Analyzing

Feature

Trajectories

for

Event

Detection

Qi

He

qihe@pmail.ntu.edu.sg

Kuiyu

Chang

ASKYChang@ntu.edu.sg

Ee-Peng

Lim

ASEPLim@ntu.edu.sg

School

of

Computer

Engineering

Nanyang

Technological

University

Block

Nanyang

Avenue,

Singapore

ABSTRACT

We

consider

the

problem

of

analyzing

word

trajectories

in

both

time

and

frequency

domains,

with

the

specific

goal

of

identifying

important

and

less-reported,

periodic

and

aperiodic

words.

A

set

of

words

with

identical

trends

can

be

grouped

together

to

reconstruct

an

event

in

a

completely

unsupervised

manner.

The

document

frequency

of

each

word

across

time

is

treated

like

a

time

series,

where

each

element

is

the

document

frequency

inverse

document

frequency

(DFIDF)

score

at

one

time

point.

In

this

paper,

we

first

applied

spectral

analysis

to

categorize

features

for

different

event

characteristics:

important

and

less-reported,

periodic

and

aperiodic;

modeled

aperiodic

features

with

Gaussian

density

and

periodic

features

with

Gaussian

mixture

densities,

and

subsequently

detected

each

feature"s

burst

by

the

truncated

Gaussian

approach;

proposed

an

unsupervised

greedy

event

detection

algorithm

to

detect

both

aperiodic

and

periodic

events.

All

of

the

above

methods

can

be

applied

to

time

series

data

in

general.

We

extensively

evaluated

our

methods

on

the

Reuters

News

Corpus

and

showed

that

they

were

able

to

uncover

meaningful

aperiodic

and

periodic

events.

Categories

and

Subject

Descriptors:

[Information

Storage

and

Retrieval]:

Information

Search

and

Retrieval

General

Terms:

Algorithms,

Experimentation.

INTRODUCTION

There

are

more

than

online

news

sources

in

the

world.

Manually

monitoring

all

of

them

for

important

events

has

become

difficult

or

practically

impossible.

In

fact,

the

topic

detection

and

tracking

(TDT)

community

has

for

many

years

been

trying

to

come

up

with

a

practical

solution

to

help

people

monitor

news

effectively.

Unfortunately,

the

holy

grail

is

still

elusive,

because

the

vast

majority

of

TDT

solutions

proposed

for

event

detection

are

either

too

simplistic

(based

on

cosine

similarity

or

impractical

due

to

the

need

to

tune

a

large

number

of

parameters

The

ineffectiveness

of

current

TDT

technologies

can

be

easily

illustrated

by

subscribing

to

any

of

the

many

online

news

alerts

services

such

as

the

industryleading

Google

News

Alerts

which

generates

more

than

false

alarms

As

further

proof,

portals

like

Yahoo

take

a

more

pragmatic

approach

by

requiring

all

machine

generated

news

alerts

to

go

through

a

human

operator

for

confirmation

before

sending

them

out

to

subscribers.

Instead

of

attacking

the

problem

with

variations

of

the

same

hammer

(cosine

similarity

and

TFIDF),

a

fundamental

understanding

of

the

characteristics

of

news

stream

data

is

necessary

before

any

major

breakthroughs

can

be

made

in

TDT.

Thus

in

this

paper,

we

look

at

news

stories

and

feature

trends

from

the

perspective

of

analyzing

a

time-series

word

signal.

Previous

work

like

has

attempted

to

reconstruct

an

event

with

its

representative

features.

However,

in

many

predictive

event

detection

tasks

(i.e.,

retrospective

event

detection),

there

is

a

vast

set

of

potential

features

only

for

a

fixed

set

of

observations

(i.e.,

the

obvious

bursts).

Of

these

features,

often

only

a

small

number

are

expected

to

be

useful.

In

particular,

we

study

the

novel

problem

of

analyzing

feature

trajectories

for

event

detection,

borrowing

a

well-known

technique

from

signal

processing:

identifying

distributional

correlations

among

all

features

by

spectral

analysis.

To

evaluate

our

method,

we

subsequently

propose

an

unsupervised

event

detection

algorithm

for

news

streams.

Easter

April

(a)

aperiodic

event

Unaudited

Ended

(b)

periodic

event

Figure

Feature

correlation

(DFIDF:time)

between

a)

Easter

and

April

b)

Unaudited

and

Ended.

As

an

illustrative

example,

consider

the

correlation

between

the

words

Easter

and

April

from

the

Reuters

From

the

plot

of

their

normalized

DFIDF

in

Figure

we

observe

the

heavy

overlap

between

the

two

words

circa

which

means

they

probably

both

belong

to

the

same

event

during

that

time

(Easter

feast).

In

this

example,

the

hidden

event

Easter

feast

is

a

typical

important

aperiodic

event

over

data.

Another

example

is

given

by

Figure

where

both

the

words

Unaudited

and

Ended

Reuters

Corpus

is

the

default

dataset

for

all

examples.

exhibit

similar

behaviour

over

periods

of

months.

These

two

words

actually

originated

from

the

same

periodic

event,

net

income-loss

reports,

which

are

released

quarterly

by

publicly

listed

companies.

Other

observations

drawn

from

Figure

are:

the

bursty

period

of

April

is

much

longer

than

Easter,

which

suggests

that

April

may

exist

in

other

events

during

the

same

period;

Unaudited

has

a

higher

average

DFIDF

value

than

Ended,

which

indicates

Unaudited

to

be

more

representative

for

the

underlying

event.

These

two

examples

are

but

the

tip

of

the

iceberg

among

all

word

trends

and

correlations

hidden

in

a

news

stream

like

Reuters.

