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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
0.01
0.1
1
10
100
100 1000 10000 100 1000 10000number of spectra
t / s
mode
●
●
Rmode
Qmode
bands
● selected
whole spectrum
12
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
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