Discrimination

of

biofilm

samples

using

pattern

recognition

techniques

Biofilms

are

complex

aggregates

formed

by

microorganisms

such

as

bacteria

fungi

and

algae

which

grow

at

the

interfaces

between

water

and

natural

or

artificial

materials

They

are

actively

involved

in

processes

of

sorption

and

desorption

of

metal

ions

in

water

and

reflect

the

environmental

conditions

in

the

recent

past

Therefore

biofilms

can

be

used

as

bioindicators

of

water

quality

The

goal

of

this

study

was

to

determine

whether

the

biofilms

developed

in

different

aquatic

systems

could

be

successfully

discriminated

using

data

on

their

elemental

compositions

Biofilms

were

grown

on

natural

or

polycarbonate

materials

in

flowing

water

standing

water

and

seawater

bodies

Using

an

unsupervised

technique

such

as

principal

component

analysis

-LRB-

PCA

-RRB-

and

several

supervised

methods

like

classification

and

regression

trees

-LRB-

CART

-RRB-

discriminant

partial

least

squares

regression

-LRB-

DPLS

-RRB-

and

uninformative

variable

elimination

DPLS

-LRB-

UVE-DPLS

-RRB-

we

could

confirm

the

uniqueness

of

sea

biofilms

and

make

a

distinction

between

flowing

water

and

standing

water

biofilms

The

CART

DPLS

and

UVE-DPLS

discriminant

models

were

validated

with

an

independent

test

set

selected

either

by

the

Kennard

and

Stone

method

or

the

duplex

algorithm

The

best

model

was

obtained

from

CART

with

correct

classification

rate

for

the

test

set

designed

by

the

Kennard

and

Stone

algorithm

With

CART

one

variable

describing

the

Mg

content

in

the

biofilm

water

phase

was

found

to

be

important

for

the

discrimination

of

flowing

water

and

standing

water

biofilms

Introduction

Water

quality

assessment

requires

monitoring

of

carefully

selected

parameters

Usually

water

and

sediment

samples

are

collected

in

the

hope

that

their

chemical

compositions

will

help

to

understand

the

nature

of

a

given

local

or

global

environmental

event

The

chemical

analysis

of

water

indicates

the

water

quality

at

the

time

of

sampling

while

analysis

of

sediments

provides

information

about

long-term

environmental

changes

in

aquatic

systems

Biofilms

reflect

the

environmental

conditions

in

the

recent

past

-LSB-

-RSB-

They

are

complex

communities

composed

of

microorganisms

which

grow

at

almost

any

water

substrate

interface

Biofilms

can

accumulate

metal

ions

and

play

an

important

role

in

the

processes

of

sorption

and

desorption

of

chemical

elements

-LSB-

-RSB-

therefore

they

can

be

very

useful

bioindicators

of

water

quality

The

aim

of

this

work

is

to

investigate

whether

the

biofilms

grown

in

different

aquatic

systems

can

be

discriminated

on

the

basis

of

their

chemical

compositions

If

the

discrimination

is

possible

the

next

interesting

question

will

be

which

measured

parameters

are

responsible

for

it

For

the

purpose

of

the

study

biofilm

samples

originating

from

different

water

bodies

such

as

flowing

water

standing

water

or

seawater

were

collected

The

elemental

concentrations

of

biofilms

and

the

water

phase

extracted

at

the

sampling

locations

were

then

analysed

using

inductively

coupled

plasma

optical

emission

spectrometry

-LRB-

ICP-OES

-RRB-

and

inductively

coupled

plasma

mass

spectrometry

-LRB-

ICP-MS

-RRB-

respectively

To

obtain

useful

information

on

the

data

collected

several

pattern

recognition

techniques

are

going

to

be

applied

These

are

principal

component

analysis

-LRB-

PCA

-RRB-

classification

and

regression

trees

-LRB-

CART

-RRB-

discriminant

partial

least

squares

regression

-LRB-

DPLS

-RRB-

and

uninformative

variable

elimination

DPLS

-LRB-

UVE-DPLS

-RRB-

PCA

is

an

unsupervised

pattern

recognition

method

that

aims

to

compress

and

to

visualise

the

data

structure

which

allows

for

an

easy

interpretation

of

relationships

between

samples

and

the

measured

parameters

The

supervised

pattern

recognition

methods

like

CART

DPLS

and

UVE-DPLS

aim

to

develop

classification

or

decision

rule

-LRB-

s

-RRB-

using

a

set

of

samples

with

known

group

origin

Then

the

classification

rule

-LRB-

s

-RRB-

determines

the

belongingness

of

unknown

samples

to

the

available

groups

-LSB-

-RSB-

The

application

of

such

approaches

in

our

study

will

provide

a

better

understanding

of

the

accumulation

behaviour

of

different

biofilms

Experimental

Description

of

the

sampling

procedure

The

biofilm

samples

investigated

can

be

divided

into

two

groups

a

group

of

systematically

sampled

biofilms

and

a

group

of

uniquely

sampled

biofilms

The

samples

of

the

group

of

systematically

sampled

biofilms

can

be

further

split

into

two

subgroups

namely

biofilms

grown

on

polycarbonate

plates

and

biofilms

developed

on

natural

substrates

A

detailed

description

of

the

samples

collected

is

presented

in

Table

Table