If

a

large

number

of

them

can

be

uncovered,

it

could

significantly

aid

TDT

tasks.

In

particular,

it

indicates

the

significance

of

mining

correlating

features

for

detecting

corresponding

events.

To

summarize,

we

postulate

that:

An

event

is

described

by

its

representative

features.

A

periodic

event

has

a

list

of

periodic

features

and

an

aperiodic

event

has

a

list

of

aperiodic

features;

Representative

features

from

the

same

event

share

similar

distributions

over

time

and

are

highly

correlated;

An

important

event

has

a

set

of

active

(largely

reported)

representative

features,

whereas

an

unimportant

event

has

a

set

of

inactive

(less-reported)

representative

features;

A

feature

may

be

included

by

several

events

with

overlaps

in

time

frames.

Based

on

these

observations,

we

can

either

mine

representative

features

given

an

event

or

detect

an

event

from

a

list

of

highly

correlated

features.

In

this

paper,

we

focus

on

the

latter,

i.e.,

how

correlated

features

can

be

uncovered

to

form

an

event

in

an

unsupervised

manner.

Contributions

This

paper

has

three

main

contributions:

To

the

best

of

our

knowledge,

our

approach

is

the

first

to

categorize

word

features

for

heterogenous

events.

Specifically,

every

word

feature

is

categorized

into

one

of

the

following

five

feature

types

based

on

its

power

spectrum

strength

and

periodicity:

HH

(high

power

and

high/long

periodicity):

important

aperiodic

events,

HL

(high

power

and

low

periodicity):

important

periodic

events,

LH

(low

power

and

high

periodicity):

unimportant

aperiodic

events,

LL

(low

power

and

low

periodicity):

non-events,

and

SW

(stopwords),

a

higher

power

and

periodicity

subset

of

LL

comprising

stopwords,

which

contains

no

information.

We

propose

a

simple

and

effective

mixture

densitybased

approach

to

model

and

detect

feature

bursts.

We

come

up

with

an

unsupervised

event

detection

algorithm

to

detect

both

aperiodic

and

periodic

events.

Our

algorithm

has

been

evaluated

on

a

real

news

stream

to

show

its

effectiveness.

RELATED

WORK

This

work

is

largely

motivated

by

a

broader

family

of

problems

collectively

known

as

Topic

Detection

and

Tracking

(TDT)

Moreover,

most

TDT

research

so

far

has

been

concerned

with

clustering/classifying

documents

into

topic

types,

identifying

novel

sentences

for

new

events,

etc.,

without

much

regard

to

analyzing

the

word

trajectory

with

respect

to

time.

Swan

and

Allan

first

attempted

using

co-occuring

terms

to

construct

an

event.

However,

they

only

considered

named

entities

and

noun

phrase

pairs,

without

considering

their

periodicities.

On

the

contrary,

our

paper

considers

all

of

the

above.

Recently,

there

has

been

significant

interest

in

modeling

an

event

in

text

streams

as

a

burst

of

activities

by

incorporating

temporal

information.

Kleinberg"s

seminal

work

described

how

bursty

features

can

be

extracted

from

text

streams

using

an

infinite

automaton

model

which

inspired

a

whole

series

of

applications

such

as

Kumar"s

identification

of

bursty

communities

from

Weblog

graphs

Mei"s

summarization

of

evolutionary

themes

in

text

streams

He"s

clustering

of

text

streams

using

bursty

features

etc.

Nevertheless,

of

the

existing

work

specifically

identified

features

for

events,

except

for

Fung

et

al.

who

clustered

busty

features

to

identify

various

bursty

events.

Our

work

differs

from

in

several

ways:

we

analyze

every

single

feature,

not

only

bursty

features;

we

classify

features

along

two

categorical

dimensions

(periodicity

and

power),

yielding

altogether

five

primary

feature

types;

we

do

not

restrict

each

feature

to

exclusively

belong

to

only

one

event.

Spectral

analysis

techniques

have

previously

been

used

by

Vlachos

et

al.

to

identify

periodicities

and

bursts

from

query

logs.

Their

focus

was

on

detecting

multiple

periodicities

from

the

power

spectrum

graph,

which

were

then

used

to

index

words

for

query-by-burst

search.

In

this

paper,

we

use

spectral

analysis

to

classify

word

features

along

two

dimensions,

namely

periodicity

and

power

spectrum,

with

the

ultimate

goal

of

identifying

both

periodic

and

aperiodic

bursty

events.

DATA

REPRESENTATION

Let

T

be

the

duration/period

(in

days)

of

a

news

stream,

and

F

represents

the

complete

word

feature

space

in

the

classical

static

Vector

Space

Model

(VSM).

Event

Periodicity

Classification

Within

T,

there

may

exist

certain

events

that

occur

only

once,

e.g.,

Tony

Blair

elected

as

Prime

Minister

of

U.K.,

and

other

recurring

events

of

various

periodicities,

e.g.,

weekly

soccer

matches.

We

thus

categorize

all

events

into

two

types:

aperiodic

and

periodic,

defined

as

follows.

Definition

(Aperiodic

Event)

An

event

is

aperiodic

within

T

if

it

only

happens

once.

Definition

(Periodic

Event)

If

events

of

a

certain

event

genre

occur

regularly

with

a

fixed

periodicity

P

we

say

that

this

particular

event

genre

is

periodic,

with

each

member

event

qualified

as

a

periodic

event.

Note

that

the

definition

of

aperiodic

is

relative,

i.e.,

it

is

true

only

for

a

given

T,

and

may

be

invalid

for

any

other

T

T.

