Mini useR! in Melbourne https://www.meetup.com/fr-FR/MelbURN-Melbourne-Users-of-R-Network/events/251933078/ MelbURN (Melbourne useR group) https://www.meetup.com/fr-FR/MelbURN-Melbourne-Users-of-R-Network July 16th, 2018 Melbourne, Australia

1. Learning from (dis)similarity data
Nathalie Vialaneix
nathalie.vialaneix@inra.fr
http://www.nathalievialaneix.eu
MelbURN 2018
July 16th, 2018 - Melbourne, Australia
Nathalie Vialaneix | Learning from (dis)similarity data 1/24

2. What are my data like?
Nathalie Vialaneix | Learning from (dis)similarity data 2/24

3. A medieval social network [Boulet et al., 2008, Rossi et al., 2013]
corpus with more than 6,000
transactions, 3 centuries, all
related to
Castelnau Montratier
Nathalie Vialaneix | Learning from (dis)similarity data 3/24

4. A medieval social network [Boulet et al., 2008, Rossi et al., 2013]
corpus with more than 6,000
transactions, 3 centuries, all
related to
Castelnau Montratier
Individual
Transaction
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
Ratier
Ratier (II) Castelnau
Jean Laperarede
Bertrande Audoy
Gailhard Gourdon
Guy Moynes (de)
Pierre Piret (de)
Bernard Audoy
Hélène Castelnau
Guiral Baro
Bernard Audoy
Arnaud Bernard Laperarede
Guilhem Bernard Prestis
Jean Manas
Jean Laperarede
Jean Laperarede
Jean Roquefeuil
Jean Pojols
Ramond Belpech
Raymond Laperarede
Bertrand Prestis (de)
Ratier
(Monseigneur) Roquefeuil (de)
Guilhem Bernard Prestis
Arnaud Gasbert Castanhier (del)
Ratier (III) Castelnau
Pierre Prestis (de)
P Valeribosc
Guillaume Marsa
Berenguier Roquefeuil
Arnaud Bernard Perarede
Jean Roquefeuil
Arnaud I Audoy
Arnaud Bernard Perarede
bipartite network with more than 17,000
nodes (∼ 10,000 individuals)
What can we learn from the French
medieval society?
Nathalie Vialaneix | Learning from (dis)similarity data 3/24

5. Career paths [Olteanu and Villa-Vialaneix, 2015]
Survey “Génération 98”: labor market
status (9 categories) on more than
16,000 people having graduated in 1998
during 94 months. 1
1. Available thanks to Génération 1998 à 7 ans - 2005, [producer] CEREQ, [diffusion] Centre Maurice Halbwachs (CMH).
Nathalie Vialaneix | Learning from (dis)similarity data 4/24

6. Career paths [Olteanu and Villa-Vialaneix, 2015]
Survey “Génération 98”: labor market
status (9 categories) on more than
16,000 people having graduated in 1998
during 94 months. 1
How to cluster career paths into
homogeneous groups?
1. Available thanks to Génération 1998 à 7 ans - 2005, [producer] CEREQ, [diffusion] Centre Maurice Halbwachs (CMH).
Nathalie Vialaneix | Learning from (dis)similarity data 4/24

7. Career paths [Olteanu and Villa-Vialaneix, 2015]
Survey “Génération 98”: labor market
status (9 categories) on more than
16,000 people having graduated in 1998
during 94 months. 1
How to cluster career paths into
homogeneous groups?
It is all about distance...
χ2
dissimilarity emphasizes the
contemporary identical situations
Optimal-matching dissimilarities is
more focused on the sequences
similarities
[Needleman and Wunsch, 1970]
(or “edit distance”, “Levenshtein
distance”)
1. Available thanks to Génération 1998 à 7 ans - 2005, [producer] CEREQ, [diffusion] Centre Maurice Halbwachs (CMH).
Nathalie Vialaneix | Learning from (dis)similarity data 4/24

8. and then I went into NGS data...
and again...
distances are everywhere
Nathalie Vialaneix | Learning from (dis)similarity data 5/24

9. a collection of NGS data...
DNA barcoding
Astraptes fulgerator
optimal matching
(edit) distances to
differentiate species
Nathalie Vialaneix | Learning from (dis)similarity data 6/24

10. a collection of NGS data...
DNA barcoding
Astraptes fulgerator
optimal matching
(edit) distances to
differentiate species
Hi-C data
pairwise measure (similarity) related to
the physical 3D distance between loci in
the cell, at genome scale
Nathalie Vialaneix | Learning from (dis)similarity data 6/24