of

the

biofilm

and

water

samples

collectedGroup

of

biofilmsSubgroup

of

biofilmsCharacter

of

the

water

phaseNumber

of

samplesSystematically

sampled

biofilmsBiofilms

grown

on

polycarbonate

platesf

the

Saale

the

Teich

grown

on

natural

substratesf

the

Leutra

sampled

biofilmsBiofilms

grown

on

natural

substratesf

Celle

-LRB-

a

b

-RRB-

Lauscha

-LRB-

a

b

c

-RRB-

Oberpöllnitz

Falken

London

Munich

New

York

Geithain

Steinach

Chemnitz

New

Hampshire

Bossow

Metebach

Erfurt

Travemünde

-LRB-

a

b

-RRB-

Punta

Skala

Nin

Majorca

Damp

b

and

c

denote

different

sampling

locations.f

a

body

of

flowing

water

s

a

body

of

standing

water

m

a

body

of

seawater

The

biofilm

samples

collected

in

the

Saale

river

in

a

pond

and

in

the

Leutra

river

were

systematically

sampled

i.e.

the

biofilm

and

water

samples

were

gathered

within

a

definite

period

of

time

The

Saale

river

was

chosen

as

a

body

of

flowing

water

The

river

flows

through

highly

populated

regions

which

are

heavily

industrialised

and

are

subjects

of

typical

geogenic

and

anthropogenic

pollution

-LSB-

-RSB-

The

Saale

water

and

biofilm

samples

were

collected

within

a

period

-LRB-

from

September

till

October

-RRB-

The

sampling

point

was

situated

in

the

village

of

Kunitz

located

downstream

of

Jena

-LRB-

Thuringia

Germany

-RRB-

This

place

was

preferred

because

it

reflects

a

characteristic

pollution

of

the

nearby

town

The

Saale

river

is

there

about

m

deep

and

Kunitz

is

remote

from

civilisation

These

conditions

facilitated

the

sampling

campaign

A

small

pond

of

depth

was

selected

as

a

typical

example

of

a

standing

water

body

It

was

located

in

the

city

of

Jena

The

sampling

campaign

duration

was

the

same

as

for

the

sampling

campaign

in

the

Saale

river

At

these

two

locations

the

biofilms

were

artificially

grown

on

polycarbonate

plates

-LRB-

cm

cm

-RRB-

exposed

vertically

to

the

water

-LRB-

in

the

Saale

river

in

a

streaming

direction

-RRB-

The

plates

were

fixed

into

polypropylene

boxes

approximately

cm

under

the

water

surface

and

m

away

from

the

riverbank

After

a

definite

time

of

exposure

the

biofilm

samples

were

immediately

transferred

into

plastic

boxes

filled

with

the

river

or

pond

water

and

transported

to

the

laboratory

The

plates

were

then

washed

with

bidistilled

water

and

the

biofilm

samples

were

scraped

off

the

whole

surface

of

the

polycarbonate

plates

using

a

Teflon

spatula

The

river

and

pond

water

samples

were

collected

every

weeks

The

Leutra

river

located

in

the

city

of

Jena

was

chosen

as

the

second

example

of

a

flowing

water

body

The

stony

bed

of

the

river

its

small

depth

and

good

accessibility

facilitated

the

sampling

campaign

The

biofilm

samples

from

the

Leutra

river

were

scraped

off

the

riverbed

stones

using

a

plastic

spatula

They

were

placed

into

polyethylene

bottles

and

transported

to

the

laboratory

The

sampling

campaign

at

the

Leutra

river

was

held

in

autumn

and

in

spring

Additionally

water

samples

were

collected

The

sampling

procedure

for

water

and

uniquely

sampled

biofilms

was

the

same

as

that

carried

out

for

the

Leutra

river

The

locations

of

the

sampling

sites

were

selected

according

to

the

availability

of

a

suitable

sampling

device

The

samples

collected

were

also

placed

into

polyethylene

bottles

and

transported

to

the

laboratory

Analytical

procedure

The

biofilm

samples

collected

were

air-dried

at

°C

Then

the

samples

containing

mg

biofilm

powder

were

dissolved

in

ml

of

perchloric

acid

and

were

heated

for

h

at

°C

The

remaining

dry

matter

of

each

sample

was

further

dissolved

in

water

so

that

the

resulting

solution

was

up

to

ml

A

Fisons

Instruments

-LRB-

Beverly

MA

USA

-RRB-

Maxim

inductively

coupled

plasma

optical

emission

spectrometer

was

used

to

analyse

Al

Ca

Fe

K

Mg

Mn

and

Sr

while

Cd

Co

Cr

Cu

Ni

P

Se

and

Zn

were

determined

with

a

PerkinElmer

-LRB-

Wellesley

MA

USA

-RRB-

Elan

inductively

coupled

plasma

mass

spectrometer

An

external

aqueous

calibration

was

adopted

for

the

analysis

by

ICP-OES

while

a

standard

addition

procedure

was

used

for

the

element

analysis

by

ICP-MS

All

contents

correspond

to

the

sample

dry

weight

The

trueness

of

the

measurements

was

tested

by

analysing

a

certified

reference

algae

material

The

element

contents

were

certified

for

an

aqua

regia

digestion

Additionally

the

element

contents

were

determined

after

microwave

digestion

with

nitric

acid

No

differences

between

these

two

digestion

methods

were

obtained

All

the

measurements

were

done

in

triplicate

and

the

relative

standard

deviation

of

the

technique

was

for

all

the

biofilms

indicating

good

repeatability

of

the

measurements

Theory

Classification

and

regression

trees

The

CART

method

was

proposed

by

Breiman

et

al.

