Time-of-flight secondary ion mass spectrometry (ToF-SIMS) imaging offers a powerful, label-free method for exploring organic, bioorganic, and biological systems. The technique is capable of very high spatial resolution, while also producing an enormous amount of information about the chemical and molecular composition of a surface. However, this information is inherently complex, making interpretation and analysis of the vast amount of data produced by a single ToF-SIMS experiment a considerable challenge. Much research over the past few decades has focused on the application and development of multivariate analysis (MVA) and machine learning (ML) techniques that find meaningful patterns and relationships in these datasets. Here, we review the unsupervised algorithms—that is, algorithms that do not require ground truth labels—that have been applied to ToF-SIMS images, as well as other algorithms and approaches that have been used in the broader family of mass spectrometry imaging (MSI) techniques. We first give a nontechnical overview of several commonly used classes of unsupervised algorithms, such as matrix factorization, clustering, and nonlinear dimensionality reduction. We then review the application of unsupervised algorithms to various organic, bioorganic, and biological systems including cells and tissues, organic films, residues and coatings, and spatially structured systems such as polymer microarrays. We then cover several novel algorithms employed for other MSI techniques that have received little attention from ToF-SIMS imaging researchers. We conclude with a brief outline of potential future directions for the application of MVA and ML algorithms to ToF-SIMS images.

1.
P.
Massonnet
and
R. M. A.
Heeren
,
J. Anal. At. Spectrom.
34
,
2217
(
2019
).
2.
J. L. S.
Lee
,
I. S.
Gilmore
, and
M. P.
Seah
,
Surf. Interface Anal.
40
,
1
(
2008
).
3.
J. L. S.
Lee
,
B. J.
Tyler
,
M. S.
Wagner
,
I. S.
Gilmore
, and
M. P.
Seah
,
Surf. Interface Anal.
41
,
76
(
2009
).
4.
J. W.
Park
,
H.
Min
,
Y. P.
Kim
,
H. K.
Shon
,
J.
Kim
,
D. W.
Moon
, and
T. G.
Lee
,
Surf. Interface Anal.
41
,
694
(
2009
).
5.
D. J.
Graham
and
D. G.
Castner
,
Biointerphases
7
,
49
(
2012
).
6.
7.
R.
Michel
and
D. G.
Castner
,
Surf. Interface Anal.
38
,
1386
(
2006
).
8.
J. S.
Fletcher
,
Analyst
134
,
2204
(
2009
).
9.
D.
Touboul
,
O.
Laprevote
, and
A.
Brunelle
,
Curr. Opin. Chem. Biol.
15
,
725
(
2011
).
10.
J. D.
Watrous
,
T.
Alexandrov
, and
P. C.
Dorrestein
,
J. Mass Spectrom.
46
,
209
(
2011
).
11.
E. G.
Armitage
,
H. L.
Kotze
, and
N. P.
Lockyer
,
Metabolomics
9
,
102
(
2013
).
12.
I. S.
Gilmore
,
J. Vac. Sci. Technol. A
31
,
050819
(
2013
).
13.
M. L.
Kraft
and
H. A.
Klitzing
,
Biochim. Biophys. Acta, Mol. Cell Biol. Lipids
1841
,
1108
(
2014
).
14.
J.
Yang
and
I.
Gilmore
,
Mater. Sci. Technol.
31
,
131
(
2015
).
15.
B.
Balluff
,
M.
Hanselmann
, and
R. M.
Heeren
,
Adv. Cancer Res.
134
,
201
(
2017
).
16.
A. R.
Buchberger
,
K.
DeLaney
,
J.
Johnson
, and
L.
Li
,
Anal. Chem.
90
,
240
(
2018
).
17.
C.
Zhao
and
Z.
Cai
,
Mass Spectrom. Rev.
(to be published).
19.
T.
Alexandrov
,
BMC Bioinform.
13
,
S11
(
2012
).
20.
E. A.
Jones
,
S.-O.
Deininger
,
P. C. W.
Hogendoorn
,
A. M.
Deelder
, and
L. A.
McDonnell
,
J. Proteomics
75
,
4962
(
2012
).
21.
N.