11. a collection of NGS data...
DNA barcoding
Astraptes fulgerator
optimal matching
(edit) distances to
differentiate species
Hi-C data
pairwise measure (similarity) related to
the physical 3D distance between loci in
the cell, at genome scale
Metagenomics
dissemblance between
samples is better
captured when
phylogeny between
species is taken into
account (unifrac
distances)
Nathalie Vialaneix | Learning from (dis)similarity data 6/24

12. Relational Self-Organizing Map
algorithm
Nathalie Vialaneix | Learning from (dis)similarity data 7/24

13. Basics on (standard) stochastic SOM
[Kohonen, 2001]
x
x
x
(xi)i=1,...,n ⊂ Rd
are affected to a unit f(xi) ∈ {1, . . . , U}
the grid is equipped with a “distance” between units: d(u, u ) and
observations affected to close units are close in Rd
every unit u corresponds to a prototype, pu (x) in Rd
Nathalie Vialaneix | Learning from (dis)similarity data 8/24

14. Basics on (standard) stochastic SOM
[Kohonen, 2001]
x
x
x
Iterative learning (assignment step): xi is picked at random within (xk )k
and affected to best matching unit:
ft
(xi) = arg min
u
xi − pt
u
2
Nathalie Vialaneix | Learning from (dis)similarity data 8/24

15. Basics on (standard) stochastic SOM
[Kohonen, 2001]
x
x
x
Iterative learning (representation step): all prototypes in neighboring units
are updated with a gradient descent like step:
pt+1
u ←− pt
u + µ(t)Ht
(d(f(xi), u))(xi − pt
u)
Nathalie Vialaneix | Learning from (dis)similarity data 8/24

16. Extension of SOM to data described by a kernel or a
dissimilarity
[Olteanu and Villa-Vialaneix, 2015]
Data: (xi)i=1,...,n ∈ Rd
1: Initialization:
randomly set p0
1
, ..., p0
U
in Rd
2: for t = 1 → T do
3: pick at random i ∈ {1, . . . , n}
4: Assignment
ft
(xi) = arg min
u=1,...,U
xi − pt
u
2
βt
u
5: for all u = 1 → U do Representation
6:
pt+1
u = pt
u + µ(t)Ht
(d(ft
(xi), u))
7: end for
8: end for
Nathalie Vialaneix | Learning from (dis)similarity data 9/24

17. Extension of SOM to data described by a kernel or a
dissimilarity
[Olteanu and Villa-Vialaneix, 2015]
Data: (xi)i=1,...,n ∈ X
1: Initialization:
randomly set p0
1
, ..., p0
U
in Rd
2: for t = 1 → T do
3: pick at random i ∈ {1, . . . , n}
4: Assignment
ft
(xi) = arg min
u=1,...,U
xi − pt
u
2
βt
u
5: for all u = 1 → U do Representation
6:
pt+1
u = pt
u + µ(t)Ht
(d(ft
(xi), u))
7: end for
8: end for
Nathalie Vialaneix | Learning from (dis)similarity data 9/24

18. Extension of SOM to data described by a kernel or a
dissimilarity
[Olteanu and Villa-Vialaneix, 2015]
Data: (xi)i=1,...,n ∈ X
1: Initialization:
p0
u ∼ n
i=1 β0
ui
xi (convex combination)
2: for t = 1 → T do
3: pick at random i ∈ {1, . . . , n}
4: Assignment
ft
(xi) = arg min
u=1,...,U
xi − pt
u
2
βt
u
5: for all u = 1 → U do Representation
6:
pt+1
u = pt
u + µ(t)Ht
(d(ft
(xi), u))
7: end for
8: end for
Nathalie Vialaneix | Learning from (dis)similarity data 9/24

19. Extension of SOM to data described by a kernel or a
dissimilarity
[Olteanu and Villa-Vialaneix, 2015]
Data: (xi)i=1,...,n ∈ X
1: Initialization:
p0
u ∼ n
i=1 β0
ui
xi (convex combination)
2: for t = 1 → T do
3: pick at random i ∈ {1, . . . , n}
4: Assignment
ft
(xi) = arg min
u=1,...,U
βt
uD(pt
u, xi)
5: for all u = 1 → U do Representation
6:
pt+1
u = pt
u + µ(t)Ht
(d(ft
(xi), u))
7: end for
8: end for
Nathalie Vialaneix | Learning from (dis)similarity data 9/24