-LSB-

-RSB-

for

data

modelling

and

classification

Depending

on

the

type

of

the

response

variable

y

-LRB-

categorical

or

continuous

-RRB-

either

classification

or

regression

trees

are

built

In

the

present

study

we

will

focus

on

constructing

classification

trees

only

The

goal

of

CART

is

to

form

a

set

of

mutually

exclusive

regions

in

the

data

space

containing

as

homogeneous

groups

of

objects

as

possible

This

is

achieved

by

finding

optimal

splits

of

some

suitable

explanatory

variables

at

a

given

threshold

value

such

that

a

defined

impurity

function

is

minimised

The

impurity

function

measures

the

homogeneity

of

each

node

obtained

from

the

split

It

takes

the

lowest

value

for

pure

nodes

-LSB-

-RSB-

The

nodes

are

split

while

a

specified

number

of

objects

are

not

present

in

the

child

nodes

or

the

nodes

are

not

pure

A

node

which

can

not

be

split

any

further

is

called

a

terminal

node

One

of

the

most

popular

impurity

functions

is

entropy

-LSB-

-RSB-

and

it

is

the

function

used

in

our

study

Owing

to

a

binary

data

splitting

the

results

of

CART

can

easily

be

visualised

as

a

binary

tree

which

consists

of

a

number

of

nodes

symbolising

subgroups

of

data

objects

In

order

to

ensure

good

prediction

properties

of

the

constructed

tree

the

number

of

the

tree

nodes

should

be

optimal

Selection

of

the

optimal

number

of

nodes

relies

upon

a

deletion

of

some

nodes

from

the

tree

which

is

done

by

means

of

the

so-called

cost-complexity

pruning

-LSB-

-RSB-

Discriminant

partial

least

squares

The

DPLS

approach

aims

to

relate

a

set

of

n

explanatory

variables

-LRB-

predictors

-RRB-

X

-LRB-

m

n

-RRB-

to

a

dependent

variable

y

The

dependent

variable

y

is

either

a

discrete

variable

representing

the

belongingness

of

m

objects

to

two

defined

groups

denoted

by

and

or

a

binary

variable

The

popularity

of

the

DPLS

method

in

chemometrics

is

due

to

its

attractive

properties

DPLS

can

successfully

deal

with

multicollinearity

in

the

data

by

constructing

a

few

-LRB-

f

-RRB-

latent

factors

T

-LRB-

m

f

-RRB-

which

maximise

the

covariance

between

X

and

y

-LSB-

-RSB-

In

order

to

obtain

DPLS

models

with

good

prediction

abilities

an

optimal

number

of

factors

should

be

chosen

The

optimal

number

of

factors

is

usually

found

with

the

help

of

a

cross-validation

procedure

-LSB-

-RSB-

The

model

with

the

smallest

root

mean

square

error

of

cross-validation

-LRB-

RMSCV

-RRB-

is

to

be

selected

The

goodness

of

model

fit

is

indicated

by

a

root

mean

square

-LRB-

RMS

-RRB-

error

whereas

the

success

of

the

prediction

is

expressed

by

a

root

mean

square

error

of

the

test

set

Moreover

the

performance

of

DPLS

depends

on

the

set

of

samples

used

for

its

construction

The

model

set

has

to

cover

all

possible

sources

of

data

variance

Furthermore

DPLS

is

sensitive

to

the

number

of

objects

used

to

build

the

model

Its

performance

is

optimal

when

the

model

set

contains

two

groups

with

the

same

number

of

objects

-LSB-

-RSB-

The

predictive

ability

of

the

model

built

also

depends

on

the

quality

of

the

variables

measured

Uninformative

variable

elimination

discriminant

partial

least

squares

Usually

the

samples

collected

are

characterised

by

a

large

number

of

variables

in

order

to

ensure

a

detailed

description

of

the

event

studied

However

some

of

the

experimental

variables

may

be

irrelevant

for

the

particular

discriminant

problem

Such

uninformative

variables

which

have

a

high

variance

but

small

covariance

with

y

lead

to

a

DPLS

model

with

unsatisfactory

predictive

ability

Therefore

finding

an

optimal

set

of

variables

by

discarding

the

uninformative

variables

from

the

data

can

substantially

improve

the

DPLS

model

by

a

decrease

of

the

prediction

error

for

test

samples

or/and

a

decrease

of

model

complexity

The

variable

selection

method

used

in

our

study

is

UVE-DPLS

-LSB-

-RSB-

With

UVE-DPLS

variables

with

unstable

regression

coefficients

are

removed

In

order

to

estimate

the

stability

of

the

regression

coefficients

a

matrix

N

-LRB-

m

p

-RRB-

containing

at

least

p

random

variables

is

augmented

with

the

matrix

of

experimental

variables

X

-LRB-

m

n

-RRB-

which

results

in

a

matrix

Z

of

dimension

m

n

p.

