T. Aste, F. Pozzi, W.-M. Song and T. Di Matteo

London 13 October 2011

A Network Approach for Information Filtering

Outline Filtering information out of complex data-sets

Local and Global information

A graph-theoretic approach for information filtering

Embedded Maximally Filtered graphs (EMFG)

Data clustering and hierarchy emerge from the graph organization

Both local and global properties of the complex dataset can be studied simultaneously

Information is encoded in the graph structure

Data clustering

Data hierarchy

Hierarchical clustering via linkage

Thresholding

Which are the genes that are co-expressed?

Gene-expression A DNA microarray is a collection of short sections of DNA regularly arranged on a support that are used to hybridize a target sample, the profiling method fluorescently labels an RNA sample during the reverse transcription when RNA is converted into complementary DNA and can detect in this way the expression of a given gene.

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Alizade et al. Nature 403 (2000) 503–511.

de Souto et al. Bioinformatics 9 (2008) 497.

Which gene is expressed in which sample?

Which is the relation with physiological properties?

Rhoan Williams

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2005 2006 2007 2008 2009−0.1

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2005 2006 2007 2008 2009−0.1

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2005 2006 2007 2008 2009−0.1

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Financial markets dynamics

Which firms behave similarly / dissimilarly?

Which is the collective price dynamics?

Which is the relation with market dynamics?

Brain activity

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Which are the relations between the different parts?

Which part of the brain are simultaneously active?

Which is the collective dynamics during a specific task?

Henrik J. Jensen

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pi(t)stocks prices

401 firms on the US equity market from 01/01/96 to 01/01/2009

401*400/2 = 80,200 entries

correlation coefficients between log-returns

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xi(t) = log(pi(t + τ ))− log(pi(t))

13 years ~ 3000 days

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p(x1,x

2) ≠ p

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Ci, j ≠ 0

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Cov(X,Y ) = P(X ≤ x,Y ≤ y) −∫∫ PX (X ≤ x)PY (Y ≤ y)dxdy

Hoeffding identity:

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ρi, j =Covi, j

σ iσ j

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Covi, j = (xi − xi )(x j − x j )

Pearson’s cross-correlations

similarity / dependency measure

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I(X;Y ) =x∈X ,y∈Y

∑ p(x,y)lnp(x,y)

pX (x)pY (y)

Mutual Information

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N(N −1)

2different elements with a lot of redundant information only order N is significant

The information of the similarity matrix is associated to the complete graph Kn

Distribution of correlation coefficients

Distribution of eigenvalues

less than 1% of the correlations are not significant within a 90% confidence factor against a null hypothesis. About 10 eigenvalues are above λmax.

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λmin

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Q =T

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p(λ) =Q

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λ

A. M. Sengupta, P. P. Mitra, Phys. Rev. E. 60 (1999) 3389–3392.

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The information of the similarity matrix is associated to the complete graph Kn

Distribution of correlation coefficients

Distribution of eigenvalues

less than 1% of the correlations are not significant within a 90% confidence factor against a null hypothesis. About 10 eigenvalues are above λmax.

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A. M. Sengupta, P. P. Mitra, Phys. Rev. E. 60 (1999) 3389–3392.

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N(N −1)

2different elements with a lot of redundant information only order N is significant

The information of the similarity matrix is associated to the complete graph Kn

Distribution of correlation coefficients

Distribution of eigenvalues

less than 1% of the correlations are not significant within a 90% confidence factor against a null hypothesis. About 10 eigenvalues are above λmax.

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=1+1

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λmax

=1+1

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Q =T

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p(λ) =Q

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(λmax − λ)(λ − λmin )

λ

A. M. Sengupta, P. P. Mitra, Phys. Rev. E. 60 (1999) 3389–3392.

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N(N −1)

2different elements with a lot of redundant information only order N is significant

The information of the similarity matrix is associated to the complete graph Kn

Distribution of correlation coefficients

Distribution of eigenvalues

less than 1% of the correlations are not significant within a 90% confidence factor against a null hypothesis. About 10 eigenvalues are above λmax.

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λmin

=1+1

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λmax

=1+1

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Q =T

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p(λ) =Q

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(λmax − λ)(λ − λmin )

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A. M. Sengupta, P. P. Mitra, Phys. Rev. E. 60 (1999) 3389–3392.

We want to filter information by keeping the network of

important links only

maximize information content connect the ‘right’ links maximizing retained ‘information’ evolve / adapt capability to re-wire links according to a local rule providing a consistent description of the system through time

reduce complexity reduce the number of links and the network interwovenness without any tresholding

Such network must:

How can we achieve this?

…but by building networks on surfaces

NOT BY Thresholding!

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N→ Sg

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g ≥ g∗ =(N − 3)(N − 4)

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G. Ringel, Map Color Theorem, Springer-Verlag, Berlin, (1974) cap. 4 P. J. Gilbin, Graphs, Surfaces and Homology, Chapman and Hall, 2nd edition (1981) G. Ringel and J. W. T. Youngs, Proc. Nat. Acad. Sci. USA 60 (1968) 438-445.

The embedding of KN is possible on an orientable surface Sg of genus

• locally planar • natural hierarchy • controlled interwovenness • elementary moves

Any network can be embedded on a surface!!

WHY SURFACES ?

any ΓN is a sub-graph of KN and can be embedded on Sg

Graph Embedded on Surfaces

The surface constraints the network complexity (the degree of interwovenness)

g = 0 sphere 0 non-contractible loops 0 cut 0 handle

g = 1 torus 2 non-contractible loops 1 cuts 1 handle

g = 2 4 non-contractible loops 2 cuts 2 handles

double torus

Which surfaces?

K4

K5 K6 K7

K8

What do we embed on such surfaces?

Embedded Maximally Filtered Graphs

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max( ai, ji, j

∑ Ii, j )

The simplest case is the spherical surface with g=0 (PMFG graphs ) M. Tumminello, T. A, T. Di Matteo and R. N. Mantegna, PNAS 102, Num. 30 (2005) 10421-10426.

