Hierarchical Cluster Analysis ofhyperspectral Raman images:

a new point of view leads to 10 000× speedup

UseR!, Aalborg, 2015-07-01

C. Beleites1, A. Bonifacio2, C. Krafft1, V. Sergo2 and J. Popp1,3

1 Dept. Spectroscopy and Imaging, IPHT Jena, Jena, Germany2 Dept. Arch. and Engineering, Univ. of Trieste, Trieste, Italy3 Inst. of Physical Chemistry and Abbe School of Photonics,

University of Jena, Jena, Germany

Vibrational Spectroscopy

Molecular vibrations:atoms vibrate against each other

n-atomic molecule:3n − 6 different vibrations

Excite vibration: discrete energy

Characteristic bands⇒ biochemical composition

Lipids, proteins, carbohydrates, . . .

Fingerprint region⇒ identify substance⇒ identify cell or tissue type

1

Chondrocytes in Articular Cartilage

2

Raman spectra: Articular Cartilage

Bonifacio et al., Analyst, 135 (2010) 3194 – 3204. DOI: 10.1039/c0an00459f 3

Hyperspectral Data

matrix

lacuna

cell

x µm

yµm

0

5

10

15

−10 0 10 20

matrix

lacuna

cell

statisticaldata analysis

spec

tral a

xis

image/lateral axes

spectral information

spatial information

4

Hyperspectral Data

spec

tral a

xis

image/lateral axesnx

ny

n = nx ny nx ny

1 1

x y p

extra/meta

information

extra/meta

informationspectra matrixspectra matrix

unfold

hyperspectraldata cube

hyperspectraldata cube

4

Cluster analysis

Hierarchical4 finds small clusters among

many other spectra4 get number of clusters from

dendrogram

8 memory use: ≈ n2

8 run time:∼ n2

out-of-memory algorithmsz. B. fastclusterMüllner D, JStatSoft, 53, 1 – 18.

k -means8 small clusters may not be

found8 number of clusters must

be known beforehand

4 memory use: uncritical4 fast8 sometimes sensitive to

initialization

5

Heatmaps

940.

555

952.

035

1190

.21

1423

.33

1384

.73

1437

.86

841.

826

912.

889

1466

.78

1066

.46

799.

373

1251

.99

1078

.75

847.

692

1033

.88

1234

.73

1457

.564

0.23

411

22.1

305333182216511281512213513515966253248115298101105251414126258246223470264464101430737633036046235224349231792448114231126346338829469485144257467465391389359366450365611491891193784664144146222479386831303953419325620978162396338401222924178489121225421380480276304244147439642474773874241637547521279175273259917226019436822652352185645345111423080423429201384313370455166371496301839441037541367255447245491141291500524264352081061343844531420028613737922647903744816817411459139241333581691635537739419718611392208488963447335346884401275262681583573217646140642234926271179346240326821122038234228531510747819512109222847464151732031601363322154123812425354919853301408456282654573901324482846242841715433529686116293499103167110436722242894823362121839210328813406047231211342418425541353184589229911815223913119632348310249712319132428117726923228347343336485148407278498971333064192361927425443145420216432225882614204043501853694601938534147125227440544124334138170112329947624929019049433915631551989320748469387495310486295443157383273493331432674872141613623859131915314522820643495403271100427367266233184374324491761042312807320337117400217409326894422133163983733615715058134188294108205233972971811654524901434022191712503723451252272368494163432382725523723411120439930277156444363446430146309127348174270288703001801203031993933272293563475045140440187259437317129277287308

O.M

.Pb Zn C

dC

u

1131171061094315998102103122121120105104146261011252414310810011411812715516229101273044281411161251311111341321381331471481561611421371261127511911014016315816423229414451957149501459915412811512343133703552324542371355886874859381611320886957394090612564151497893136150149921571519615297911298384130153851247681464779808221536736516019626366641718568960551234154

6

Cluster analysis the other way round

What happens if images are clustered rather than spectra?

  Clusters of spectral bands that have similar (spatial) distribution.

4 Similar to spectra interpretation work flow

! Several substances may share the same spectral band positionband may be assigned with only one substance, orneighbour channels are assigned to different substancessubstances form subclusters

4 (Spatial) distribution is not any more separated into hard clusters,agrees well with continuous concentration distributions.

Bonifacio, Beleites & Sergo: Anal Bioanal Chem, 407 (2015), 1089 – 1095DOI: 10.1007/s00216-014-8321-7 7

Cluster analysis the other way round

What happens if images are clustered rather than spectra?

  Clusters of spectral bands that have similar (spatial) distribution.

4 Similar to spectra interpretation work flow

! Several substances may share the same spectral band positionband may be assigned with only one substance, orneighbour channels are assigned to different substancessubstances form subclusters

4 (Spatial) distribution is not any more separated into hard clusters,agrees well with continuous concentration distributions.