Verbeeck
,
R. M.
Caprioli
, and
R.
Van de Plas
,
Mass Spectrom. Rev.
39
,
245
(
2020
).
22.
T.
Alexandrov
,
Annu. Rev. Biomed. Data Sci.
3
,
61
(
2020
).
23.
W.
Gardner
,
S. M.
Cutts
,
D. R.
Phillips
, and
P. J.
Pigram
,
Biopolymers
112
,
e23400
(
2021
).
24.
D. J.
Graham
,
M. S.
Wagner
, and
D. G.
Castner
,
Appl. Surf. Sci.
252
,
6860
(
2006
).
25.
M. R.
Keenan
and
P. G.
Kotula
,
Surf. Interface Anal.
36
,
203
(
2004
).
26.
M. R.
Keenan
and
P. G.
Kotula
,
Appl. Surf. Sci.
231
,
240
(
2004
).
27.
M. R.
Keenan
,
V. S.
Smentkowski
,
J. A.
Ohlhausen
, and
P. G.
Kotula
,
Surf. Interface Anal.
40
,
97
(
2008
).
28.
S.
Vaidyanathan
,
J. S.
Fletcher
,
A.
Henderson
,
N. P.
Lockyer
, and
J. C.
Vickerman
,
Appl. Surf. Sci.
255
,
1599
(
2008
).
29.
T.
Stephan
,
J.
Zehnpfenning
, and
A.
Benninghoven
,
J. Vac. Sci. Technol. A
12
,
405
(
1994
).
30.
B. J.
Tyler
and
R. E.
Peterson
,
Surf. Interface Anal.
45
,
475
(
2013
).
31.
M. A.
Robinson
,
D. J.
Graham
, and
D. G.
Castner
,
Anal. Chem.
84
,
4880
(
2012
).
32.
M. S.
Wagner
,
D. J.
Graharn
, and
D. G.
Castner
,
Appl. Surf. Sci.
252
,
6575
(
2006
).
33.
M. R.
Keenan
,
J. Vac. Sci. Technol. A
23
,
746
(
2005
).
34.
M. R.
Keenan
,
Surf. Interface Anal.
41
,
79
(
2009
).
35.
M. R.
Keenan
and
V. S.
Smentkowski
,
Surf. Interface Anal.
48
,
218
(
2016
).
36.
A.
de Juan
,
J.
Jaumot
, and
R.
Tauler
,
Anal. Methods
6
,
4964
(
2014
).
37.
G. F.
Trindade
,
M. L.
Abel
,
C.
Lowe
,
R.
Tshulu
, and
J. F.
Watts
,
Anal. Chem.
90
,
3936
(
2018
).
38.
G. F.
Trindade
,
M. L.
Abel
, and
J. F.
Watts
,
Chemom. Intell. Lab. Syst.
163
,
76
(
2017
).
39.
G. F.
Trindade
,
M. L.
Abel
, and
J. F.
Watts
,
Chemom. Intell. Lab. Syst.
182
,
180
(
2018
).
40.
G. F.
Trindade
,
D. F.
Williams
,
M. L.
Abel
, and
J. F.
Watts
,
Surf. Interface Anal.
50
,
1180
(
2018
).
41.
A.
de Juan
and
R.
Tauler
,
Anal. Chim. Acta
1145
,
59
(
2021
).
42.
W. H.
Lawton
and
E. A.
Sylvestre
,
Technometrics
13
,
617
(
1971
).
43.
A.
de Juan
and
R.
Tauler
,
Crit. Rev. Anal. Chem.
36
,
163
(
2006
).
44.
N. B.
Gallagher
,
J. M.
Shaver
,
E. B.
Martin
,
J.
Morris
,
B. M.
Wise
, and
W.
Windig
,
Chemom. Intell. Lab. Syst.
73
,
105
(
2004
).
45.
D. J.
Scurr
,
A. L.
Hook
,
J.
Burley
,
P. M.
Williams
,
D. G.
Anderson
,
R.
Langer
,
M. C.
Davies
, and
M. R.
Alexander
,
Surf. Interface Anal.
45
,
466
(
2013
).
46.
H.
Lai
,
Q.