N - E + F = χ = 2(1-g) 3 F = 2 E <k> N = 2 E (6 - <k>)N = 12(1-g)

K5 K3,3

Kuratowski’s theorem A finite graph is planar if and only if it does not contain a subgraph that is an expansion of K5 or K3,3

K4 K3

Planar graphs g = 0

PMFG

http://www.mathworks.com/matlabcentral/fileexchange/27360

Sort similarities form the largest to the smallest

Connect the first two nodes on the top line of the list

Is the resulting graph planar?

Delete the top line from the list

Discard the edge Keep the edge

Have we reached the maximum number of edges?

yes no

yes

BUILDING THE PMFG

no

Building EMFG Start from a arbitrary triangulation of a surface. Make it evolve towards an optimal graph through Alexander Moves

J. W. Alexander, “The combinatorial theory of complexes” Ann. Math. 31 (1930) 292.

T1 T2

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-1 Moves T1 and T2 are topological invariants therefore we can apply them freely without changing the surface embedding.

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E(G) = ai, ji, j

∑ Ii, j

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E(G') = a'i, ji, j

∑ Ii, j

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p(G' |G) =1

1+ eβ (E(G' )−E (G ))

T A, Ruggero Gramatica and T. Di Matteo, Exploring complex networks via topological embedding on surfaces arXiv:1107.3456v1 (2011) T A, Ruggero Gramatica and T. Di Matteo, Random and frozen states in complex triangulations, Philosophical Magazine (2011). TA and D. Sherrington, "Glass transition in self organizing cellular patterns'', J. Phys. A 32 (1999) 7049-56.

PMFG for 395 US stocks

PMFG for 34 interest rates

v4!

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k3!{v3,v4,v6}!

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k2!{v2,v4,v5}!

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EXTRACTING CLUSTERS AND HIERARCHIES We extract clusters and hierarchies form the PMFG in 5 main steps built around the properties of 3-cliques in maximal planar graphs

Some cliques contain inside others providing a natural hierarchy v9!

3-cliques

Bubbles are portions of the graph which are attached to the rest of the graph by a 3-clique

Looking for “bubbles”

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v9!“bubble tree”

Identifying clusters & hierarchies (I) the bubble tree

Won-Min Song, T. Di Matteo, Tomaso Aste, Nested hierarchies in planar graphs ,Discrete Applied Mathematics 159 (2011) 2135-2146.

b1!

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in / ex= AG (v,u)

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Identifying clusters & hierarchies (II) the directed bubble tree

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Identifying clusters & hierarchies (IV) non-discrete clustering

α! β!

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k2!k1! bβ = b4!

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Identifying clusters & hierarchies (V) discrete clustering

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Clusters & hierarchies

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k2!

Won-Min Song, T. Di Matteo, TA, Hierarchical information clustering by means of topologically embedded graphs (2011)

Validation

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Fishers’ Iris data Dataset 50 iris plants from three different types of iris, (1) Iris Setosa; (2) Iris Versicolour; (3) Iris Virginica. Measures (i) sepal length; (ii) sepal width; (iii) petal length; (iv) petal width,

Fisher RA (1936) The use of multiple measurements in taxonomic problems. Annals Eugen., 7:179–188.

Test on synthetic data: clustering

Artificial time series generated with MVG with a reference correlation structure and added noise.

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FIG. 1: Pearson’s cross-correlation matrices for synthetic data generated via multivariate Gaussian generator with added

noise. Partitions with clusters with sizes: 4, 8, 16, 32, 64. First row: Gaussian noise with amplitudes c = 0.77, 2.33, 3.88

respectively (from left to right) and !!intra

= 0.9. Second row: Gaussian noise with c = 1 and three values of the intra-cluster

correlation in R!, !intra = 0.9, 0.6 and 0.3 respectively (from left to right). Third row: Power law noise with exponent at

" = 1.5 and amplitudes c = 0.09, 0.27 and 0.41 respectively (from left to right). Fourth row: Power law noise with amplitude

c = 0.1 and exponents " = 2.1, 1.4 and 1.2 respectively (from left to right).

B. Comparison between the artificial ‘true’ cluster structure and the one retrieved

from the data

We used the adjusted Rand index [2] to compare the ‘true’ clusters artificially inserted in

the correlation structure and the clusters retrieved from the analysis of the data in presence

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Figure 4. Adjusted Rand index for various data sets simulated via Gaussian and Log-normaldistribution with !!in = 0.9, !!out = 0 and Nran = 25. This case refer to a cluster structure with eightclusters of size 5 elements, and one cluster of size 64 elements. For each value of C, 30 data sets weregenerated in order to get stable statistics for < dR > and adjusted Rand score. Figure (a) and (f) arethe same of Fig.1 in the paper and are here reported for completeness and for an easier comparison.

for the DBHT, and the average linkage and the complete linkage methods are respectively reported inFigs.??(b,c,d). The comparison between the adjusted Rand index is reported in Fig.??.

Test on synthetic data: hierarchy

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1.2

1.3

1.4

1.5

1.6

(d)

FIG. 4: (a) The synthetic data structure R!. (b) Dendrogram associated with the DBHT hierarchical structure. (c)

Dendrogram associated with the Average linkage. (d) Dendrogram associated with the Complete linkage.

of the 16 ‘true’ clusters and achieving also an adjusted Rand index of 0.94. The complete

and average linkages, reported in Figs.4(c,d) give a less clear hierarchical structure. This is

indeed consistently quantified by the adjusted Rand indexes reported in Fig.4 in the paper

that are consistently lower and misplaced at the wrong number of elements with respect to

the ones associated with the DBHT hierarchy.

We tested other partitions and di!erent levels of noise verifying that the DBHT method is

consistently delivering good performances in comparison with the other established methods.