To

keep

the

influence

of

the

variables

added

negligible

their

elements

are

generated

from

the

normal

distribution

and

are

multiplied

by

a

small

constant

with

magnitude

The

matrix

of

regression

coefficients

is

constructed

by

the

use

of

a

leave-one-out

cross-validation

procedure

i.e.

m

PLS

models

are

built

and

each

one

by

using

objects

The

stability

of

a

variable

is

determined

by

the

ratio

of

the

mean

of

m

regression

coefficients

and

their

standard

deviation

The

variables

with

absolute

stabilities

of

regression

coefficients

below

a

given

cutoff

value

are

uninformative

and

are

deleted

from

the

data

The

cutoff

value

is

defined

as

the

largest

absolute

value

of

all

stability

values

for

the

random

variables

added

The

goodness

of

a

discrimination

model

is

characterised

by

the

percentage

of

correct

classification

or

the

so-called

correct

classification

rate

It

is

commonly

agreed

that

the

higher

the

correct

classification

rate

the

better

the

model

Additionally

one

should

consider

sensitivity

and

selectivity

of

the

model

For

a

two-class

problem

for

instance

sensitivity

is

defined

as

the

percentage

of

correctly

classified

samples

of

class

A

while

selectivity

is

the

percentage

of

correctly

classified

samples

of

class

B.

Results

and

discussion

All

the

data

collected

were

organised

in

a

matrix

X

of

dimension

All

biofilm

samples

-LRB-

Table

-RRB-

were

characterised

by

the

contents

of

chemical

elements

analysed

in

the

biofilms

and

in

the

water

phases

extracted

at

the

sampling

locations

Three

groups

of

samples

were

distinguished

depending

on

the

type

of

water

body

namely

flowing

water

standing

water

and

seawater

Firstly

PCA

was

used

for

an

overall

exploration

of

the

data

structure

PCA

is

an

unsupervised

approach

and

is

frequently

employed

for

data

compression

and

visualisation

-LSB-

-RSB-

With

PCA

the

original

data

matrix

X

-LRB-

m

n

-RRB-

is

decomposed

into

two

matrices

a

scores

matrix

T

-LRB-

m

n

-RRB-

the

columns

of

which

contain

principal

components

-LRB-

PCs

-RRB-

and

a

loadings

matrix

P

-LRB-

n

n

-RRB-

PCs

are

found

as

linear

combinations

of

explanatory

variables

by

maximising

the

variance

of

projected

data

The

loadings

matrix

P

describes

the

contributions

of

each

variable

to

the

constructed

PCs

Prior

to

the

PCA

analysis

the

explanatory

variables

were

autoscaled

because

they

had

been

measured

in

different

units

Autoscaling

is

performed

by

subtracting

the

column

mean

from

each

data

element

and

dividing

it

by

the

corresponding

standard

deviation

It

gives

variables

the

same

importance

in

the

PCA

analysis

The

results

of

PCA

for

autoscaled

data

are

presented

in

Fig.

Fig.

component

analysis

of

the

data

set

containing

the

uniquely

sampled

biofilms

and

the

systematically

sampled

biofilms

a

scree

plot

of

the

cumulative

percentage

of

data

variance

explained

by

the

consecutive

principal

components

-LRB-

PC

-RRB-

b

projection

of

biofilms

on

the

plane

defined

by

PC

and

PC

c

projection

of

biofilms

on

the

plane

defined

by

PC

and

PC

d

projection

of

variables

on

the

plane

defined

by

PC

and

PC

and

e

projection

of

variables

on

the

plane

defined

by

PC

and

PC

The

first

three

PCs

explain

about

of

the

total

data

variance

-LRB-

Fig.

-RRB-

Figure

indicates

that

the

compression

is

not

very

effective

because

the

data

variance

is

distributed

over

all

PCs

However

some

general

trends

in

the

data

structure

can

be

revealed

All

the

seawater

samples

are

differentiated

from

the

standing

water

and

flowing

water

samples

in

the

PC

PC

score

plot

-LRB-

Fig.

-RRB-

The

sea

samples

can

be

divided

into

two

subgroups

The

first

subgroup

contains

the

samples

from

Steinbeck

-LRB-

Germany

-RRB-

Travemünde

-LRB-

Germany

-RRB-

and

Damp

-LRB-

Germany

-RRB-

located

in

the

Baltic

Sea

while

the

second

subgroup

includes

the

samples

from

Punta

Skala

-LRB-

Croatia

-RRB-

Nin

-LRB-

Croatia

-RRB-

and

Majorca

-LRB-

Spain

-RRB-

situated

in

the

Mediterranean

Sea

The

standing

water

and

flowing

water

biofilm

samples

overlap

The

flowing

water

biofilm

sample

from

Munich

can

also

be

distinguished

from

all

the

other

samples

along

PC

This

distinction

is

even

more

evident

along

PC

-LRB-

Fig.

-RRB-

Looking

at

the

loading

plots

shown

in

Fig.

and

e

one

finds

the

reasons

for

the

objects

distributions

observed

in

the

score

plots

PC

represents

the

Sr

Cu

Mg

Se

K

and

contents

in

the

water

phase

-LRB-

W-Sr

W-Cu

W-Mg

W-Se

W-K

W-Na

-RRB-

This

factor

can

be

related

to

the

salt

content

of

the

water

phase

and

is

conditionally

called

the

salt

factor

The

second

PC

PC

is

mainly

associated

with

Fe

and

Mg

-LRB-

Fig.