Liu
,
J.
Deng
,
S.
Wen
, and
Z.
Liu
,
Appl. Surf. Sci.
518
,
146270
(
2020
).
47.
A. L.
Hook
,
P. M.
Williams
,
M. R.
Alexander
, and
D. J.
Scurr
,
Biointerphases
10
,
019005
(
2015
).
48.
R.
Larsen
,
J. Chemom.
16
,
427
(
2002
).
49.
B. J.
Tyler
,
G.
Rayal
, and
D. G.
Castner
,
Biomaterials
28
,
2412
(
2007
).
50.
J.
Hanrieder
and
A. G.
Ewing
,
Sci. Rep.
4
,
5266
(
2014
).
51.
J.
Hanrieder
,
L.
Gerber
,
A. P.
Sandelius
,
E. B.
Brittebo
,
A. G.
Ewing
, and
O.
Karlsson
,
ACS Chem. Neurosci.
5
,
568
(
2014
).
52.
A.
Henderson
,
J. S.
Fletcher
, and
J. C.
Vickerman
,
Surf. Interface Anal.
41
,
666
(
2009
).
53.
B. J.
Tyler
,
Appl. Surf. Sci.
252
,
6875
(
2006
).
54.
J.
Hanrieder
,
P.
Malmberg
,
O. R.
Lindberg
,
J. S.
Fletcher
, and
A. G.
Ewing
,
Anal. Chem.
85
,
8741
(
2013
).
55.
M.
Nijs
,
T.
Smets
,
E.
Waelkens
, and
B.
De Moor
,
Rapid Commun. Mass Spectrom.
35
,
e9181
(
2021
).
56.
M.
Brulet
,
A.
Seyer
,
A.
Edelman
,
A.
Brunelle
,
J.
Fritsch
,
M.
Ollero
, and
O.
Laprevote
,
J. Lipid Res.
51
,
3034
(
2010
).
57.
A. R.
Konicek
,
J.
Lefman
, and
C.
Szakal
,
Analyst
137
,
3479
(
2012
).
58.
C.
Szakal
,
K.
Narayan
,
J.
Fu
,
J.
Lefman
, and
S.
Subramaniam
,
Anal. Chem.
83
,
1207
(
2011
).
59.
J. M.
Fonville
 et al,
Anal. Chem.
85
,
1415
(
2013
).
60.
P.
Franceschi
and
R.
Wehrens
,
Proteomics
14
,
853
(
2014
).
61.
W.
Gardner
,
S. M.
Cutts
,
B. W.
Muir
,
R. T.
Jones
, and
P. J.
Pigram
,
Anal. Chem.
91
,
13855
(
2019
).
62.
W.
Gardner
,
A. L.
Hook
,
M. R.
Alexander
,
D.
Ballabio
,
S. M.
Cutts
,
B. W.
Muir
, and
P. J.
Pigram
,
Anal. Chem.
92
,
6587
(
2020
).
63.
P.
Inglese
,
J. S.
McKenzie
,
A.
Mroz
,
J.
Kinross
,
K.
Veselkov
,
E.
Holmes
,
Z.
Takats
,
J. K.
Nicholson
, and
R. C. J. C. S.
Glen
,
Chem. Sci.
8
,
3500
(
2017
).
64.
T.
Smets
,
T.
De Keyser
,
T.
Tousseyn
,
E.
Waelkens
, and
B.
De Moor
,
Anal. Chem.
93
,
3452
(
2021
).
65.
T.
Smets
,
N.
Verbeeck
,
M.
Claesen
,
A.
Asperger
,
G.
Griffioen
,
T.
Tousseyn
,
W.
Waelput
,
E.
Waelkens
, and
B.
De Moor
,
Anal. Chem.
91
,
5706
(
2019
).
66.
T.
Smets
,
E.
Waelkens
, and
B.
De Moor
,
Anal. Chem.
92
,
5240
(
2020
).
67.
W.
Gardner
,
R.
Maliki
,
S. M.
Cutts
,
B. W.
Muir
,
D.
Ballabio
,
D. A.
Winkler
, and
P. J.
Pigram
,
Anal. Chem.
92
,
10450
(
2020
).