For

example,

the

event

Christmas

feast

is

aperiodic

for

T

but

periodic

for

T

Representative

Features

Intuitively,

an

event

can

be

described

very

concisely

by

a

few

discriminative

and

representative

word

features

and

vice-versa,

e.g.,

hurricane,

sweep,

and

strike

could

be

representative

features

of

a

Hurricane

genre

event.

Likewise,

a

set

of

strongly

correlated

features

could

be

used

to

reconstruct

an

event

description,

assuming

that

strongly

correlated

features

are

representative.

The

representation

vector

of

a

word

feature

is

defined

as

follows:

Definition

(Feature

Trajectory)

The

trajectory

of

a

word

feature

f

can

be

written

as

the

sequence

yf

[yf

yf

yf

(T)],

where

each

element

yf

(t)

is

a

measure

of

feature

f

at

time

t,

which

could

be

defined

using

the

normalized

DFIDF

yf

(t)

DFf

(t)

N(t)

log(

N

DFf

where

DFf

(t)

is

the

number

of

documents

(local

DF)

containing

feature

f

at

day

t,

DFf

is

the

total

number

of

documents

(global

DF)

containing

feature

f

over

T,

N(t)

is

the

number

of

documents

for

day

t,

and

N

is

the

total

number

of

documents

over

T.

IDENTIFYING

FEATURES

FOR

EVENTS

In

this

section,

we

show

how

representative

features

can

be

extracted

for

(un)important

or

(a)periodic

events.

Spectral

Analysis

for

Dominant

Period

Given

a

feature

f,

we

decompose

its

feature

trajectory

yf

[yf

yf

yf

(T)]

into

the

sequence

of

T

complex

numbers

XT

via

the

discrete

Fourier

transform

(DFT):

Xk

T

yf

(t)e−

T

k

T.

DFT

can

represent

the

original

time

series

as

a

linear

combination

of

complex

sinusoids,

which

is

illustrated

by

the

inverse

discrete

Fourier

transform

(IDFT):

yf

(t)

T

T

Xke

T

t

T,

where

the

Fourier

coefficient

Xk

denotes

the

amplitude

of

the

sinusoid

with

frequency

k/T.

The

original

trajectory

can

be

reconstructed

with

just

the

dominant

frequencies,

which

can

be

determined

from

the

power

spectrum

using

the

popular

periodogram

estimator.

The

periodogram

is

a

sequence

of

the

squared

magnitude

of

the

Fourier

coefficients,

Xk

k

which

indicates

the

signal

power

at

frequency

k/T

in

the

spectrum.

From

the

power

spectrum,

the

dominant

period

is

chosen

as

the

inverse

of

the

frequency

with

the

highest

power

spectrum,

as

follows.

Definition

(Dominant

Period)

The

dominant

period

(DP)

of

a

given

feature

f

is

Pf

T/

arg

max

k

Xk

Accordingly,

we

have

Definition

(Dominant

Power

Spectrum)

The

dominant

power

spectrum

(DPS)

of

a

given

feature

f

is

Sf

Xk

with

Xk

Xj

∀j

k.

Categorizing

Features

The

DPS

of

a

feature

trajectory

is

a

strong

indicator

of

its

activeness

at

the

specified

frequency;

the

higher

the

DPS,

the

more

likely

for

the

feature

to

be

bursty.

Combining

DPS

with

DP,

we

therefore

categorize

all

features

into

four

types:

We

normalize

yf

(t)

as

yf

(t)

yf

(t)/

T

yf

(i)

so

that

it

could

be

interpreted

as

a

probability.

HH:

high

Sf

aperiodic

or

long-term

periodic

(Pf

HL:

high

Sf

short-term

periodic

(Pf

LH:

low

Sf

aperiodic

or

long-term

periodic;

LL:

low

Sf

short-term

periodic.

The

boundary

between

long-term

and

short-term

periodic

is

set

to

However,

distinguishing

between

a

high

and

low

DPS

is

not

straightforward,

which

will

be

tackled

later.

Properties

of

Different

Feature

Sets

To

better

understand

the

properties

of

HH,

HL,

LH

and

LL,

we

select

four

features,

Christmas,

soccer,

DBS

and

your

as

illustrative

examples.

Since

the

boundary

between

high

and

low

power

spectrum

is

unclear,

these

chosen

examples

have

relative

wide

range

of

power

spectrum

values.

Figure

shows

the

DFIDF

trajectory

for

Christmas

with

a

distinct

burst

around

Christmas

day.

For

the

Reuters

dataset,

Christmas

is

classified

as

a

typical

aperiodic

event

with

Pf

and

Sf

as

shown

in

Figure

Clearly,

the

value

of

Sf

is

reasonable

for

a

well-known

bursty

event

like

Christmas.

(a)

Christmas(DFIDF:time)

(b)

Christmas(S:frequency)

Figure

Feature

Christmas

with

relative

high

Sf

and

long-term

Pf

The

DFIDF

trajectory

for

soccer

is

shown

in

Figure

from

which

we

can

observe

that

there

is

a

regular

burst

every

days,

which

is

again

verified

by

its

computed

value

of

Pf

as

shown

in

Figure

Using

the

domain

knowledge

that

soccer

games

have

more

matches

every

Saturday,

which

makes

it

a

typical

and

heavily

reported

periodic

event,

we

thus

consider

the

value

of

Sf

to

be

high.

(a)

soccer(DFIDF:time)

(b)

soccer(S:frequency)

Figure

Feature

soccer

with

relative

high

Sf

and

short-term

Pf

From

the

DFIDF

trajectory

for

DBS

in

Figure

we

can

immediately

deduce

DBS

to

be

an

infrequent

word

with

a

trivial

burst

on

corresponding

to

DBS

Land

Raﬄes

Holdings

plans.

