Event Detection In Activity Networks

Introduction

involve monitoring routinely collected data

• Want to detect “events of interest”

•events typically affect a subgroup of the data rather than an individual data point

Introduction

Introduction

Introduction

Goals of event detection:

• Identify if an event of interest has occurred

• Characterize the event

• Detect as accurately as possible

• Detect as early as possible

Introduction

difference supervised learning

clustering

outlier detection

Event

a subset of nodes in the network that are close

to each other and have high activity levels.

Application

sensor network

deployed in a certain region and recording a measurement of interest social network

model social interactions between individuals.

Two definitions

sum of pairs of distances

Steiner-tree cost

Statictical mehods

a null hypothesis

heuristic in nature

shape is predefined

assume that there exists an underlying Euclidean geometry on the space

Formulation

G = (V,E,w,c), w : V ->R, c(u,v),

VS

Sv

vwSW )()(

Sv Su

AP vudSD ),(2

1)(

TvuSGT

T vudSD),(

])[(),(min)(

Formulation

Formulation

prize-collecting Steiner Tree

Formulation

Lemma 1. The problem EventAllPairs+ is NP-hard

Lemma 2. The problem EventTree+ is NP-hard.

Lemma 3. The function Q+AP is submodular.

Algorithm

Trival Algorithm

GreedyAP

Lemma 4. Consider a submodular function F and let S

be the solution given by the greedy algorithm optimizing F.

Then, F(S) is no less than F(V ).

GreedyAP

MaxCut Formulation

EventAllPairs+ problem

MaxCut Formulation

PD

prize-collection Steiner-tree

2 phases

Test Result

Test Result

Test Result

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