68.
T.
Kohonen
,
Biol. Cybern.
43
,
59
(
1982
).
69.
C. D.
Wijetunge
,
I.
Saeed
,
S. K.
Halgamuge
,
B.
Boughton
, and
U.
Roessner
, “
Unsupervised learning for exploring MALDI imaging mass spectrometry ‘omics’ data
,”
7th International Conference on Information and Automation for Sustainability
, Sri Lanka, 22–24 Dec. 2014 (IEEE, Colombo,
2014
), pp.
1
6
.
70.
X.
Xiong
 et al,
J. Am. Soc. Mass Spectrom.
23
,
1147
(
2012
).
72.
S. S.
Basu
 et al,
NPJ Precis. Oncol.
3
,
17
(
2019
).
73.
L.
van der Maaten
and
G.
Hinton
,
J. Mach. Learn. Res.
9
,
2579
(
2008
).
74.
L.
McInnes
 et al, “UMAP: Uniform Manifold Approximation and Projection,”
J. Open Source Software
3
(29),
861
(
2018
).
75.
W. M.
Abdelmoula
,
B.
Balluff
,
S.
Englert
,
J.
Dijkstra
,
M. J. T.
Reinders
,
A.
Walch
,
L. A.
McDonnell
, and
B. P. F.
Lelieveldt
,
Proc. Natl. Acad. Sci. U.S.A.
113
,
12244
(
2016
).
76.
M. C.
Biesinger
,
P. Y.
Paepegaey
,
N. S.
McIntyre
,
R. R.
Harbottle
, and
N. O.
Petersent
,
Anal. Chem.
74
,
5711
(
2002
).
77.
C. R.
Anderton
,
B.
Vaezian
,
K.
Lou
,
J. F.
Frisz
, and
M. L.
Kraft
,
Surf. Interface Anal.
44
,
322
(
2011
).
78.
M. C.
Biesinger
,
D. J.
Miller
,
R. R.
Harbottle
,
F.
Possmayer
,
N. S.
McIntyre
, and
N. O.
Petersen
,
Appl. Surf. Sci.
252
,
6957
(
2006
).
79.
C. M.
McQuaw
,
A. G.
Sostarecz
,
L.
Zheng
,
A. G.
Ewing
, and
N.
Winograd
,
Appl. Surf. Sci.
252
,
6716
(
2006
).
80.
Y.
Yokoyama
,
S.
Aoyagi
,
T.
Shimanouchi
,
M.
Iwamura
, and
H.
Iwai
,
Biointerphases
11
,
02A314
(
2016
).
81.
L.
Zheng
,
C. M.
McQuaw
,
M. J.
Baker
,
N. P.
Lockyer
,
J. C.
Vickerman
,
A. G.
Ewing
, and
N.
Winograd
,
Appl. Surf. Sci.
255
,
1190
(
2008
).
82.
M. K.
Passarelli
and
N.
Winograd
,
Biochim. Biophys. Acta, Mol. Cell Biol. Lipids
1811
,
976
(
2011
).
83.
M. J.
Baker
,
L.
Zheng
,
N.
Winograd
,
N. P.
Lockyer
, and
J. C.
Vickerman
,
Langmuir
24
,
11803
(
2008
).
84.
B.
Vaezian
,
C. R.
Anderton
, and
M. L.
Kraft
,
Anal. Chem.
82
,
10006
(
2010
).
85.
Y. T. R.
Lau
,
L. T.
Weng
,
K. M.
Ng
, and
C. M.
Chan
,
Surf. Interface Anal.
43
,
340
(
2010
).
86.
S.
Aoyagi
,
K.
Abe
,
T.
Yamagishi
,
H.
Iwai
,
S.
Yamaguchi
, and
T.
Sunohara
,
Anal. Bioanal. Chem.
409
,
6387
(
2017
).
87.
S.
Ravati
,
S.
Poulin
,
K.
Piyakis
, and
B. D.
Favis
,
Polymer
55
,
6110
(
2014
).
88.
Y.
Yokoyama
,
T.
Kawashima
,
M.
Ohkawa
,
H.
Iwai
, and
S.
Aoyagi
,
Surf. Interface Anal.