An example with power law noise with the same parameters as for the analysis in Fig.4 of

the main paper (and Fig.4 in the present supplementary information) but with clusters

of scaling sizes respectively of 4, 8, 16, 32 and 64 elements is reported in Figs.5(a). The

dendrograms for the DBHT, and the average linkage and the complete linkage methods

are respectively reported in Figs.5(b,c,d). The comparison between the the adjusted Rand

indexes are reported in Figs.6. Th results for another example with clusters of uniform sizes

6

Test on synthetic data: hierarchy

Gene-expression

Case study 1

Won-Min Song,T. Di Matteo, TA, Hierarchical information clustering by means of topologically embedded graphs (2011)

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gene expression patterns 62 cancer samples 4026 gene clones

Gene-expression

Alizade et al. Nature 403 (2000) 503–511.

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1PMFG from correlations between cancer-samples

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CDK1

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Mean Profile

SYK

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Mean Profile

TGF−B1

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Mean Profile

CDKN1B, CDKN2D

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Mean Profile

IL−6

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Mean Profile

IRF1

DCDC

D

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GG

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DD

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DTo

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LN

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AA

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DCTC

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TCTC

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F F

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RC

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D9

D: Diffuse Large B−cell Lymphoma

D9: DLCL−0009

D41: DLCL−0041

DC: DLBCL cell line

F: Follicular Lymphoma

C: Chronic Lymphocytic leukemia

A: Activated Blood B

G: Germinal Centre B

R: Resting Blood B

TC: Transformed Cell line

T: Activated/Resting Blood T

LN: Lymph Node

To: Tonsil

cluster 1

cluster 2

cluster 3

cluster 4

cluster 5

cluster 6

cluster 7

cluster 8

cluster 9

cluster 10

cluster 11

Won-Min Song,T. Di Matteo, TA, Hierarchical information clustering by means of topologically embedded graphs (2011)

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Gene-Gene correlations

PMFG

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94 380 381 382 383 3842502250322732274152118951657 277159624322433 421 422 13816001601159924222435 223 284 286 281 282 285 2832506 45 48 47 49 4611211742 287 288 290 294 289 291 292 293 295 2961554 11211861467185420212022 251 2522334 826 827 828182017661832 865 866107212201221177717861861186218771878 2221829183018281815181618381839 574 5751881117916831685181217551757181717531790169518211555176816981847167217561915169616972405154415611868160316041516198623771667328432863287 48815911403159220083321 835160517931967196815512351194019843076307517521850217118962324 164 481 825 479 486 480 4823382 248 249 250 814 816 817 819 818 820 821 823 829133213331334133521440

2

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8

10

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14

16

18

20

Gene Clustering

500 1000 1500 2000 2500 3000 3500 4000

500

1000

1500

2000

2500

3000

3500

4000

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

PMFG & DBHT from correlations between genes

(180 gene-clusters)

280528162490281528222907280631033100284429093097201726152280314529512984312212341235321924022403136627323092308525931656290126552783278428382715304628583227313919232496251314982192283930993098307930803125308630873126246930402597278726022900277727782663282427292990317528403109316928263230283230273026315231763153315431552518303629882540282132983140 1432985322821773307248324843008259828772665272427882606286428652730273111753000303932312996316130013068306530663067142239963429351138713616149235072059 115246331943195245624571470147114722471247226462908285728602903255526472648 493159519691594267827381593234523461660189118921705290217062929185225611236123712381250125121162196286122542604240422472248224926792680268136853686 127366236633664 206256626143002136335043505 12925843210 1992940298339563957293831243229 158 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233 234 235 236 237 506 507 508 509 510 511 512 514 515 513 516 517 144 145 146 147 14810792242242424152416241722433605224422452450 169 1702355 179 1802121 181 183 184 18514143214 1732445 177 197 176 1781424 17533433373 17123633629363036313960367239613962 174236221173209 52106210914101411 445 447 446 448 449 450 451241015602065 571 57214882064 970 988196416423431164434061514196533493974192120934005 98715872026158814992054 22 579 9361737 96418091779 93315702009 569 570 881173517381741 578 9742091 9322007 51 719 900 931 935 958 519 883 8891309 5651864 166 167 168 483 573 489 884 88519501951 959 9611041 968 9691093 989 990186314831641180816451675195719881989 8312069152415251526 832 8331101 52414661468 5253355 60220832073 65420821106205733561148114920563385 534 537 830190915281910 536 53840154014151015114021 5352087 5392070 545 546 6 7 8 6271044 42312851283128619941995 8611218128412823422 12 13 15 14 347 348 473 808 809 872 9761015 47218601188 498 499 824101910221020102110232327 52 665 761 7561071 186 757 758 752 753 759 760 770 310 311 905 941 800 801 802 341 342 343 411 412 746 747 748 749 750 751 6351565 7801421156615671568 340118011811151 469 7251030 568 952 7241699 730 901 904 956112811291130113111321133113411351136 18 19 20 547165116501770 60917581653175918191849171517611746193918141848 9601787176017881762 9661700165416771782 4771577157815891646167316741647132213231324 96314691473 484 4851573177517672390 5291558155917311783 610 898 89717891952 57617741874 96217491671179917501751179618851614176317841532195517181719 528 858177118181906155719051922140116801681122212231224164817721649217519201933179540221907194630883095191219131914195822842285232822862287 475103715751613173217331745 9101739174011001734174717481550177817361813168219661729177617301954170117021901 50167919561998 550188815011190 490 621 54915121513 46819024013 6201073 623119133051040208420613499208020793484 582130 670 4941127236122302468 3791405 385 675 703 704 701 702 90 91 92 93 45710571638 795 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3374012185718372289185819831859 464 4781870 541 868184310591652 836178017811517 492184518941529 867190315491773187118721831181019961997 118 11914571458 189 597 598 261 263 262 2641014101610172140214121422174111118341835183618331855185623532354332433253326332733283329348934903491 16 1710311805108418031949 25 470 728 727 729 3361693 555 556157418042321 208 20913641365 3391215 812 8132543 220 221 8371867 838 95316841694 977121918021402 4201081 520 5571429 5521070106810692006 324 3262429 327 3251120213121692170 49119811534153523292330197719791978115611571161116216881687328812021203120412051233186632901726172717281195120012013093309411451146115911601360136125453289142724282425242624271545184624792480 161 202 205 2041158 200 2013022 318 320 3213320 319 323 32211772394239513861387168618861887 962493 97 98 99 400 4011355135613572145 395 39612111372137313741375 238 27014751853226522662301 271 2721380 424 273 276 274 275 33 34 35 36 373564 39 44 38 42 40 41 43228811711172208914283291 7425072508 94 380 381 382 383 3842502250322732274152118951657 277159624322433 421 422 13816001601159924222435 223 284 286 281 282 285 2832506 45 48 47 49 4611211742 287 288 290 294 289 291 292 293 295 2961554 11211861467185420212022 251 2522334 826 827 828182017661832 865 866107212201221177717861861186218771878 2221829183018281815181618381839 574 5751881117916831685181217551757181717531790169518211555176816981847167217561915169616972405154415611868160316041516198623771667328432863287 48815911403159220083321 835160517931967196815512351194019843076307517521850217118962324 164 481 825 479 486 480 4823382 248 249 250 814 816 817 819 818 820 821 823 829133213331334133521440

