of Szeged)

Budapest, 2010.06.06

Graph optimisation for business issues

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Introduction

Motivation

Purchaser transaction Supplier

•Own database, monthly aggregated data from 2008.01.01

•Outsourcing is not secure enough

•Data mining experience

•Easy to use,

•Flexible target software

•Innovative developers

Database

Software

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Reports

Two reports , two methodology

Forecasting Attrition (Churn model)Bankruptcy forecast

Here we use infection models(Cascade model)

We examine the communities

recovery

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Parameter estimation

Finding the parameters

Defining dataset •clients or debtors,

•finding the optimal observation period,

•directed or undirected edges

Connections•Relevancy & Stability,

•Probability of influence on the edges Weighting the edges

ClientsFlag clients by 0-1

Vs.

Weighting the clients?(company size, PD, etc)

23%

100%

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Weighting the edges I

Variables

Municipalities are not effected by the companies…

These edges are stronger which are in a community.

community information flagis it a company or a munucipality? flagamount sent on (i, j) /total sum arrived to j numericqueueing on the account numericlimit exceeded numericnumber of debits numericage of the company numeric

Sup

plie

r

Heuristic

Client behavior and application data

Normalizing functions

Affine function; F1 = c0 + fn

Logarithmic function 11explog)( 22

1 xxf

Exponential1exp1exp

)(2

21

x

xf

Gaussian function

1212)( 1

aaxaxf 1st

2nd

3rd

4th

GRID- search

Iteration

Distribution

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Weighting the edges II.

1. Edge attributes

2. Function transformations

3. Train and test data

2.Parameter settings for grid-search, simulation number.

Purchaser –supplier connections Observed bankruptcy

Which companies have become bankrupt?

2009.08 2010.02 2010.05 2010.08

GRAPH

Deatils

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Weighting the edges - RESULTS

Modell performance: Three months after the infection at theTOP1, TOP2 és TOP5%

Constant graph(uniform infection probability)

Heuristic graph(by using one variable)

„Weighting” graph

(optimalizied by 4 attributes)

TOP1% 1,25 1,47 3,06TOP2% 1,64 1,94 4,18!

1,13 1,10 1,97TOP5%

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Relevancy & stability I.

UNCHANGED

GROWS/ SHRINKS

MERGES

FADES

BIRTH

SPLITS; FRACTURES

Transitions of the communities Edge connection parameters

Relative amount=Incoming amount on the edge/ total income from the partners

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Relevancy & stability II.

TWO PERIODS

2009.10 2010.04 2010.09 2011.03

GRAPH 1

GRAPH 2

6 months

Graph type (frequency, amount, relative amount)

vertices/edges

%vertices in communities

%edges in communities fades% unchanged%

GGG 27,1% 24,9% 20,6% 71% 15%GGY 28,9% 26,8% 26,9% 65% 17%

GGR 43,1% 16,6% 20,0% 47% 30%….

YYY 28,6% 20,7% 29,6% 57% 21%          

RGR 40,0% 12,0% 20,6% 40% 37%…

RRY 29,9% 16,4% 30,8% 49% 27%

RRR 38,6% 12,5% 23,4% 39% 37%

6 months

CHANGES at 6 months

G=TOP 100%; Y=TOP 66%; R= TOP 33% by ordering that edge parameter

50% of the vertices; 12,5% of the edges

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Dense graph small communities!

Relevancy & stability - RESULTS

Infection via edges Churn via communities

23%

100%

23%

100%

+++

+++

GGG

RRR

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Thank you for your attention!