This

is

confirmed

by

the

long

period

of

Pf

and

low

power

of

Sf

as

shown

in

Figure

Moreover,

since

this

aperiodic

event

is

only

reported

in

a

few

news

stories

over

a

very

short

time

of

few

days,

we

therefore

say

that

its

low

power

value

of

Sf

is

representative

of

unimportant

events.

The

most

confusing

example

is

shown

in

Figure

for

the

word

feature

your,

which

looks

very

similar

to

the

graph

for

soccer

in

Figure

At

first

glance,

we

may

be

tempted

to

group

both

your

and

soccer

into

the

same

category

of

HL

or

LL

since

both

distributions

look

similar

and

have

the

same

dominant

period

of

approximately

a

week.

However,

further

(a)

DBS(DFIDF:time)

(b)

DBS(S:frequency)

Figure

Feature

DBS

with

relative

low

Sf

and

long-term

Pf

analysis

indicates

that

the

periodicity

of

your

is

due

to

the

differences

in

document

counts

for

weekdays

(average

per

day)

and

(average

per

day).

One

would

have

expected

the

periodicity

of

a

stopword

like

your

to

be

a

day.

Moreover,

despite

our

DFIDF

normalization,

the

weekday/weekend

imbalance

still

prevailed;

stopwords

occur

times

more

frequently

on

weekends

than

on

weekdays.

Thus,

the

DPS

remains

the

only

distinguishing

factor

between

your

(Sf

and

soccer

(Sf

However,

it

is

very

dangerous

to

simply

conclude

that

a

power

value

of

S

corresponds

to

a

stopword

feature.

(a)

your(DFIDF:time)

(b)

your(S:frequency)

Figure

Feature

your

as

an

example

confusing

with

feature

soccer.

Before

introducing

our

solution

to

this

problem,

let"s

look

at

another

LL

example

as

shown

in

Figure

for

beenb,

which

is

actually

a

confirmed

typo.

We

therefore

classify

beenb

as

a

noisy

feature

that

does

not

contribute

to

any

event.

Clearly,

the

trajectory

of

your

is

very

different

from

beenb,

which

means

that

the

former

has

to

be

considered

separately.

(a)

beenb(DFIDF:time)

(b)

beenb(S:frequency)

Figure

Feature

beenb

with

relative

low

Sf

and

short-term

Pf

Stop

Words

(SW)

Feature

Set

Based

on

the

above

analysis,

we

realize

that

there

must

be

another

feature

set

between

HL

and

LL

that

corresponds

to

the

set

of

stopwords.

Features

from

this

set

has

moderate

DPS

and

low

but

known

dominant

period.

Since

it

is

hard

to

distinguish

this

feature

set

from

HL

and

LL

only

based

on

DPS,

we

introduce

another

factor

called

average

DFIDF

(DFIDF).

As

shown

in

Figure

features

like

your

usually

have

a

lower

DPS

than

a

HL

feature

like

soccer,

but

have

a

much

higher

DFIDF

than

another

LL

noisy

feature

such

as

beenb.

Since

such

properties

are

usually

characteristics

of

stopwords,

we

group

features

like

your

into

the

newly

defined

stopword

(SW)

feature

set.

Since

setting

the

DPS

and

DFIDF

thresholds

for

identifying

stopwords

is

more

of

an

art

than

science,

we

proposed

a

heuristic

HS

algorithm,

Algorithm

The

basic

idea

is

to

only

use

news

stories

from

weekdays

to

identify

stopwords.

The

weekends

here

also

include

public

holidays

falling

on

weekdays.

The

SW

set

is

initially

seeded

with

a

small

set

of

popular

stopwords

utilized

by

Google

search

engine.

Algorithm

Heuristic

Stopwords

detection

(HS)

Input:

Seed

SW

set,

weekday

trajectories

of

all

words

From

the

seed

set

SW,

compute

the

maximum

DPS

as

UDPS,

maximum

DFIDF

as

UDFIDF,

and

minimum

of

DFIDF

as

LDFIDF.

for

fi

F

do

Compute

DFT

for

fi.

if

Sfi

UDPS

and

DFIDFfi

[LDFIDF,

UDFIDF]

then

fi

SW

F

F

fi

end

if

end

for

Overview

of

Feature

Categorization

After

the

SW

set

is

generated,

all

stopwords

are

removed

from

F.

We

then

set

the

boundary

between

high

and

low

DPS

to

be

the

upper

bound

of

the

SW

set"s

DPS.

An

overview

of

all

five

feature

sets

is

shown

in

Figure

Figure

The

feature

sets

for

events.

IDENTIFYING

BURSTS

FOR

FEATURES

Since

only

features

from

HH,

HL

and

LH

are

meaningful

and

could

potentially

be

representative

to

some

events,

we

pruned

all

other

feature

classified

as

LL

or

SW.

In

this

section,

we

describe

how

bursts

can

be

identified

from

the

remaining

features.

Unlike

Kleinberg"s

burst

identification

algorithm

we

can

identify

both

significant

and

trivial

bursts

without

the

need

to

set

any

parameters.

Detecting

Aperiodic

Features"

Bursts

For

each

feature

in

HH

and

HL,

we

truncate

its

trajectory

by

keeping

only

the

bursty

period,

which

is

modeled

with

a

Gaussian

distribution.

For

example,

Figure

shows

the

word

feature

Iraq

with

a

burst

circa

being

modeled

as

a

Gaussian.