2

4

6

8

10

12

14

16

18

20

500 1000 1500 2000 2500 3000 3500 4000

500

1000

1500

2000

2500

3000

3500

4000

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

2

8

0

5

2

8

1

6

2

4

9

0

2

8

1

5

2

8

2

2

2

9

0

7

2

8

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02468

1

0

1

2

1

4

1

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1

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2

0

Gene Clustering

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0

5

1

0

3

8

8

4

1

8

4

7

1

0

5

4

9

2

8

9

3

0

1

4

5

4

1

1

5

4

2

0

2

8

3

3

7

6

9

3

4

1

0

9

0

1

0

9

1

1

0

4

3

9

7

3

1

0

4

2

1

6

3

9

3

3

7

7

3

3

8

1

5

0

3

5

0

4

9

4

6

9

5

0

2

0

2

7

3

4

9

3

3

4

9

4

9

4

7

2

0

8

8

1

9

2

9

2

0

2

9

5

2

6

1

0

1

0

6

6

8

9

4

5

1

2

1

2

1

2

1

3

1

2

1

4

6

8

8

1

0

1

1

1

0

1

2

1

0

1

3

1

0

7

4

1

0

7

5

1

1

3

8

1

0

7

6

3

4

9

2

2

3

5

8

3

5

1

6

2

3

5

9

1

1

4

1

8

9

0

1

9

8

2

4

6

6

1

5

0

8

1

6

5

5

2

4

7

7

2

4

7

8

3

1

9

9

2

3

2

6

5

2

7

2

6

1

6

1

5

5

9

4

9

4

4

9

4

3

2

0

7

4

2

0

7

5

6

9

4

3

4

8

3

6

9

5

9

8

1

7

9

7

9

8

2

9

8

3

1

1

1

2

1

0

6

2

1

0

6

3

7

9

8

7

9

9

1

0

8

6

1

1

2

6

1

4

3

3

1

4

5

1

1

4

5

2

6

8

9

3

5

8

1

3

5

8

2

3

5

8

3

3

5

7

7

3

5

8

0

1

4

4

1

3

5

2

3

3

5

2

4

6

3

0

7

7

5

7

7

8

7

7

2

1

2

1

7

7

7

3

7

7

4

7

7

6

7

7

1

1

0

3

2

8

1

5

7

7

7

9

9

3

1

0

3

3

1

1

3

7

1

1

9

4

1

0

3

4

1

0

3

5

1

0

3

6

1

3

7

7

4

3

0

4

3

5

4

3

9

4

4

2

4

3

3

4

4

0

4

3

4

4

3

6

4

3

7

4

3

8

4

4

1

4

4

3

4

3

1

4

3

2

4

4

4

4

9

5

5

5

9

5

6

0

5

6

1

5

6

2

5

6

3

7

8

8

9

2

0

1

5

4

6

1

5

4

7

8

5

1

2

1

5

4

2

1

5

6

2

1

5

2

2

1

5

3

2

1

5

5

2

1

5

7

2

1

5

8

2

1

5

9

2

1

6

0

3

4

4

1

1

9

2

4

5

9

1

4

4

8

1

4

4

9

4

6

0

1

1

1

3

1

1

1

4

5

8

6

7

9

1

2

4

3

5

2

2

1

8

7

1

9

5

2

2

6

2

5

7

2

5

9

2

6

0

2

4

4

2

4

5

5

5

8

1

0

0

7

1

0

0

8

1

0

0

9

2

3

9

2

4

0

2

4

1

2

4

2

2

4

3

2

4

6

2

4

7

2

5

8

5

9

7

3

2

7

3

3

7

3

4

3

3

2

7

3

6

7

3

5

7

3

9

7

4

0

2

3

6

0

9

4

9

1

0

5

2

2

4

2

1

2

1

0

7

8

4

7

8

6

7

8

5

1

8

2

3

1

2

1

0

6

6

1

0

6

7

1

1

1

8

1

1

1

9

7

3

7

7

3

8

1

1

6

3

2

1

1

8

1

1

6

8

1

1

6

9

9

5

3

3

1

8

7

6

3

2

9

1

6

0

6

2

4

4

7

2

4

4

0

3

2

8

3

3

0

1

1

3

9

1

5

4

2

1

5

4

3

1

5

4

8

4

1

9

6

0

7

1

6

1

8

7

4

3

7

9

0

1

0

0

6

4

7

1

7

4

4

7

4

5

8

4

2

2

3

2

2

2

3

2

3

1

1

6

4

1

1

6

5

2

1

7

3

1

7

3

4

7

5

3

1

3

3

1

4

3

1

5

3

1

6

5

0

0

5

0

1

5

0

2

6

5

6

6

3

5

7

8

2

1

8

2

1

9

1

4

5

9

2

1

3

3

3

4

3

3

5

6

1

2

7

9

3

8

5

3

1

0

1

8

4

2

6

4

2

7

2

5

3

2

5

4

2

5

5

2

5

6

6

6

9

1

8

2

5