Bonifacio, Beleites & Sergo: Anal Bioanal Chem, 407 (2015), 1089 – 1095DOI: 10.1007/s00216-014-8321-7 7

Cluster analysis the other way round

What happens if images are clustered rather than spectra?

  Clusters of spectral bands that have similar (spatial) distribution.

4 Similar to spectra interpretation work flow

! Several substances may share the same spectral band positionband may be assigned with only one substance, orneighbour channels are assigned to different substancessubstances form subclusters

4 (Spatial) distribution is not any more separated into hard clusters,agrees well with continuous concentration distributions.

Bonifacio, Beleites & Sergo: Anal Bioanal Chem, 407 (2015), 1089 – 1095DOI: 10.1007/s00216-014-8321-7 7

Cluster analysis the other way round

What happens if images are clustered rather than spectra?

  Clusters of spectral bands that have similar (spatial) distribution.

4 Similar to spectra interpretation work flow

! Several substances may share the same spectral band positionband may be assigned with only one substance, orneighbour channels are assigned to different substancessubstances form subclusters

4 (Spatial) distribution is not any more separated into hard clusters,agrees well with continuous concentration distributions.

Bonifacio, Beleites & Sergo: Anal Bioanal Chem, 407 (2015), 1089 – 1095DOI: 10.1007/s00216-014-8321-7 7

Cluster analysis the other way round

What happens if images are clustered rather than spectra?

  Clusters of spectral bands that have similar (spatial) distribution.

4 Similar to spectra interpretation work flow

! Several substances may share the same spectral band positionband may be assigned with only one substance, orneighbour channels are assigned to different substancessubstances form subclusters

4 (Spatial) distribution is not any more separated into hard clusters,agrees well with continuous concentration distributions.

Bonifacio, Beleites & Sergo: Anal Bioanal Chem, 407 (2015), 1089 – 1095DOI: 10.1007/s00216-014-8321-7 7

Hierarchical Cluster Analysis: Run time

cartilage crystals

0.001

0.01

0.1

1

10

100

100 1000 10000 100 1000 10000number of spectra

t / s

R-mode (p x p)Q-mode (n x n)

●

●

cartilage from articular jointn = 9 304 Raman spectra ×p = 1 272 wavenumber channels

crystals heterogeneous mixture of 4 different substancesn = 22 801 Raman spectra ×p = 1 019 wavenumber channels 8

Raman spectra: cartilage

600 800 1000 1200 1400 1600 1800

0.00

0.02

0.04

0.06

0.08

Wellenzahl cm−1

I nor

ma.

u.

9

Raman spectra: cartilage

600 800 1000 1200 1400 1600 1800

0.00

0.02

0.04

0.06

0.08

Wellenzahl cm−1

I nor

ma.

u.

9

Dendrogram selected bands

1670

1444

1658

1606

1615 828

1003

1207

1486

1333

1310

1577

1271

1244

1635

1139

1053

1069

1378

1422

813

921

855

939

705

731

02

46

Cluster Dendrogram

hclust (*, "ward")

Dis

tanz

10

Results

Bonifacio et al., Analyst, 135 (2010) 3194 – 3204. DOI: 10.1039/c0an00459f

Bonifacio, Beleites & Sergo: Anal Bioanal Chem, 407 (2015), 1089 – 1095DOI: 10.1007/s00216-014-8321-7 11

Results

Bonifacio et al., Analyst, 135 (2010) 3194 – 3204. DOI: 10.1039/c0an00459f

Bonifacio, Beleites & Sergo: Anal Bioanal Chem, 407 (2015), 1089 – 1095DOI: 10.1007/s00216-014-8321-7 11

Results

Bonifacio et al., Analyst, 135 (2010) 3194 – 3204. DOI: 10.1039/c0an00459f

Bonifacio, Beleites & Sergo: Anal Bioanal Chem, 407 (2015), 1089 – 1095DOI: 10.1007/s00216-014-8321-7 11

Hierarchical Cluster Analysis: Run time

cartilage crystals

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0.001

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10

100

100 1000 10000 100 1000 10000number of spectra

t / s

mode

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Rmode

Qmode

bands

● selected

whole spectrum

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Summary and AcknowledgementsUse domain-specific information

Vibrational spectroscopy: Clustering spectra vs. images  similar resultsSpectroscopic interpretationReduce run-time by orders of magnitude

Bonifacio et al., Analyst, 135 (2010) 3194 – 3204.DOI: 10.1039/c0an00459f

Bonifacio et al.: Anal Bioanal Chem, 407 (2015), 1089 – 1095.DOI: 10.1007/s00216-014-8321-7

13