Its

bursty

period

is

defined

by

[μf

σf

μf

σf

as

shown

in

Figure

Detecting

Periodic

Features"

Bursts

Since

we

have

computed

the

DP

for

a

periodic

feature

f,

we

can

easily

model

its

periodic

feature

trajectory

yf

using

(a)

original

DFIDF:time

burst=

[μ-σ,

μ+σ]

(b)

identifying

burst

Figure

Modeling

Iraq"s

time

series

as

a

truncated

Gaussian

with

μ

and

σ

a

mixture

of

K

T/Pf

Gaussians:

f(yf

yf

(t)|θf

K

αk

2πσ2

k

e

k

(yf

where

the

parameter

set

θf

{αk,

μk,

σk}K

comprises:

αk

is

the

probability

of

assigning

yf

into

the

kth

Gaussian.

αk

∀k

K]

and

K

αk

μk/σk

is

mean/standard

deviation

of

the

kth

Gaussian.

The

well

known

Expectation

Maximization

(EM)

algorithm

is

used

to

compute

the

mixing

proportions

αk,

as

well

as

the

individual

Gaussian

density

parameters

μk

and

σK

Each

Gaussian

represents

one

periodic

event,

and

is

modeled

similarly

as

mentioned

in

Section

EVENTS

FROM

FEATURES

After

identifying

and

modeling

bursts

for

all

features,

the

next

task

is

to

paint

a

picture

of

the

event

with

a

potential

set

of

representative

features.

Feature

Correlation

If

two

features

fi

and

fj

are

representative

of

the

same

event,

they

must

satisfy

the

following

necessary

conditions:

fi

and

fj

are

identically

distributed:

yfi

yfj

fi

and

fj

have

a

high

document

overlap.

Measuring

Feature

Distribution

Similarity

We

measure

the

similarity

between

two

features

fi

and

fj

using

discrete

KL-divergence

defined

as

follows.

Definition

(feature

similarity)

KL(fi,

fj

is

given

by

max(KL(fi|fj

KL(fj

|fi)),

where

KL(fi|fj

T

f(yfi

(t)|θfi

)log

f(yfi

(t)|θfi

f(yfj

(t)|θfj

Since

KL-divergence

is

not

symmetric,

we

define

the

similarity

between

between

fi

and

fj

as

the

maximum

of

KL(fi|fj

and

KL(fj

|fi).

Further,

the

similarity

between

two

aperiodic

features

can

be

computed

using

a

closed

form

of

the

KL-divergence

The

same

discrete

KL-divergence

formula

of

Eq.

is

employed

to

compute

the

similarity

between

two

periodic

features,

Next,

we

define

the

overal

similarity

among

a

set

of

features

R

using

the

maximum

inter-feature

KL-Divergence

value

as

follows.

Definition

(set"s

similarity)KL(R)

max

∀fi,fj

∈R

KL(fi,

fj

Document

Overlap

Let

Mi

be

the

set

of

all

documents

containing

feature

fi.

Given

two

features

fi

and

fj

the

overlapping

document

set

containing

both

features

is

Mi

Mj

Intuitively,

the

higher

the

|Mi

Mj

the

more

likelty

that

fi

and

fj

will

be

highly

correlated.

We

define

the

degree

of

document

overlap

between

two

features

fi

and

fj

as

follows.

Definition

(Feature

DF

Overlap)

d(fi,

fj

|Mi∩Mj|

min(|Mi|,|Mj|)

Accordingly,

the

DF

Overlap

among

a

set

of

features

R

is

also

defined.

Definition

(Set

DF

Overlap)

d(R)

min

∀fi,fj

∈R

d(fi,

fj).

Unsupervised

Greedy

Event

Detection

We

use

features

from

HH

to

detect

important

aperiodic

events,

features

from

LH

to

detect

less-reported/unimportant

aperiodic

events,

and

features

from

HL

to

detect

periodic

events.

All

of

them

share

the

same

algorithm.

Given

bursty

feature

fi

HH,

the

goal

is

to

find

highly

correlated

features

from

HH.

The

set

of

features

similar

to

fi

can

then

collectively

describe

an

event.

Specifically,

we

need

to

find

a

subset

Ri

of

HH

that

minimizes

the

following

cost

function:

C(Ri)

KL(Ri)

d(Ri)

fj

∈Ri

Sfj

Ri

HH.

The

underlying

event

e

(associated

with

the

burst

of

fi)

can

be

represented

by

Ri

as

y(e)

fj

∈Ri

Sfj

fu∈Ri

Sfu

yfj

The

burst

analysis

for

event

e

is

exactly

the

same

as

the

feature

trajectory.

The

cost

in

Eq.

can

be

minimized

using

our

unsupervised

greedy

UG

event

detection

algorithm,

which

is

described

in

Algorithm

The

UG

algorithm

allows

a

feature

Algorithm

Unsupervised

Greedy

event

detection

(UG).

Input:

HH,

document

index

for

each

feature.

Sort

and

select

features

in

descending

DPS

order:

Sf|HH|

k

for

fi

HH

do

k

k

Init:

Ri

fi,

C(Ri)

and

HH

HH

fi.

while

HH

not

empty

do

m

arg

min

m

C(Ri

fm).

if

C(Ri

fm)

C(Ri)

then

Ri

fm

and

HH

HH

fm.

else

break

while.

end

if

end

while

Output

ek

as

Eq.

end

for

to

be

contained

in

multiple

events

so

that

we

can

detect

several

events

happening

at

the

same

time.