2

3

0

6

4

0

2

4

0

5

4

0

6

5

0

5

4

0

3

4

0

4

4

0

9

4

0

7

4

0

8

4

1

0

1

3

8

3

1

4

4

0

1

4

1

5

1

5

6

3

1

5

6

4

1

4

3

2

1

6

6

9

2

4

4

6

1

0

4

2

1

9

5

1

1

8

2

1

1

8

3

1

1

8

4

1

1

8

5

1

5

5

6

1

9

9

2

1

0

8

1

3

9

1

5

1

9

1

7

9

4

1

7

2

0

1

7

9

1

1

7

9

2

1

1

7

1

2

5

2

1

2

5

3

1

2

5

4

1

2

5

5

8

5

9

1

6

8

9

1

7

6

9

3

3

7

4

0

1

2

1

8

5

7

1

8

3

7

2

2

8

9

1

8

5

8

1

9

8

3

1

8

5

9

4

6

4

4

7

8

1

8

7

0

5

4

1

8

6

8

1

8

4

3

1

0

5

9

1

6

5

2

8

3

6

1

7

8

0

1

7

8

1

1

5

1

7

4

9

2

1

8

4

5

1

8

9

4

1

5

2

9

8

6

7

1

9

0

3

1

5

4

9

1

7

7

3

1

8

7

1

1

8

7

2

1

8

3

1

1

8

1

0

1

9

9

6

1

9

9

7

1

1

8

1

1

9

1

4

5

7

1

4

5

8

1

8

9

5

9

7

5

9

8

2

6

1

2

6

3

2

6

2

2

6

4

1

0

1

4

1

0

1

6

1

0

1

7

2

1

4

0

2

1

4

1

2

1

4

2

2

1

7

4

1

1

1

1

1

8

3

4

1

8

3

5

1

8

3

6

1

8

3

3

1

8

5

5

1

8

5

6

2

3

5

3

2

3

5

4

3

3

2

4

3

3

2

5

3

3

2

6

3

3

2

7

3

3

2

8

3

3

2

9

3

4

8

9

3

4

9

0

3

4

9

1

1

6

1

7

1

0

3

1

1

8

0

5

1

0

8

4

1

8

0

3

1

9

4

9

2

5

4

7

0

7

2

8

7

2

7

7

2

9

3

3

6

1

6

9

3

5

5

5

5

5

6

1

5

7

4

1

8

0

4

2

3

2

1

2

0

8

2

0

9

1

3

6

4

1

3

6

5

3

3

9

1

2

1

5

8

1

2

8

1

3

2

5

4

3

2

2

0

2

2

1

8

3

7

1

8

6

7

8

3

8

9

5

3

1

6

8

4

1

6

9

4

9

7

7

1

2

1

9

1

8

0

2

1

4

0

2

4

2

0

1

0

8

1

5

2

0

5

5

7

1

4

2

9

5

5

2

1

0

7

0

1

0

6

8

1

0

6

9

2

0

0

6

3

2

4

3

2

6

2

4

2

9

3

2

7

3

2

5

1

1

2

0

2

1

3

1

2

1

6

9

2

1

7

0

4

9

1

1

9

8

1

1

5

3

4

1

5

3

5

2

3

2

9

2

3

3

0

1

9

7

7

1

9

7

9

1

9

7

8

1

1

5

6

1

1

5

7

1

1

6

1

1

1

6

2

1

6

8

8

1

6

8

7

3

2

8

8

1

2

0

2

1

2

0

3

1

2

0

4

1

2

0

5

1

2

3

3

1

8

6

6

3

2

9

0

1

7

2

6

1

7

2

7

1

7

2

8

1

1

9

5

1

2

0

0

1

2

0

1

3

0

9

3

3

0

9

4

1

1

4

5

1

1

4

6

1

1

5

9

1

1

6

0

1

3

6

0

1

3

6

1

2

5

4

5

3

2

8

9

1

4

2

7

2

4

2

8

2

4

2

5

2

4

2

6

2

4

2

7

1

5

4

5

1

8

4

6

2

4

7

9

2

4

8

0

1

6

1

2

0

2

2

0

5

2

0

4

1

1

5

8

2

0

0

2

0

1

3

0

2

2

3

1

8

3

2

0

3

2

1

3

3

2

0

3

1

9

3

2

3

3

2

2

1

1

7

7

2

3

9

4

2

3

9

5

1

3

8

6

1

3

8

7

1

6

8

6

1

8

8

6

1

8

8

7

9

6

2

4

9

3

9

7

9

8

9

9

4

0

0

4

0

1

1

3

5

5

1

3

5

6

1

3

5

7

2

1

4

5

3

9

5

3

9

6

1

2

1

1

1

3

7

2

1

3

7

3

1

3

7

4

1

3

7

5

2

3

8

2

7

0

1

4

7

5

1

8

5

3

2

2

6

5

2

2

6

6

2

3

0

1

2

7

1

2

7

2

1

3

8

0

4

2

4

2

7

3

2

7

6

2

7

4

2

7

5

3

3

3

4

3

5

3

6

3

7

3

5

6

4

3

9

4

4

3

8

4

2

4

0

4

1

4

3

2

2

8

8

1

1

7

1

1

1

7

2

2

0

8

9

1

4

2

8

3

2

9

1

7

4

2

5

0

7

2

5

0

8

9

4

3

8

0

3

8

1

3

8

2

3

8

3

3

8

4

2

5

0

2

2

5

0

3

2

2