47
,
439
(
2015
).
89.
J. R.
Stroka
and
R. E.
Goacher
,
J. Vac. Sci. Technol. B
34
,
03H101
(
2016
).
90.
B. J.
Tyler
,
C.
Bruening
,
S.
Rangaranjan
, and
H. F.
Arlinghaus
,
Biointerphases
6
,
135
(
2011
).
91.
N.
Tuccitto
,
G.
Capizzi
,
A.
Torrisi
, and
A.
Licciardello
,
Anal. Chem.
90
,
2860
(
2018
).
92.
N.
Tuccitto
,
A.
Bombace
,
A.
Torrisi
,
A.
Licciardello
,
G.
Lo Sciuto
,
G.
Capizzi
, and
M.
Woźniak
,
Chemom. Intell. Lab. Syst.
191
,
138
(
2019
).
93.
C.
Bich
,
D.
Touboul
, and
A.
Brunelle
,
Mass Spectrom. Rev.
33
,
442
(
2014
).
94.
S.
Rabbani
,
A. M.
Barber
,
J. S.
Fletcher
,
N. P.
Lockyer
, and
J. C.
Vickerman
,
Anal. Chem.
83
,
3793
(
2011
).
95.
J.
Xu
,
S.
Ostrowski
,
C.
Szakal
,
A. G.
Ewing
, and
N.
Winograd
,
Appl. Surf. Sci.
231-232
,
159
(
2004
).
96.
H.
Nygren
and
P.
Malmberg
,
J. Microsc. (Oxford)
215
,
156
(
2004
).
97.
C. A.
Barnes
,
J.
Brison
,
M.
Robinson
,
D. J.
Graham
,
D. G.
Castner
, and
B. D.
Ratner
,
Anal. Chem.
84
,
893
(
2012
).
98.
B. J.
Tyler
,
M. M.
Takeno
, and
K. D.
Hauch
,
Surf. Interface Anal.
43
,
336
(
2010
).
99.
H. L.
Kotze
,
E. G.
Armitage
,
J. S.
Fletcher
,
A.
Henderson
,
K. J.
Williams
,
N. P.
Lockyer
, and
J. C.
Vickerman
,
Surf. Interface Anal.
45
,
277
(
2013
).
100.
B. J.
Tyler
,
S.
Rangaranjan
,
J.
Moller
,
A.
Beumer
, and
H. E.
Arlinghaus
,
Appl. Surf. Sci.
252
,
6712
(
2006
).
101.
K.
Borner
,
H.
Nygren
,
P.
Malmberg
,
E.
Tallarek
, and
B.
Hagenhoff
,
Appl. Surf. Sci.
252
,
6777
(
2006
).
102.
L. G.
Wu
,
X. H.
Lu
,
K. S.
Kulp
,
M. G.
Knize
,
E. S. F.
Berman
,
E. J.
Nelson
,
J. S.
Felton
, and
K. J. J.
Wu
,
Int. J. Mass Spectrom.
260
,
137
(
2007
).
103.
J. W.
Park
,
H. K.
Shon
,
B. C.
Yoo
,
I. H.
Kim
,
D. W.
Moon
, and
T. G.
Lee
,
Appl. Surf. Sci.
255
,
1119
(
2008
).
104.
105.
T. B.
Angerer
,
M. D.
Pour
,
P.
Malmberg
, and
J. S.
Fletcher
,
Anal. Chem.
87
,
4305
(
2015
).
106.
B. M.
Bluestein
,
F.
Morrish
,
D. J.
Graham
,
J.
Guenthoer
,
D.
Hockenbery
,
P. L.
Porter
, and
L. J.
Gamble
,
Analyst
141
,
1947
(
2016
).
107.
B. M.
Bluestein
,
F.
Morrish
,
D. J.
Graham
,
L.
Huang
,
D.
Hockenbery
, and
L. J.
Gamble
,
Biointerphases
13
,
06D402
(
2018
).
108.
S.
Aoyagi
,
T.
Matsuzaki
,
M.
Takahashi
,
Y.
Sakurai
, and
M.
Kudo
,
Surf. Interface Anal.
44
,
772
(
2012
).