Furthermore,

trivial

events

only

containing

year/month

features

(i.e.,

an

event

only

containing

feature

Aug

could

be

identified

over

a

news

stream)

could

be

removed,

although

such

events

will

have

inherent

high

cost

and

should

already

be

ranked

very

low.

Note

that

our

UG

algorithm

only

requires

one

data-dependant

parameter,

the

boundary

between

high

and

low

power

spectrum,

to

be

set

once,

and

this

parameter

can

be

easily

estimated

using

the

HS

algorithm

(Algorithm

EXPERIMENTS

In

this

section,

we

study

the

performances

of

our

feature

categorizing

method

and

event

detection

algorithm.

We

first

introduce

the

dataset

and

experimental

setup,

then

we

subjectively

evaluate

the

categorization

of

features

for

HH,

HL,

LH,

LL

and

SW.

Finally,

we

study

the

(a)periodic

event

detection

problem

with

Algorithm

Dataset

and

Experimental

Setup

The

Reuters

Corpus

contains

English

news

stories

from

to

at

a

day

resolution.

Version

of

the

open

source

Lucene

software

was

used

to

tokenize

the

news

text

content

and

generate

the

document-word

vector.

In

order

to

preserve

the

time-sensitive

past/present/future

tenses

of

verbs

and

the

differences

between

lower

case

nouns

and

upper

case

named

entities,

no

stemming

was

done.

Since

dynamic

stopword

removal

is

one

of

the

functionalities

of

our

method,

no

stopword

was

removed.

We

did

remove

nonEnglish

characters,

however,

after

which

the

number

of

word

features

amounts

to

All

experiments

were

implemented

in

Java

and

conducted

on

a

GHz

Pentium

PC

running

Windows

Server

with

GB

of

memory.

Categorizing

Features

We

downloaded

well-known

stopwords

utilized

by

the

Google

search

engine

as

our

seed

training

features,

which

includes

a,

about,

an,

are,

as,

at,

be,

by,

de,

for,

from,

how,

in,

is,

it,

of,

on,

or,

that,

the,

this,

to,

was,

what,

when,

where,

who,

will,

with,

la,

com,

und,

en

and

We

excluded

the

last

five

stopwords

as

they

are

uncommon

in

news

stories.

By

only

analyzing

news

stories

over

weekdays,

we

computed

the

upper

bound

of

the

power

spectrum

for

stopwords

at

and

corresponding

DFIDF

ranges

from

to

Any

feature

f

satisfying

Sf

and

DFIDFf

over

weekdays

will

be

considered

a

stopword.

In

this

manner,

stopwords

were

found

and

removed

as

visualized

in

Figure

Some

detected

stopwords

are

A

(P

S

DFIDF

At

(P

S

DFIDF

GMT

(P

S

DFIDF

and

much

(P

S

DFIDF

After

the

removal

of

these

stopwords,

the

distribution

of

weekday

and

weekend

news

are

more

or

less

matched,

and

in

the

ensuing

experiments,

we

shall

make

use

of

the

full

corpus

(weekdays

and

weekends).

The

upper

bound

power

spectrum

value

of

for

stopwords

training

was

selected

as

the

boundary

between

the

high

power

and

low

power

spectrum.

The

boundary

between

high

and

low

periodicity

was

set

to

All

word

features

were

categorized

into

feature

sets:

HH

features),

HL

features),

LH

features),

and

LL

features)

as

shown

in

Figure

In

Figure

each

gray

level

denotes

the

relative

density

of

features

in

a

square

region,

measured

by

Dk),

where

Dk

is

the

number

of

features

within

the

k-th

square

region.

From

the

figure,

we

can

make

the

S(f)

P(f)

LH

HH

LL

HL

Figure

Distribution

of

SW

(stopwords)

in

the

HH,

HL,

LH,

and

LL

regions.

S(f)

P(f)

LH

HH

LL

HL

Figure

Distribution

of

categorized

features

over

the

four

quadrants

(shading

in

log

scale).

following

observations:

Most

features

have

low

S

and

are

easily

distinguishable

from

those

features

having

a

much

higher

S,

which

allows

us

to

detect

important

(a)periodic

events

from

trivial

events

by

selecting

features

with

high

S.

Features

in

the

HH

and

LH

quadrants

are

aperiodic,

which

are

nicely

separated

(big

horizontal

gap)

from

the

periodic

features.

This

allows

reliably

detecting

aperiodic

events

and

periodic

events

independently.

The

(vertical)

boundary

between

high

and

low

power

spectrum

is

not

as

clearcut

and

the

exact

value

will

be

application

specific.

By

checking

the

scatter

distribution

of

features

from

SW

on

HH,

HL,

LH,

and

LL

as

shown

in

Figure

we

found

that

of

the

detected

stopwords

originated

from

LL.

The

LL

classification

and

high

DFIDF

scores

of

stopwords

agree

with

the

generally

accepted

notion

that

stopwords

are

equally

frequent

over

all

time.

Therefore,

setting

the

boundary

between

high

and

low

power

spectrum

using

the

upper

bound

Sf

of

SW

is

a

reasonable

heuristic.

Detecting

Aperiodic

Events

We

shall

evaluate

our

two

hypotheses,

aperiodic

events

can

be

defined

by

a

set

of

HH

features,

and

reported

aperiodic

events

can

be

defined

by

a

set

of

LH

features.

Since

no

benchmark

news

streams

exist

for

event

detection

(TDT

datasets

are

not

proper

streams),

we

evaluate

the

quality

of

the

automatically

detected

events

by

comparing

them

to

manually-confirmed

events

by

searching

through

the

corpus.

Among

the

HH

features,

we

detected

important

aperiodic

events

as

shown

in

Table

Note

that

the

entire

identification

took

less

than

second,

after

removing

events

containing

only

the

month

feature.