7

3

2

2

7

4

1

5

2

1

1

8

9

5

1

6

5

7

2

7

7

1

5

9

6

2

4

3

2

2

4

3

3

4

2

1

4

2

2

1

3

8

1

6

0

0

1

6

0

1

1

5

9

9

2

4

2

2

2

4

3

5

2

2

3

2

8

4

2

8

6

2

8

1

2

8

2

2

8

5

2

8

3

2

5

0

6

4

5

4

8

4

7

4

9

4

6

1

1

2

1

1

7

4

2

2

8

7

2

8

8

2

9

0

2

9

4

2

8

9

2

9

1

2

9

2

2

9

3

2

9

5

2

9

6

1

5

5

4

1

1

2

1

1

8

6

1

4

6

7

1

8

5

4

2

0

2

1

2

0

2

2

2

5

1

2

5

2

2

3

3

4

8

2

6

8

2

7

8

2

8

1

8

2

0

1

7

6

6

1

8

3

2

8

6

5

8

6

6

1

0

7

2

1

2

2

0

1

2

2

1

1

7

7

7

1

7

8

6

1

8

6

1

1

8

6

2

1

8

7

7

1

8

7

8

2

2

2

1

8

2

9

1

8

3

0

1

8

2

8

1

8

1

5

1

8

1

6

1

8

3

8

1

8

3

9

5

7

4

5

7

5

1

8

8

1

1

1

7

9

1

6

8

3

1

6

8

5

1

8

1

2

1

7

5

5

1

7

5

7

1

8

1

7

1

7

5

3

1

7

9

0

1

6

9

5

1

8

2

1

1

5

5

5

1

7

6

8

1

6

9

8

1

8

4

7

1

6

7

2

1

7

5

6

1

9

1

5

1

6

9

6

1

6

9

7

2

4

0

5

1

5

4

4

1

5

6

1

1

8

6

8

1

6

0

3

1

6

0

4

1

5

1

6

1

9

8

6

2

3

7

7

1

6

6

7

3

2

8

4

3

2

8

6

3

2

8

7

4

8

8

1

5

9

1

1

4

0

3

1

5

9

2

2

0

0

8

3

3

2

1

8

3

5

1

6

0

5

1

7

9

3

1

9

6

7

1

9

6

8

1

5

5

1

2

3

5

1

1

9

4

0

1

9

8

4

3

0

7

6

3

0

7

5

1

7

5

2

1

8

5

0

2

1

7

1

1

8

9

6

2

3

2

4

1

6

4

4

8

1

8

2

5

4

7

9

4

8

6

4

8

0

4

8

2

3

3

8

2

2

4

8

2

4

9

2

5

0

8

1

4

8

1

6

8

1

7

8

1

9

8

1

8

8

2

0

8

2

1

8

2

3

8

2

9

1

3

3

2

1

3

3

3

1

3

3

4

1

3

3

5

2

1

4

4

02468

1

0

1

2

1

4

1

6

1

8

2

0

−4

−3

−2

−1

0

1

2

3

4

5

6

1 5 3 6 2 10 7 9 4 8 11

−2

0

2

Gene Cluster44

Mean Profile

CDK1

1 5 3 6 2 10 7 9 4 8 11−4

−2

0

2

4Gene Cluster109

Mean Profile

SYK

1 5 3 6 2 10 7 9 4 8 11

−2

0

2

Gene Cluster1

Mean Profile

TGF−B1

1 5 3 6 2 10 7 9 4 8 11

−2

0

2

Gene Cluster4

Mean Profile

CDKN1B, CDKN2D

1 5 3 6 2 10 7 9 4 8 11

−5

0

5Gene Cluster125

Mean Profile

IL−6

1 5 3 6 2 10 7 9 4 8 11

−4

−2

0

2

4Gene Cluster102

Mean Profile

IRF1

Gene clusters that are significantly differentiating in the sample clusters Maximally differentiating gene clusters from a p-value threshold of 0.01 with Bonferroni correction

Gene cluster ‘44’ (significant for sample-cluster ‘1’) Key gene: CDK1 (over expressed) commonly over-expression in DLBCL cancer types Gene cluster ‘4’ (significant for sample-cluster ‘4’) Key gene: SYK (over expressed) promising target gene for antitumor therapy, inhibition of SYK increases the chance of survival Gene cluster ‘1’ (significant for sample-cluster ‘5’) Key gene: TGF-B1 (under expressed) regulates proliferation Gene cluster ‘4’ (significant for sample-cluster ‘7’) Key genes: CDKN1B/p27Kip1 and CDKN2D/p19, tumor suppressor genes (under expressed) Gene cluster ‘125’ (significant for sample-cluster ‘9’) Key genes: ‘IL-6’. IL-6 (over expressed) specific of some DLBCL related to STAT3 activation Gene cluster ‘102’ (significant for sample-cluster ‘11’) Contains IRF1 (under expressed) mediator for cell fate and tumor suppressor