-RRB-

These

elements

are

basic

components

participating

in

the

biofilm

formation

PC

reflects

the

Mn

Zn

Cd

Pb

Fe

and

Co

contents

in

the

water

phase

The

presence

of

Cd

and

Pb

is

usually

a

result

of

environmental

contamination

and

that

is

why

PC

is

associated

with

the

anthropogenic

influence

From

the

information

obtained

from

the

score

and

loading

plots

it

follows

that

the

water

phase

of

the

biofilm

grown

in

seawater

is

indeed

richer

in

dissolved

salts

than

the

water

phase

of

the

standing

water

and

flowing

water

bodies

The

levels

of

Fe

and

Mg

in

sea

biofilms

are

also

higher

in

comparison

with

those

for

the

other

biofilms

The

salt

content

pH

and

temperature

of

water

vary

at

different

sampling

locations

and

they

influence

the

biofilm

formation

It

was

reported

in

-LSB-

-RSB-

that

Mg

strongly

influences

attachment

and

biofilm

structure

The

surface

colonisation

and

biofilm

depth

increase

with

the

increasing

Mg

concentration

The

biofilms

collected

in

Punta

Skala

Nin

and

Majorca

contain

higher

levels

of

dissolved

salts

in

the

water

phase

and

higher

Fe

and

Mg

contents

in

comparison

with

the

biofilms

collected

in

Travemünde

Damp

and

Steinbeck

The

sample

originating

from

Munich

shows

a

high

anthropogenic

influence

i.e.

it

has

higher

Mn

Zn

Cd

Pb

Fe

and

Co

contents

in

the

water

phase

and

lower

Fe

and

Mg

contents

in

the

biofilm

in

comparison

with

the

other

samples

In

order

to

see

whether

the

biofilms

developed

in

standing

water

could

be

distinguished

from

the

biofilms

grown

in

flowing

water

supervised

approaches

such

as

CART

DPLS

and

UVE-DPLS

were

applied

Furthermore

it

was

important

to

determine

if

the

models

constructed

could

predict

the

origin

of

new

biofilm

samples

and

how

well

Another

question

to

be

answered

was

what

variables

are

responsible

for

an

eventual

discrimination

of

groups

Only

seven

biofilms

were

grown

in

seawater

therefore

they

were

excluded

from

the

forthcoming

analysis

To

construct

a

reliable

discriminant

model

and

to

test

its

predictive

ability

the

data

were

divided

into

two

subsets

-LRB-

model

and

test

-RRB-

with

the

Kennard

and

Stone

-LSB-

-RSB-

and

duplex

-LSB-

-RSB-

algorithms

enabling

a

uniform

subset

selection

In

the

Kennard

and

Stone

method

objects

in

the

model

set

are

selected

sequentially

starting

with

the

object

closest

to

the

data

mean

The

next

object

included

in

the

subset

is

the

one

situated

furthest

away

from

the

first

one

The

third

object

selected

is

the

most

distant

one

from

the

objects

selected

in

the

model

set

The

selection

of

objects

continues

while

a

predefined

number

of

objects

are

not

assigned

to

the

model

set

The

remaining

objects

form

the

test

set

As

a

similarity

measure

the

Euclidian

distance

was

used

With

the

duplex

algorithm

the

two

most

distant

objects

in

the

data

are

found

and

included

in

the

model

set

The

next

two

most

distant

objects

are

assigned

to

the

test

set

The

remaining

objects

are

consecutively

added

to

the

subsets

switching

over

to

the

most

distant

unassigned

object

with

respect

to

the

model

set

and

to

the

most

distant

unassigned

object

with

respect

to

the

test

set

The

Kennard

and

Stone

algorithm

ensures

that

the

objects

in

the

model

set

cover

all

possible

sources

of

data

variance

while

the

duplex

method

guarantees

the

representativeness

of

both

subsets

Selection

of

model

and

test

sets

should

be

done

for

each

group

separately

When

a

preprocessing

procedure

is

required

the

selection

of

objects

is

applied

to

preprocessed

data

In

our

study

the

model

and

test

sets

were

selected

using

autoscaled

data

in

order

to

remove

the

scale

differences

among

variables

while

evaluating

the

Euclidean

distances

among

objects

It

should

be

mentioned

that

the

performance

of

CART

is

not

influenced

by

autoscaling

In

our

study

the

model

set

of

dimension

contains

flowing

water

and

standing

water

biofilm

samples

whereas

the

test

set

of

dimension

includes

biofilms

of

flowing

water

and

seven

biofilms

of

standing

water

Results

of

CART

DPLS

and

UVE-DPLS

for

model

and

test

sets

designed

with

the

Kennard

and

Stone

algorithm

To

trace

the

importance

of

variables

responsible

for

the

discrimination

of

both

groups

a

classification

tree

was

built

After

tenfold

cross-validation

an

optimal

tree

containing

two

terminal

nodes

was

selected

The

cross-validation

error

is

indicating

a

relatively

good

predictive

ability

of

the

constructed

tree

shown

in

Fig.