20. Extension of SOM to data described by a kernel or a
dissimilarity
[Olteanu and Villa-Vialaneix, 2015]
Data: (xi)i=1,...,n ∈ X
1: Initialization:
p0
u ∼ n
i=1 β0
ui
xi (convex combination)
2: for t = 1 → T do
3: pick at random i ∈ {1, . . . , n}
4: Assignment
ft
(xi) = arg min
u=1,...,U
βt
uD(pt
u, xi)
5: for all u = 1 → U do Representation
6:
pt+1
u = pt
u + µ(t)Ht
(d(ft
(xi), u)) ∼ xi − pt
u
7: end for
8: end for
Nathalie Vialaneix | Learning from (dis)similarity data 9/24

21. Extension of SOM to data described by a kernel or a
dissimilarity
[Olteanu and Villa-Vialaneix, 2015]
Data: (xi)i=1,...,n ∈ X
1: Initialization:
p0
u ∼ n
i=1 β0
ui
xi (convex combination)
2: for t = 1 → T do
3: pick at random i ∈ {1, . . . , n}
4: Assignment
ft
(xi) = arg min
u=1,...,U
βt
u(βt
u) D(., xi) −
1
2
(βt
u) Dβt
u
5: for all u = 1 → U do Representation
6:
βt+1
u = βt
u + µ(t)Ht
(d(ft
(xi), u)) 1i − βt
u
7: end for
8: end for
Nathalie Vialaneix | Learning from (dis)similarity data 9/24

22. Note on drawbacks of RSOM
Two main drawbacks:
For T ∼ γn iterations, complexity of RSOM is O(γn3
U) (compared to
O(γUdn) for numeric) [Rossi, 2014]
Nathalie Vialaneix | Learning from (dis)similarity data 10/24

23. Note on drawbacks of RSOM
Two main drawbacks:
For T ∼ γn iterations, complexity of RSOM is O(γn3
U) (compared to
O(γUdn) for numeric) [Rossi, 2014]
Exact solution proposed in [Mariette et al., 2017] to reduce the
complexity to O(γn2
U) with additional storage memory of O(Un)
Nathalie Vialaneix | Learning from (dis)similarity data 10/24

24. Note on drawbacks of RSOM
Two main drawbacks:
For T ∼ γn iterations, complexity of RSOM is O(γn3
U) (compared to
O(γUdn) for numeric) [Rossi, 2014]
Exact solution proposed in [Mariette et al., 2017] to reduce the
complexity to O(γn2
U) with additional storage memory of O(Un)
For the non Euclidean case, the learning algorithm can be very
unstable (saddle points)
Nathalie Vialaneix | Learning from (dis)similarity data 10/24

25. Note on drawbacks of RSOM
Two main drawbacks:
For T ∼ γn iterations, complexity of RSOM is O(γn3
U) (compared to
O(γUdn) for numeric) [Rossi, 2014]
Exact solution proposed in [Mariette et al., 2017] to reduce the
complexity to O(γn2
U) with additional storage memory of O(Un)
For the non Euclidean case, the learning algorithm can be very
unstable (saddle points)
clip or flip? [Chen et al., 2009]
Nathalie Vialaneix | Learning from (dis)similarity data 10/24

26. SOMbrero
[Villa-Vialaneix, 2017]
SOMbrero is an R package implementing stochastic variants of SOM
for non vectorial data
Specifically well adapted to...
non expert use and teaching
use with graphs and obtain simplified representations
first release: March 2013; latest release: Feb. 2018 (version 1.2.3)
depends on R (version ≥ 3.1.0) http://www.r-project.org
and on several packages available on CRAN:
wordcloud, igraph, RColorBrewer, scatterplot3d, knitr, shiny
available at https://cran.r-project.org/package=SOMbrero
(licence GPL) and can be installed from inside R using
install.packages("SOMbrero")
Nathalie Vialaneix | Learning from (dis)similarity data 11/24

27. Training
mysom <- trainSOM(iris[ ,1:4], ...)
Options to train the SOM:
grid: square grid, with arbitrary width and length
distance between units: standard distances as in dist or "letremy" (Euclidean then
"maximum")
neighborhood relationship: Gaussian or "letremy"
prototypes: initialized randomly, with a PCA, with random observations from the training
sample
preprocessing: centering, scaling to unit variance or nothing
training: number of iterations, standard or Heskes’s assignment step
ft
(xi) ← arg min
u=1,...,U
U
u =1
Ht
(d(u, u )) xi − pt−1
u
2
Nathalie Vialaneix | Learning from (dis)similarity data 12/24

28. Diagnostic tools
quality(mysom)
topographic error: average frequency (over the samples) for which the
prototypes that comes closest is in the direct neighborhood on the
grid of the BMU
quantization error
Q =
1
n
n
i=1
xi − pf(xi)
2
Nathalie Vialaneix | Learning from (dis)similarity data 13/24