Among

the

events,

other

than

the

overlaps

between

and

(both

describes

the

same

hostage

event),

and

(both

about

company

reports),

the

identified

events

are

extremely

accurate

and

correspond

very

well

to

the

major

events

of

the

period.

For

example,

the

defeat

of

Bob

Dole,

election

of

Tony

Blair,

Missile

attack

on

Iraq,

etc.

Recall

that

selecting

the

features

for

one

event

should

minimize

the

cost

in

Eq.

such

that

the

number

of

features

span

different

events,

and

not

all

features

relevant

to

an

event

will

be

selected,

e.g.,

the

feature

Clinton

is

representative

to

but

since

Clinton

relates

to

many

other

events,

its

time

domain

signal

is

far

different

from

those

of

other

representative

features

like

Dole

and

Bob.

The

number

of

documents

of

a

detected

event

is

roughly

estimated

by

the

number

of

indexed

documents

containing

the

representative

features.

We

can

see

that

all

important

aperiodic

events

are

popularly

reported

events.

After

minutes

of

computation

time,

we

detected

less

reported

aperiodic

events

from

LH

features.

Table

lists

the

top

detected

aperiodic

events

with

respect

to

the

cost.

We

found

that

these

events

are

actually

very

trivial

events

with

only

a

few

news

reports,

and

are

usually

subsumed

by

some

larger

topics.

For

example,

is

one

of

the

rescue

events

in

an

airplane

hijack

topic.

One

advantage

of

our

UG

Algorithm

for

discovering

less-reported

aperiodic

events

is

that

we

are

able

to

precisely

detect

the

true

event

period.

Detecting

Periodic

Events

Among

the

HL

features,

important

periodic

events

were

detected

within

minutes

of

computing

time.

Table

lists

the

top

detected

periodic

events

with

respect

to

the

cost

All

of

the

detected

periodic

events

are

indeed

valid,

and

correspond

to

real

life

periodic

events.

The

GMM

model

is

able

to

detect

and

estimate

the

bursty

period

nicely

although

it

cannot

distinguish

the

slight

difference

between

every

Monday-Friday

and

all

weekdays

as

shown

in

We

also

notice

that

is

actually

a

subset

of

(soccer

game),

which

is

acceptable

since

the

Sheffield

league

results

are

announced

independently

every

weekend.

CONCLUSIONS

This

paper

took

a

whole

new

perspective

of

analyzing

feature

trajectories

as

time

domain

signals.

By

considering

the

word

document

frequencies

in

both

time

and

frequency

domains,

we

were

able

to

derive

many

new

characteristics

about

news

streams

that

were

previously

unknown,

e.g.,

the

different

distributions

of

stopwords

during

weekdays

and

weekends.

For

the

first

time

in

the

area

of

TDT,

we

applied

a

systematic

approach

to

automatically

detect

important

and

less-reported,

periodic

and

aperiodic

events.

The

key

idea

of

our

work

lies

in

the

observations

that

(a)periodic

events

have

(a)periodic

representative

features

and

(un)important

events

have

(in)active

representative

features,

differentiated

by

their

power

spectrums

and

time

periods.

To

address

the

real

event

detection

problem,

a

simple

and

effective

mixture

density-based

approach

was

used

to

identify

feature

bursts

and

their

associated

bursty

periods.

We

also

designed

an

unsupervised

greedy

algorithm

to

detect

both

aperiodic

and

periodic

events,

which

was

successful

in

detecting

real

events

as

shown

in

the

evaluation

on

a

real

news

stream.

Although

we

have

not

made

any

benchmark

comparison

against

another

approach,

simply

because

there

is

no

previous

work

in

the

addressed

problem.

Future

work

includes

evaluating

the

recall

of

detected

events

for

a

labeled

news

stream,

and

comparing

our

model

against

the

closest

equivalent

methods,

which

currently

are

limited

to

the

methods

of

Kleinberg

(which

can

only

detect

certain

type

of

bursty

events

depending

on

parameter

settings),

Fung

et

al.

and

Swan

and

Allan

Nevertheless,

we

believe

our

simple

and

effective

method

will

be

useful

for

all

TDT

practitioners,

and

will

be

especially

useful

for

the

initial

exploratory

analysis

of

news

streams.

REFERENCES

Apache

lucene-core

Google

news

alerts,

Reuters

corpus,

J.

Allan.

Topic

Detection

and

Tracking.

Event-based

Information

Organization.

Kluwer

Academic

Publishers,

J.

Allan,

V.

Lavrenko,

and

H.

Jin.

First

story

detection

in

tdt

is

hard.

In

CIKM,

pages

J.

Allan,

C.

Wade,

and

A.

Bolivar.

Retrieval

and

novelty

detection

at

the

sentence

level.

In

SIGIR,

pages

T.

Brants,

F.

Chen,

and

A.

Farahat.

A

system

for

new

event

detection.

In

SIGIR,

pages

A.

P.

Dempster,

N.

M.

Laird,

and

D.

B.

Rubin.

Maximum

likelihood

from

incomplete

data

via

the

EM

algorithm.

Journal

of

the

Royal

Statistical

Society,

G.

P.

C.

Fung,

J.

X.

Yu,

P.

S.

Yu,

and

H.

Lu.

Parameter

free

bursty

events

detection

in

text

streams.

In

VLDB,

pages

Q.

He,

K.

Chang,

and

E.-P.

Lim.

A

model

for

anticipatory

event

detection.

In

ER,

pages

Q.

He,

K.

Chang,

E.-P.

Lim,

and

J.