109.
J.
Hanrieder
,
K.
Oskar
,
E. B.
Brittebo
,
P.
Malmberg
, and
A. G.
Ewing
,
Surf. Interface Anal.
46
,
375
(
2014
).
110.
K.
Dimovska Nilsson
,
N.
Neittaanmäki
,
O.
Zaar
,
T. B.
Angerer
,
J.
Paoli
, and
J. S.
Fletcher
,
Biointerphases
15
,
041012
(
2020
).
111.
P.
Kulkarni
,
M.
Dost
,
O. D.
Bulut
,
A.
Welle
,
S.
Bocker
,
W.
Boland
, and
A.
Svatos
,
Plant J.
93
,
193
(
2018
).
112.
B. J.
Tyler
,
R. E.
Peterson
,
T. G.
Lee
,
F.
Draude
,
A.
Pelster
, and
H. F.
Arlinghaus
,
Biointerphases
11
,
02A327
(
2016
).
113.
S.
Baudis
and
M.
Behl
,
Macromol. Rapid Commun.
43,
2100400
(
2021
).
114.
J.
Kerner
,
A.
Dogan
, and
H.
von Recum
,
Acta Biomater.
130
,
54
(
2021
).
115.
H. M.
Rostam
 et al,
Matter
2
,
1564
(
2020
).
116.
M. J.
Vassey
 et al,
Adv. Sci.
7
,
1903392
(
2020
).
117.
C. Y.
Lee
,
G. M.
Harbers
,
D. W.
Grainger
,
L. J.
Gamble
, and
D. G.
Castner
,
J. Am. Chem. Soc.
129
,
9429
(
2007
).
118.
B. T.
Wickes
,
Y.
Kim
, and
D. G.
Castner
,
Surf. Interface Anal.
35
,
640
(
2003
).
119.
T. G.
Lee
,
H. K.
Shon
,
K. B.
Lee
,
J.
Kim
,
I. S.
Choi
, and
D. W.
Moon
,
J. Vac. Sci. Technol. A
24
,
1203
(
2006
).
120.
H. K.
Shon
,
J. G.
Son
,
K. B.
Lee
,
J.
Kim
,
M. S.
Kim
,
I. S.
Choi
, and
T. G.
Lee
,
Bull. Korean Chem. Soc.
34
,
815
(
2013
).
121.
N.
Scoutaris
,
A. L.
Hook
,
P. R.
Gellert
,
C. J.
Roberts
,
M. R.
Alexander
, and
D. J.
Scurr
,
J. Mater. Sci. Mater.Med.
23
,
385
(
2012
).
122.
D. J.
Scurr
,
T.
Horlacher
,
M. A.
Oberli
,
D. B.
Werz
,
L.
Kroeck
,
S.
Bufali
,
P. H.
Seeberger
,
A. G.
Shard
, and
M. R.
Alexander
,
Langmuir
26
,
17143
(
2010
).
123.
P. J.
Cumpson
,
N.
Sano
,
I. W.
Fletcher
,
J. F.
Portoles
,
M.
Bravo-Sanchez
, and
A. J.
Barlow
,
Surf. Interface Anal.
47
,
986
(
2015
).
124.
N.
Halko
,
P.-G.
Martinsson
, and
J. A.
Tropp
,
SIAM Rev.
53
,
217
(
2011
).
125.
P. J.
Cumpson
,
I. W.
Fletcher
,
N.
Sano
, and
A. J.
Barlow
,
Surf. Interface Anal.
48
,
1328
(
2016
).
126.
I. M.
Sobol
,
USSR Comput. Math. Math. Phys.
7
,
86
(
1967
).
127.
S.
Van Nuffel
,
C.
Parmenter
,
D. J.
Scurr
,
N. A.
Russell
, and
M.
Zelzer
,
Analyst
141
,
90
(
2016
).
128.
W.
Gardner
,
D. A.
Winkler
,
D.
Ballabio
,
B. W.
Muir
, and
P. J.
Pigram
,
Biointerphases
15
,
061004
(
2020
).
129.
J.
Zhang
,
Q.
Du
,
X.
Song
,
S.
Gao
,
X.