29. Plots...
plot(mysom,
what = c("observations", "prototypes", "add"),
type = ..., ...)
Nathalie Vialaneix | Learning from (dis)similarity data 14/24

30. Super-clustering
mysom.sc <- superClass(mysom)
Nathalie Vialaneix | Learning from (dis)similarity data 15/24

31. Start with SOMbrero
3 datasets corresponding to the three types of data that SOMbrero
can handle (iris, presidentielles2002 and lesmis, a graph from
“Les Misérables”)
Nathalie Vialaneix | Learning from (dis)similarity data 16/24

32. Start with SOMbrero
3 datasets corresponding to the three types of data that SOMbrero
can handle (iris, presidentielles2002 and lesmis, a graph from
“Les Misérables”)
comprehensive (HTML) vignettes included in the package and
available on the website
Nathalie Vialaneix | Learning from (dis)similarity data 16/24

33. Start with SOMbrero
3 datasets corresponding to the three types of data that SOMbrero
can handle (iris, presidentielles2002 and lesmis, a graph from
“Les Misérables”)
comprehensive (HTML) vignettes included in the package and
available on the website
Web User Interface (made with shiny) for using the package even if
you do not know R programming language (included in the package
with sombreroGUI() Tested and approved on an historian!
Nathalie Vialaneix | Learning from (dis)similarity data 16/24

34. RSOM for mining a medieval social network
with the heat kernel
Individual
Transaction
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
Ratier
Ratier (II) Castelnau
Jean Laperarede
Bertrande Audoy
Gailhard Gourdon
Guy Moynes (de)
Pierre Piret (de)
Bernard Audoy
Hélène Castelnau
Guiral Baro
Bernard Audoy
Arnaud Bernard Laperarede
Guilhem Bernard Prestis
Jean Manas
Jean Laperarede
Jean Laperarede
Jean Roquefeuil
Jean Pojols
Ramond Belpech
Raymond Laperarede
Bertrand Prestis (de)
Ratier
(Monseigneur) Roquefeuil (de)
Guilhem Bernard Prestis
Arnaud Gasbert Castanhier (del)
Ratier (III) Castelnau
Pierre Prestis (de)
P Valeribosc
Guillaume Marsa
Berenguier Roquefeuil
Arnaud Bernard Perarede
Jean Roquefeuil
Arnaud I Audoy
Arnaud Bernard Perarede
[Boulet et al., 2008]
Graph induced by clusters:
has nice relations with space and time
emphasizes leading people
has helped to identify problems in the
database (namesakes)
But: biggest communities are still
very complex
Nathalie Vialaneix | Learning from (dis)similarity data 17/24

35. RSOM for typology of Astraptes fulgerator from DNA
barcoding
Edit distances between DNA sequences [Olteanu and Villa-Vialaneix, 2015]
Almost perfect clustering (identifying a possible label error on one sample)
with (in addition) information on relations between species.
Nathalie Vialaneix | Learning from (dis)similarity data 18/24

36. RSOM for typology of school-to-time transitions
Edit distance between 12,000 categorical time series
Nathalie Vialaneix | Learning from (dis)similarity data 19/24

37. Also in SOMbrero: KORRESP
[Cottrell and Letrémy, 2005]
Data: contingency table T = (nij)ij with p rows and q columns transformed
into a numeric dataset X:
X =
columns rows
columns
rows
column profile
row profile
with
∀ i = 1, . . . , p and ∀ j = 1, . . . , q, xij =
nij
ni.
× n
n.j
Nathalie Vialaneix | Learning from (dis)similarity data 20/24

38. Also in SOMbrero: KORRESP
[Cottrell and Letrémy, 2005]
Data: contingency table T = (nij)ij with p rows and q columns transformed
into a numeric dataset X:
X =
columns rows
columns
rows
augmented
column profile
augmented row
profile
with
∀ i = 1, . . . , p and ∀ j = q + 1, . . . , q + p, xij = xk(i)+p,j with
k(i) = arg maxk=1,...,q xik
Nathalie Vialaneix | Learning from (dis)similarity data 20/24

39. Also in SOMbrero: KORRESP
[Cottrell and Letrémy, 2005]
Data: contingency table T = (nij)ij with p rows and q columns transformed
into a numeric dataset X:
X =
columns rows
columns
rows
augmented
column profile
augmented row
profile
column profile
row profile
assignment uses reduced profile
representation uses augmented profile
alternatively process row profiles and column profiles
Nathalie Vialaneix | Learning from (dis)similarity data 20/24