Fig.

tree

constructed

for

biofilm

model

samples

with

target

variable

describing

the

type

of

the

water

-LRB-

flowing

f

or

standing

s

-RRB-

in

which

the

biofilms

were

grown

Since

there

is

only

one

split

in

the

tree

the

discriminant

problem

is

rather

simple

and

the

most

discriminative

variable

describes

the

Mg

content

in

the

water

phase

-LRB-

W-Mg

-RRB-

As

mentioned

before

Mg

plays

an

important

role

during

the

biofilm

formation

-LSB-

-RSB-

All

the

model

set

samples

belonging

to

the

group

of

standing

water

-LRB-

samples

-RRB-

have

Mg

content

in

water

phase

below

mg

g

The

remaining

samples

-LRB-

flowing

water

biofilms

and

four

standing

water

biofilms

-RRB-

are

placed

in

the

left

terminal

node

which

results

in

a

misclassification

error

of

for

the

complete

tree

Although

four

model

standing

water

biofilms

are

recognised

as

flowing

water

biofilms

the

constructed

classification

tree

provides

a

correct

classification

of

for

the

test

samples

-LRB-

Table

-RRB-

Therefore

the

model

yields

fairly

high

sensitivity

-LRB-

percentage

of

correct

classification

of

the

test

flowing

water

biofilms

-RRB-

and

selectivity

-LRB-

percentage

of

correct

classification

of

the

test

standing

water

biofilms

-RRB-

Table

classification

rate

-LRB-

CCR

-RRB-

sensitivity

and

selectivity

of

the

modelsSelection

of

model

and

test

setsKennard

and

StoneDuplexTechniqueCARTaDPLSUVE-DPLSbCARTcDPLSUVE-DPLSdFlowing

water

vs.