Gene-Ontology analysis

DCDC

D

D

D

D

D

D

D

GG

DC

DD

D

D

D

D

D

DTo

D

LN

D

DD

DD

D DD

D

D

D

D

D D

D

D DD

D

D

D

D

D D

A

A

A

A

AA

A

A

A

AT

T

TT

T

T

DCTC

TC

TCTC

TC

TC

D41

F

F

F

F F

F

F

F

F

RR

R

RC

C

C

C

C

C

C

C

C

CC

D9

D: Diffuse Large B−cell Lymphoma

D9: DLCL−0009

D41: DLCL−0041

DC: DLBCL cell line

F: Follicular Lymphoma

C: Chronic Lymphocytic leukemia

A: Activated Blood B

G: Germinal Centre B

R: Resting Blood B

TC: Transformed Cell line

T: Activated/Resting Blood T

LN: Lymph Node

To: Tonsil

cluster 1

cluster 2

cluster 3

cluster 4

cluster 5

cluster 6

cluster 7

cluster 8

cluster 9

cluster 10

cluster 11

Financial markets dynamics

Case study 2

AA

AE

PA

GC

AIG

AIT

AR

CA

VP

AX

PB

AB

AC

BA

XB

CB

CC

BD

KB

EL

BH

IB

MY

BN

IB

SC

EN

CG

PC

HA

CH

V CI

CL

CO

LC

PB

CS

CC

SC

OD

AL

DD

DIS

DO

WE

KE

TR F

FD

XF

LR

GD

GE

GM

GT

EH

AL

HM

HN

ZH

ON

HR

SH

WP

IBM

IFF

INT

C IPJN

JJP

MK

MK

OLT

DM

AY

MC

DM

ER

MK

GM

MM

MO

MO

BM

RK

MS

FT

MT

CN

SC

NS

MN

TO

NE

OR

CL

OX

YP

EP

PG

PN

UP

RD

RA

LR

OK

RT

NB S

SLB

SO

SU

NW T

TA

NT

EK

TO

YT

XN

UC

MU

ISU

SB

UT

XV

OW

FC

WM

BW

MT

WY

XO

NX

RX

AA AEP AGC AIG AIT

ARC AVP AXP BA

BAC BAX BC

BCC BDK BEL BHI

BMY BNI BS

CEN CGP CHA CHV

CI CL

COL CPB CSC

CSCODAL DD DIS

DOW EK

ETR F

FDX FLR GD GE GM GTE HAL HM HNZ HON HRS HWP IBM IFF

INTCIP

JNJ JPM KM KO LTD MAY MCD MER MKG MMM

MO MOB MRK MSFTMTC NSC NSM

NT ONE

ORCLOXY PEP PG

PNU PRD RAL ROK RTNB

S SLB SO

SUNWT

TAN TEK TOY TXN UCM

UIS USB UTX VO

WFC WMB WMT WY XON XRX

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

M. Tumminello, T. Aste, T. Di Matteo and R. N. Mantegna, A tool for filtering information in complex systems, Proceedings of the National Academy of Sciences of the United States of America Vol. 102, Num. 30 (2005) 10421-10426.

Cross-correlation from daily returns on 100 most capitalized US from 1995 to 1998. !

AGC AIG

AVP

AXP

BA

BAC

BAX

BC

BDK

BMY

BNI

BS

CEN

CI

CL

COL

CPB

CSC

DAL DIS

EK

F

FDX

FLR

GD

GE

GM

HNZ HON

IFF

JNJ

JPM

KM

KO

LTD

MAY

MCD

MER

MKG

MMM

MO MRK

MTC

NSC

NT

ONE

PEP

PG

PNU

PRD

RAL

ROK

RTNB

S

TAN

TEK

TOY

USB

UTX

VO

WFC

WMT

XRX

AA BCC

CHA

DD

DOW

IP

WY

ARC

BHI

CGP

CHV

HAL

HM

MOB

OXY

SLB

WMB

XON

CSCOHRS

HWP

IBM

INTC

MSFT

NSM

ORCL

SUNW

TXN

UIS

AEP

AIT

BEL

ETR

GTE

SO

T

UCM

0 20 40 60 80 100 120 140 160 180 2000

10

20

30

40

50

60

70

80

90

100

AGC

AIG

AVP

AXP

BA

BAC

BAX

BC

BDK

BMY

BNI

BS

CEN

CI

CL

COL

CPB

CSC

DAL

DIS

EK

F

FDX

FLR

GD

GE

GM HNZ

HON

IFF

JNJ

JPM

KM

KO

LTD MAY

MCD

MER

MKG

MMM

MO MRK

MTC

NSC

NT

ONE

PEP

PG

PNU

PRD

RAL

ROK RTNB

S

TAN TEK

TOY

USB

UTX

VO

WFC

WMT

XRX

AA

BCCCHA

DD DOW

IP

WY

ARC

BHI

CGP

CHVHALHM

MOBOXY

SLB

WMB

XON

CSCO

HRS HWP

IBM

INTC

MSFT

NSM

ORCL

SUNWTXN

UIS

AEP

AIT

BELETR

GTESO T UCM

PMFG

M. Tumminello, T. Aste, T. Di Matteo and R. N. Mantegna, A tool for filtering information in complex systems, Proceedings of the National Academy of Sciences of the United States of America Vol. 102, Num. 30 (2005) 10421-10426.

Basic Materials (B) (Pink) Utilities (U) (Yellow) Financial (F) (Cyan) Consumer Non Cyclical (C) (Purple) Consumer Cyclical (CC) (Orange) Capital Goods (CG) (Magenta) Healthcare (H) (Brown) Services (S) (Red) Technology (T) (Green) Conglomerates (CO) (Gray) Energy (E) (Blue) Transportation (TR) (White)

Cross-correlation from daily returns on 100 most capitalized US from 1995 to 1998. !