Zhang.

Bursty

feature

reprensentation

for

clustering

text

streams.

In

SDM,

accepted,

J.

Kleinberg.

Bursty

and

hierarchical

structure

in

streams.

In

SIGKDD,

pages

R.

Kumar,

J.

Novak,

P.

Raghavan,

and

A.

Tomkins.

On

the

bursty

evolution

of

blogspace.

In

WWW,

pages

G.

Kumaran

and

J.

Allan.

Text

classification

and

named

entities

for

new

event

detection.

In

SIGIR,

pages

Q.

Mei

and

C.

Zhai.

Discovering

evolutionary

theme

patterns

from

text:

an

exploration

of

temporal

text

mining.

In

SIGKDD,

pages

W.

D.

Penny.

Kullback-liebler

divergences

of

normal,

gamma,

dirichlet

and

wishart

densities.

Technical

report,

N.

Stokes

and

J.

Carthy.

Combining

semantic

and

syntactic

document

classifiers

to

improve

first

story

detection.

In

SIGIR,

pages

R.

Swan

and

J.

Allan.

Automatic

generation

of

overview

timelines.

In

SIGIR,

pages

M.

Vlachos,

C.

Meek,

Z.

Vagena,

and

D.

Gunopulos.

Identifying

similarities,

periodicities

and

bursts

for

online

search

queries.

In

SIGMOD,

pages

Y.

Yang,

T.

Pierce,

and

J.

Carbonell.

A

study

of

retrospective

and

on-line

event

detection.

In

SIGIR,

pages

Y.

Yang,

J.

Zhang,

J.

Carbonell,

and

C.

Jin.

Topic-conditioned

novelty

detection.

In

SIGKDD,

pages

Table

All

important

aperiodic

events

top

less-reported

aperiodic

events

and

top

important

periodic

events

Detected

Event

and

Bursty

Period

Doc

True

Event

Albanian"s

president

Sali

Berisha

lost

in

an

early

election

and

resigned,

Zaire"s

president

Mobutu

Sese

coordinated

the

native

rebellion

and

failed

on

Peru

rebels

(Tupac

Amaru

revolutionary

Movement)

led

a

hostage

siege

in

Lima

in

early

e4(Movement,Tupac,Amaru,Lima,hostage,hostages)

The

same

as

Zaire

was

renamed

the

Democratic

Republic

of

Congo

on

Following

the

early

General

Elections

circa

Lionel

Jospin

was

appointed

Prime

Minister

on

U.S.

fired

missile

at

Iraq

on

and

Iraqi

troop

fought

with

Kurdish

faction

circa

Tony

Blair

became

the

Primary

Minister

of

the

United

Kingdom

on

Slalom

Game

of

Alpine

Skiing

in

Tokyo

released

company

interim

results

for

the

past

several

months

in

Dole

Bob

lost

the

US

presidential

election.

Cambodia"s

Prime

Minister

Hun

Sen

launched

a

bloody

military

coup

in

Hebron

was

divided

into

two

sectors

in

early

Easter

feasts

circa

(for

western

and

Orthodox).

Tokyo

released

all

group

results

in

Christmas

feast

in

late

e18(Kolaceva,winter,Together,promenades,Zajedno,

Slobodan,Belgrade,Serbian,Serbia,Draskovic,municipal,

Kragujevac)

University

students

organized

a

vigil

on

Kolaceva

street

against

government

on

e19(Tutsi,Luvengi,Burundi,Uvira,fuel,Banyamulenge,

Burundian,Kivu,Kiliba,Runingo,Kagunga,Bwegera)

Fresh

fighting

erupted

around

Uvira

between

Zaire

armed

forces

and

Banyamulengs

Tutsi

rebels

on

e20(Malantacchi,Korea,Guy,Rider,Unions,labour,

Trade,unions,Confederation,rammed,Geneva,stoppages,

Virgin,hire,Myongdong,Metalworkers)

Marcello

Malantacchi

secretary

general

of

the

International

Metalworkers

Federation

and

Guy

Rider

who

heads

the

Geneva

office

of

the

International

Confederation

of

Free

Trade

Unions

attacked

the

new

labour

law

of

South

Korea

on

The

list

of

the

unit

of

Singapore

DBS

Land

Raﬄes

Holdings

plans

on

e22(preserver,fuel,Galawa,Huddle,Leul,Beausse)

Rescued

a

woman

and

her

baby

during

a

hijacked

Ethiopian

plane

that

ran

out

of

fuel

and

crashed

into

the

sea

near

Le

Galawa

beach

on

MOODY,AMT,FIRST,ISS,TYPE,PAY,BORROWER)

Monday-Friday/week

Announce

bond

price

on

all

weekdays.

e24(Unaudited,Ended,Months,Weighted,Provision,Cost,

Selling,Revenues,Loss,Income,except,Shrs,Revs)

every

season

Net

income-loss

reports

released

by

companies

in

every

season.

Monday-Friday/week

Stock

reports

from

Wall

Street

on

all

weekdays.

e26(Sheffield,league,scoring,goals,striker,games)

every

Friday,

Saturday

and

Sunday

Match

results

of

Sheffield

soccer

league

were

published

on

Friday,

Saturday

and

Sunday

times

than

other

days.

e27(soccer,matches,Results,season,game,Cup,match,

victory,beat,played,play,division)

every

Friday,

Saturday

and

Sunday

Soccer

games

held

on

Friday,

Saturday

and

Sunday

times

than

other

days.

O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O B O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

event detection
word trajectory
aperiodic event
periodic event
word signal
spectral analysis
topic detection
news stream
time series
feature categorization
dft
gaussian