standing

water

samplesCCR

-LRB-

-RRB-

Sensitivity

-LRB-

-RRB-

Selectivity

-LRB-

-RRB-

CART

classification

and

regression

trees

DPLS

discriminant

partial

least

squares

regression

UVE

uninformative

variable

eliminationaSelected

variable

W-MgbSelected

variables

W-Mg

W-Ca

and

W-SrcSelected

variable

W-MgdSelected

variables

Fe

Mg

Al

W-Cr

W-Cu

W-Mg

W-Ca

W-Sr

and

W-K

Additionally

good

discrimination

results

can

be

obtained

when

the

primary

split

is

made

on

the

variable

describing

the

Ca

content

in

the

water

phase

-LRB-

W-Ca

-RRB-

This

variable

is

a

competitive

variable

selected

after

removing

W-Mg

The

split

on

W-Ca

leads

to

a

total

misclassification

error

of

The

presence

of

Ca

has

been

shown

to

have

an

influence

on

mechanical

properties

of

biofilms

-LSB-

-RSB-

In

the

next

step

of

the

investigation

DPLS

was

considered

in

order

to

check

if

a

discrimination

model

using

linear

combinations

of

explanatory

variables

can

perform

better

than

CART

The

DPLS

model

has

complexity

The

RMSCV

is

and

RMS

error

is

The

DPLS

model

constructed

allows

for

correct

classification

of

the

test

set

samples

The

analysis

of

the

misclassified

test

samples

indicates

that

four

out

of

-LRB-

-RRB-

flowing

water

biofilms

collected

in

the

Leutra

river

are

incorrectly

predicted

as

standing

water

biofilms

therefore

the

model

has

a

lower

sensitivity

-LRB-

-RRB-

than

the

CART

model

All

the

test

samples

belonging

to

the

group

of

standing

water

biofilms

are

well

predicted

which

again

indicates

the

high

selectivity

-LRB-

-RRB-

of

the

model

constructed

-LRB-

Table

-RRB-

An

improved

DPLS

model

was

obtained

by

use

of

the

UVE-DPLS

approach

after

discarding

the

uninformative

variables

The

one-factor

UVE-DPLS

model

constructed

with

three

informative

variables

-LRB-

W-Mg

W-Ca

W-Sr

-RRB-

offers

a

total

correct

classification

of

for

the

test

set

It

yields

a

selectivity

of

and

a

better

sensitivity

-LRB-

-RRB-

in

comparison

with

the

DPLS

model

because

only

two

out

of

-LRB-

-RRB-

biofilms

grown

in

the

flowing

water

of

the

Leutra

river

are

now

assigned

to

the

group

of

standing

water

biofilms

-LRB-

Table

-RRB-

The

best

discrimination

results

are

obtained

from

CART

even

though

this

model

shows

a

misclassification

error

of

for

the

complete

tree

Since

the

splits

are

done

in

a

univariate

way

the

correlation

between

variables

is

not

taken

into

account

Therefore

CART

provides

unsatisfactory

results

when

a

linear

combination

of

variables

is

responsible

for

discriminating

the

samples

This

however

can

not

be

verified

unless

multivariate

approaches

such

as

DPLS

and

UVE-DPLS

are

used

Although

CART

and

UVE-DPLS

have

different

objective

functions

common

variables

are

selected

as

essential

for

the

discrimination

The

primary

variable

W-Mg

and

two

competitive

variables

W-Ca

and

W-Sr

in

CART

are

also

selected

by

UVE-DPLS

Results

of

CART

DPLS

and

UVE-DPLS

for

model

and

test

sets

designed

with

the

duplex

algorithm

Results

of

CART

DPLS

and

UVE-DPLS

were

obtained

using

data

designed

with

the

duplex

algorithm

which

ensures

the

representativeness

of

the

model

and

test

sets

The

classification

tree

built

has

two

terminal

nodes

and

the

primary

split

is

again

made

on

the

variable

representing

the

Mg

content

-LRB-

W-Mg

-RRB-

in

the

water

phase

The

cross-validation

error

is

Two

out

of

model

set

samples

are

wrongly

classified

which

leads

to

a

misclassification

error

of

for

the

complete

tree

Compared

with

the

previous

results

the

constructed

tree

shows

a

better

performance

for

the

model

set

samples

but

worse

prediction

rates

-LRB-

Table

-RRB-

therefore

the

model

has

again

a

fairly

high

sensitivity

-LRB-

-RRB-

but

quite

low

selectivity

-LRB-

-RRB-

The

DPLS

model

constructed

for

the

data

designed

by

the

duplex

algorithm

shows

slightly

better

prediction

ability

-LRB-

-RRB-

than

the

model

built

for

the

data

designed

by

the

Kennard

and

Stone

algorithm

-LRB-

-RRB-

It

presents

a

better

sensitivity

-LRB-

-RRB-

but

a

reduced

selectivity

with

only

of

standing

water

samples

being

well

recognised

A

discriminant

model

characterised

by

relatively

high

sensitivity

and

selectivity

parameters

is

to

be

preferred

over

a

model

with

a

high

sensitivity

and

a

low

selectivity

Therefore

the

UVE-DPLS

model

for

data

designed

by

the

Kennard

and

Stone

algorithm

is

to

be

favoured

-LRB-

Table

-RRB-

All

the

methods

allow

a

correct

prediction

for

of

samples

The

samples

collected

at

Chemnitz

and

White

Dak

Pond

Metebach

are

improperly

classified

by

all

methods

In

fact

this

is

not

a

striking

observation

though

when

the

data

contain

some

samples

that

are

different

in

comparison

with

the

majority

of

samples

These

samples

are

always

assigned

to

the

model

set

using

the

Kennard

and

Stone

method

and

then

the

test

samples

are

correctly

predicted

Using

the

duplex

method

we

assigned

some

atypical

samples

to

the

test

set

which

results

in

a

construction

of

models

with

too

pessimistic

predictive

abilities

Results

of

CART

DPLS

and

UVE-DPLS

for

biofilm

samples

grown

on

natural

substrates

Another

important

issue

to

be

discussed

is

whether

the

biofilm

samples

grown

on

natural

substrates

-LRB-

see

the

group

of

uniquely

sampled

biofilms

in

Table

-RRB-

can

be

used

to

derive

similar

conclusions

as

those

drawn

using

the

whole

data

If

this

is

possible

the

sampling

procedure

will

be

carried

out

in

a

simpler

way

which

will

be

less

time-consuming

and

relatively

low

in

price

For

an

initial

inspection

of

the

data

structure

PCA

was

considered

PCA

was

applied

to

autoscaled

data

-LRB-

-RRB-

containing

only

uniquely

sampled

biofilms

and

the

results

are

presented

in

Fig.

component

analysis

of

the

data

set

containing

the

uniquely

sampled

biofilms

a

scree

plot

of

the

cumulative

percentage

of

data

variance

explained

by

the

consecutive

PCs

b

projection

of

biofilms

on

the

plane

defined

by

PC

and

PC

c

projection

of

biofilms

on

the

plane

defined

by

PC

and

PC

d

projection

of

variables

on

the

plane

defined

by

PC

and

PC

and

e

projection

of

variables

on

the

plane

defined

by

PC

and

PC

The

first

three

PCs

account

for

of

the

total

data

variance

-LRB-

Fig.

-RRB-

Similar

to

PCA

of

the

whole

data

the

compression

is

not

very

effective

The

biofilms

grown

in

seawater

can

again

be

distinguished

along

PC

-LRB-

Fig.

-RRB-

Moreover

two

subgroups

of

sea

biofilms

are

distinguished

along

PC

-LRB-

Fig.

-RRB-

The

content

of

the

subgroups

is

the

same

as

before

The

biofilm

sample

collected

in

Munich

is

again

found

far

away

from

all

the

other

samples

Another

extreme

biofilm

sample

collected

in

the

Aller

river

-LRB-

Celle

Germany

-RRB-

appears

along

PC

Regarding

the

variable

loadings

-LRB-

Fig.

e

-RRB-

PC

is

again

associated

with

the

salt

content

of

the

biofilm

water

phases

while

PC

probably

is

now

linked

to

the

contamination

of

the

biofilm

water

phases

because

the

variables

W-Zn

W-Cd

W-Ni

W-Fe

W-Co

W-Mn

and

W-Pb

possess

high

loading

values

PC

consists

of

Zn

Cd

and

Pb

which

are

usually

associated

with

an

anthropogenic

influence

and

this

factor

is

therefore

associated

with

contaminants

accumulated

by

the

biofilm

Summarising

the

results

of

PCA

one

can

additionally

point

out

that

the

biofilm

samples

collected

in

Majorca

Punta

Skala

and

Nin

are

richer

in

Zn

Cd

and

Pb

in

comparison

with

the

remaining

sea

biofilm

samples

Moreover

the

highest

Zn

Cd

and

Pb

contents

are

characteristic

for

the

biofilm

sample

from

Celle

In

order

to

construct

the

CART

DPLS

and

UVE-DPLS

models

only

data

of

natural

biofilms

grown

in

flowing

water

and

in

standing

water

were

considered

Since

the

number

of

samples

in

each

group

is

small

-LRB-

Table

-RRB-

the

models

were

used

for

an

exploratory

purpose

only

Because

of

this

the

predictive

abilities

of

the

models

were

not

tested

using

an

independent

test

set

The

complete

classification

tree

with

three

terminal

nodes

is

shown

in

Fig.