40. Also available in SOMbrero
mysom <- trainSOM(presidentielles2002 , type = "korresp")
plot(mysom, what = "obs", type = "names")
Nathalie Vialaneix | Learning from (dis)similarity data 21/24

41. SOMbrero
Madalina Olteanu,
Fabrice Rossi, Marie Cottrell,
Laura Bendhaïba and
Julien Boelaert
SOMbrero and mixKernel
Jérôme Mariette
adjclust
Pierre Neuvial, Guillem Rigail, Christophe Ambroise and
Shubham Chaturvedi
Nathalie Vialaneix | Learning from (dis)similarity data 22/24

42. Don’t miss useR! 2019
user2019.r-project.org
Nathalie Vialaneix | Learning from (dis)similarity data 23/24

43. Credits for pictures
Slide 2: Linking Open Data cloud diagram 2017, by Andrejs Abele, John P. McCrae,
Paul Buitelaar, Anja Jentzsch and Richard Cyganiak. http://lod-cloud.net/
Slide 3: Picture of Castelnau Montratier from
https://commons.wikimedia.org/wiki/File:
Place_Gambetta,_Castelnau-Montratier.JPG by Duch.seb CC BY-SA 3.0
Slide 4: image based on ENCODE project, by Darryl Leja (NHGRI), Ian Dunham
(EBI) and Michael Pazin (NHGRI)
Slide 6: Astraptes picture is from
https://www.flickr.com/photos/39139121@N00/2045403823/ by Anne Toal
(CC BY-SA 2.0), Hi-C experiment is taken from the article Matharu et al., 2015
DOI:10.1371/journal.pgen.1005640 (CC BY-SA 4.0) and metagenomics illustration is
taken from the article Sommer et al., 2010 DOI:10.1038/msb.2010.16 (CC BY-NC-SA
3.0)
Slide 12: TADS picture is from the article Fraser et al., 2015
DOI:10.15252/msb.20156492 (CC BY-SA 4.0)
Nathalie Vialaneix | Learning from (dis)similarity data 24/24

44. References
Boulet, R., Jouve, B., Rossi, F., and Villa, N. (2008).
Batch kernel SOM and related Laplacian methods for social network analysis.
Neurocomputing, 71(7-9):1257–1273.
Chen, Y., Garcia, E., Gupta, M., Rahimi, A., and Cazzanti, L. (2009).
Similarity-based classification: concepts and algorithm.
Journal of Machine Learning Research, 10:747–776.
Cottrell, M. and Letrémy, P. (2005).
How to use the Kohonen algorithm to simultaneously analyse individuals in a survey.
Neurocomputing, 63:193–207.
Kohonen, T. (2001).
Self-Organizing Maps, 3rd Edition, volume 30.
Springer, Berlin, Heidelberg, New York.
Mariette, J., Rossi, F., Olteanu, M., and Villa-Vialaneix, N. (2017).
Accelerating stochastic kernel som.
In Verleysen, M., editor, XXVth European Symposium on Artificial Neural Networks, Computational Intelligence and Machine
Learning (ESANN 2017), pages 269–274, Bruges, Belgium. i6doc.
Needleman, S. and Wunsch, C. (1970).
A general method applicable to the search for similarities in the amino acid sequence of two proteins.
Journal of Molecular Biology, 48(3):443–453.
Olteanu, M. and Villa-Vialaneix, N. (2015).
On-line relational and multiple relational SOM.
Neurocomputing, 147:15–30.
Rossi, F. (2014).
How many dissimilarity/kernel self organizing map variants do we need?
Nathalie Vialaneix | Learning from (dis)similarity data 24/24

45. In Villmann, T., Schleif, F., Kaden, M., and Lange, M., editors, Advances in Self-Organizing Maps and Learning Vector
Quantization (Proceedings of WSOM 2014), volume 295 of Advances in Intelligent Systems and Computing, pages 3–23,
Mittweida, Germany. Springer Verlag, Berlin, Heidelberg.
Rossi, F., Villa-Vialaneix, N., and Hautefeuille, F. (2013).
Exploration of a large database of French notarial acts with social network methods.
Digital Medievalist, 9.
Villa-Vialaneix, N. (2017).
Stochastic self-organizing map variants with the R package SOMbrero.
In Lamirel, J., Cottrell, M., and Olteanu, M., editors, 12th International Workshop on Self-Organizing Maps and Learning Vector
Quantization, Clustering and Data Visualization (Proceedings of WSOM 2017), Nancy, France. IEEE.
Nathalie Vialaneix | Learning from (dis)similarity data 24/24