Pang
,
Y.
Li
,
R.
Zhang
,
Z.
Abliz
, and
J.
He
,
Theranostics
10
,
2621
(
2020
).
130.
L.
Van Der Maaten
,
Artif. Intell. Stat.
5
,
384
(
2009
).
131.
M.
Ankerst
,
M. M.
Breunig
,
H.-P.
Kriegel
, and
J.
Sander
,
J SIGMOD Rec.
28
,
49
(
1999
).
132.
T.
Alexandrov
and
J. H.
Kobarg
,
Bioinformatics
27
,
i230
(
2011
).
133.
T.
Alexandrov
,
M.
Becker
,
S.-O.
Deininger
,
G.
Ernst
,
L.
Wehder
,
M.
Grasmair
,
F.
von Eggeling
,
H.
Thiele
, and
P.
Maass
,
J. Proteome Res.
9
,
6535
(
2010
).
134.
M.
Grasmair
, “
Locally adaptive total variation regularization
,” in
Scale Space and Variational Methods in Computer Vision
, edited by
X. C.
Tai
,
K.
Mørken
,
M.
Lysaker
, and
K.-A.
Lie
(
Springer
,
Berlin
,
2009
). pp
331
342
.
135.
D.
Trede
 et al,
Anal. Chem.
84
,
6079
(
2012
).
136.
C.
Faloutsos
and
K.-I.
Lin
, “
FastMap: A fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets
,”
Proceedings of the 1995 ACM SIGMOD International Conference on Management of Data, Association for Computing Machinery
,
San Jose, CA
, March 22–25, 1992 (Association for Computing Machinery, San Jose, CA,
1995
), pp.
163
174
.
137.
T.
Alexandrov
,
I.
Chernyavsky
,
M.
Becker
,
F.
von Eggeling
, and
S.
Nikolenko
,
Anal. Chem.
85
,
11189
(
2013
).
138.
W.
Zhang
,
M.
Claesen
,
T.
Moerman
,
M. R.
Groseclose
,
E.
Waelkens
,
B.
De Moor
, and
N.
Verbeeck
,
Anal. Bioanal. Chem.
413
,
2803
(
2021
).
139.
F.
Chollet
, “
Xception: Deep learning with depthwise separable convolutions
,”
2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
, Hawaii, 21–26 July 2017 (IEEE, Honolulu, HI,
2017
), pp.
1800
1807
.
140.
J.
Deng
,
W.
Dong
,
R.
Socher
,
L.
Li
,
L.
Kai
, and
F.-F.
Li
, “
ImageNet: A large-scale hierarchical image database
,”
IEEE Conference on Computer Vision and Pattern Recognition
, Florida, 20–25 June 2009 (IEEE, Miami, FL,
2009
), pp.
248
255
.
141.
N.
Tuccitto
,
A.
Bombace
,
A.
Auditore
,
A.
Valenti
,
A.
Torrisi
,
G.
Capizzi
, and
A.
Licciardello
,
Anal. Chem.
93
,
14099
(
2021
).
142.
R.
Tibshirani
,
G.
Walther
, and
T.
Hastie
,
J. R. Stat. Soc., Ser. B
63
,
411
(
2001
).
143.
T.
Caliński
and
J.
Harabasz
,
Commun. Stat.
3
,
1
(
1974
).
144.
P. J.
Rousseeuw
,
J. Comput. Appl. Math.
20
,
53
(
1987
).
145.
D. L.
Davies
and
D. W.
Bouldin
, “A cluster separation measure,”
IEEE Trans. Patt. Anal. Mach. Intell.
1
, 224 (1979).
146.
D.
Ballabio
,
V.
Consonni
, and
R.
Todeschini
,
Chemom. Intell. Lab. Syst.
98
,
115
(
2009
).
147.
D.
Ballabio
and
M.
Vasighi
,
Chemom. Intell. Lab. Syst.
118
,
24
(
2012
).
148.
See the supplementary material at https://www.scitation.org/doi/suppl/10.1116/6.0001590 for expanded discussion on the ToF-SIMS imaging literature comparing various MF techniques.

Supplementary Material

You do not currently have access to this content.