The

primary

split

is

made

on

the

variable

describing

the

Pb

content

in

the

water

phase

-LRB-

W-Pb

-RRB-

W-Pb

is

the

most

discriminant

variable

The

next

split

on

variable

Al

corrects

the

improper

assignment

of

one

sample

and

it

is

of

a

lower

importance

Owing

to

the

small

number

of

samples

the

required

tenfold

cross-validation

procedure

could

not

be

applied

and

therefore

the

cross-validation

error

was

not

reported

All

the

biofilms

grown

in

standing

water

are

well

classified

but

two

biofilm

samples

grown

in

flowing

water

are

wrongly

classified

which

results

in

a

total

classification

rate

of

The

incorrectly

classified

samples

originate

from

Steinach

-LRB-

Germany

-RRB-

and

Geithain

-LRB-

Germany

-RRB-

Fig.

tree

constructed

for

biofilm

samples

with

target

variable

describing

the

type

of

the

water

-LRB-

flowing

f

or

standing

s

-RRB-

in

which

the

biofilms

were

grown

The

DPLS

model

constructed

has

complexity

RMSCV

is

and

RMS

error

accounts

for

Two

samples

are

incorrectly

classified

One

of

them

belongs

to

the

biofilms

of

standing

water

and

originates

from

Chemnitz

-LRB-

Germany

-RRB-

while

the

other

one

is

the

biofilm

collected

in

the

flowing

water

body

-LRB-

São

Lourenço

-RRB-

located

in

Juquitiba

-LRB-

Brazil

-RRB-

The

DPLS

model

built

yields

a

total

classification

rate

of

It

should

be

emphasised

that

DPLS

can

lead

to

a

too

optimistic

result

when

the

number

of

variables

outnumbers

the

number

of

samples

-LSB-

-RSB-

A

remedy

for

this

problem

is

to

reduce

the

number

of

variables

by

the

use

of

a

feature

selection

technique

e.g.

UVE-DPLS

The

UVE-DPLS

model

has

RMSCV

of

One

variable

namely

W-Pb

is

selected

However

all

biofilms

grown

in

flowing

water

are

correctly

classified

with

the

model

constructed

but

all

biofilms

grown

in

standing

water

are

improperly

classified

Conclusions

Discrimination

between

sea

biofilms

and

the

remaining

standing

water

and

flowing

water

biofilms

is

straightforward

by

investigating

the

score

plots

obtained

from

PCA

The

loading

plots

emphasise

the

expected

higher

salt

content

of

the

water

phases

extracted

from

the

sea

biofilms

as

well

as

their

higher

levels

of

Fe

and

Mg

in

comparison

with

the

other

biofilms

A

further

discrimination

between

flowing

water

and

standing

water

biofilms

is

possible

by

means

of

supervised

methods

like

CART

DPLS

and

UVE-DPLS

The

best

discriminant

model

is

obtained

from

CART

One

variable

describing

the

Mg

content

in

the

water

phase

-LRB-

W-Mg

-RRB-

is

enough

to

build

a

model

with

misclassification

error

All

test

samples

selected

by

the

Kennard

and

Stone

algorithm

are

correctly

classified

using

the

constructed

CART

model

The

DPLS

and

UVE-DPLS

methods

do

not

outperform

CART

for

the

data

set

studied

and

therefore

it

can

be

pointed

out

that

a

linear

combination

of

explanatory

variables

does

not

lead

to

a

better

prediction

for

new

samples

Moreover

CART

appears

as

a

very

simple

and

efficient

discriminant

technique

leading

to

a

straightforward

data

interpretation

in

terms

of

explanatory

variables

Hence

CART

can

be

considered

as

a

pilot

discriminant

approach

When

the

CART

model

is

not

satisfactory

one

can

apply

discriminant

methods

such

as

DPLS

and

UVE-DPLS

or

if

necessary

to

use

a

nonlinear

multivariate

classifier

like

e.g.

support

vector

machines

All

discriminant

models

CART

DPLS

and

UVE-DPLS

lead

to

correct

classification

for

the

test

set

designed

by

the

duplex

algorithm

However

CART

uses

only

one

variable

-LRB-

W-Mg

-RRB-

UVE-DPLS

selects

nine

variables

and

DPLS

uses

all

explanatory

variables

to

build

the

model

Discrimination

of

flowing

water

and

standing

water

biofilms

that

are

uniquely

sampled

using

CART

DPLS

and

UVE-DPLS

models

is

done

only

for

a

better

understanding

of

the

data

collected

For

a

definite

conclusion

whether

these

two

groups

of

samples

can

be

discriminated

more

samples

are

required

to

properly

validate

the

discriminant

models

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

biofilms
chemometrics
classification and regression trees

uninformative variable elimination–discriminant partial least squares regression