Structure & Communities

BUBBLE TREE

AIG,AXP,BAC,GEAIG,AXP,BAC,JPM

AIG,AXP,GE,UTX

AGC,AIG,BAC,GE

AXP,BAC,GE,KO

AGC,AIG,BAC,CI

AGC,AIG,GE,NTAGC,BAC,DOW,GE

AIG,AXP,F,JPM

AIG,AXP,FLR,UTX

AIG,BAC,JPM,ONEAIG,GE,HON,UTX

AXP,BAC,JPM,MER

AXP,GE,KO,RAL

AXP,BA,GE,UTX

BAC,BMY,GE,KO

AIG,AXP,COL,FLR

AIG,BAC,ONE,USBAIG,GE,HON,S

AIG,CSCO,GE,NT

AXP,BAC,MER,XRX

AXP,F,GM,JPM

BA,GE,ROK,UTX

BAC,BMY,DIS,GE

BAC,DD,DOW,GE

BAC,JPM,MER,TAN

BAC,JPM,ONE,WFC

BMY,GE,JNJ,KO

CPB,GE,KO,RAL

AIG,CSC,CSCO,GE

AIG,GE,S,WMT

AXP,BS,F,GM

BAC,CHA,DD,DOW

BAC,DD,GE,MMM

BAC,MER,TEK,XRX

BMY,JNJ,KO,MRK

CPB,GE,KO,XON

CPB,HNZ,KO,RAL

DD,DOW,GE,MTC

GE,JNJ,KO,PG

GE,MKG,ROK,UTX

AIG,CEN,CSC,GE

AIG,GE,NSC,WMT

BAC,BC,MER,TEK

BAX,BMY,JNJ,MRK

CHA,DD,DOW,WY

CHV,CPB,GE,XON

AEP,CPB,HNZ,KO

CSC,CSCO,GE,IBM

DD,EK,GE,MTC

GE,JNJ,MO,PG

CL,GE,KO,PG

GE,KO,PEP,XON

GE,MKG,RTNB,UTX

GE,MAY,S,WMT

AEP,CPB,GTE,KO

AIG,CEN,GD,GE

AIG,GE,NSC,VO

BAX,BMY,MRK,PNU

CHA,DOW,IP,WY

CHV,GE,SLB,XON

CL,GE,IFF,KOCL,GE,MCD,PG

AVP,CL,KO,PG

CSCO,GE,IBM,MSFT

DD,EK,GE,PRD

GE,MAY,TOY,WMT

LTD,MAY,S,WMT

AEP,AIT,GTE,KO

AIG,FDX,GE,VO

AIG,BNI,NSC,VO

BCC,CHA,IP,WY

CHV,MOB,SLB,XON

CSCO,IBM,INTC,MSFT

AA,DOW,IP,WY

KM,LTD,S,WMT

AEP,AIT,BEL,GTE

AIG,DAL,FDX,GE

CHV,HAL,MOB,SLB

ARC,CHV,MOB,XON

CSCO,IBM,INTC,ORCL

CSCO,INTC,MSFT,SUNW

CGP,MOB,SLB,XON

AEP,AIT,BEL,SO

AIG,BDK,DAL,GE

AIT,BEL,GTE,T

ARC,CHV,MOB,OXY

CGP,MOB,SLB,WMB

CSCO,INTC,ORCL,UIS

CSCO,INTC,SUNW,TXN

BHI,HAL,MOB,SLB

AEP,AIT,SO,UCM

BHI,HAL,HM,SLB

CSCO,HWP,INTC,TXNCSCO,HRS,SUNW,TXN

AEP,ETR,SO,UCM

HWP,INTC,NSM,TXN

number of clusters 5

number of bubbles 97

number of cliques 292

1

2

3

4

5

6

AIG

AXP

COL

FLR

BNI

NSCVO

AGC CI

ONE

USB

WFC

JPM

TAN

XRX

BAC

MER

TEK

BCBS F

GM

AVPCL

KO

PEP

IFF

CPB

HNZ

RAL

BA

ROK

DIS

MCD

PGNT

HON

GD

GE

JNJ

MO

BDK

DAL

FDX

CEN

CSC

MMM

MTC

MKG

UTX

RTNBEK

PRD

BAX

BMY

MRK

PNU

KM

LTD S

MAY

TOY

WMT

ARC

OXY

CHV

XON

MOB

CGP

WMB

BHI

HAL

SLB

HM

CSCO

INTC

ORCL

UIS

HRS

SUNW

HWP

NSM

TXN

IBM

MSFT

AA IP

WY

BCC

CHA

DD

DOW

AEP

SO

UCM

ETR

AIT

BEL

GTE T

1

2

3

4

5

6

AIG

AXP

COL

FLR

BNI

NSCVO

AGC CI

ONE

USB

WFC

JPM

TAN

XRX

BAC

MER

TEK

BCBS F

GM

AVPCL

KO

PEP

IFF

CPB

HNZ

RAL

BA

ROK

DIS

MCD

PGNT

HON

GD

GE

JNJ

MO

BDK

DAL

FDX

CEN

CSC

MMM

MTC

MKG

UTX

RTNB

EK

PRD

BAX

BMY

MRK

PNU

KM

LTD S

MAY

TOY

WMT

ARC

OXY

CHV

XON

MOB

CGP

WMB

BHI

HAL

SLB

HM

CSCO

INTC

ORCL

UIS

HRS

SUNW

HWP

NSM

TXN

IBM

MSFT

AA IP

WY

BCC

CHA

DD

DOW

AEP

SO

UCM

ETR

AIT

BEL

GTE T

1

2

3

4

5

6

AIG

AXP

COL

FLR

BNI

NSC

VO

AGC CI

ONE

USB

WFC

JPM

TAN

XRX

BAC

MER

TEK

BCBS F

GM

AVPCL

KO

PEP

IFF

CPB

HNZ

RAL

BA

ROK

DIS

MCD

PGNT

HON

GD

GE

JNJ

MO

BDK

DAL

FDX

CEN

CSC

MMM

MTC

MKG

UTX

RTNB

EK

PRD

BAX

BMY

MRK

PNU

KM

LTD S

MAY

TOY

WMT

ARC

OXY

CHV

XON

MOB

CGP

WMB

BHI

HAL

SLB

HM

CSCO

INTC

ORCL

UIS

HRS

SUNW

HWP

NSM

TXN

IBM

MSFT

AA IP

WY

BCC

CHA

DD

DOW

AEP

SO

UCM

ETR

AIT

BEL

GTE T

CSCO INTEL ORACLE UniSys (IT) Harris Corporation (IT) SUN Hewlett-Packard National Semiconductor Corporation Texas Instruments IBM Microsoft

Avon Products (Beauty) Colgate-Palmolive Coca-cola Pepsi Cola, International Flavors & Fragrances

123456

AIG AXP COL FLR BNI NSCVO AGCCI ONE USB WFC JPM TAN XRX BAC MER TEKBCBSF GM AVPCL KO PEP IFF CPB HNZ RAL BA ROK DIS MCDPGNT HONGDGE JNJ MO BDK DAL FDX CEN CSC MMM MTC MKG UTXRTNBEK PRD BAX BM

Y MRK PNUKMLTDS MAY TOY WMT ARC OXY CHV XON MOB CGP WMB BHI HAL SLB HM CSCO INTC ORCL UIS HRS

SUNW HWP NSM TXN IBM MSFTAAIP WY BCC CHADD DOWAEPSO UCM ETRAIT BEL GTET

1

2

3

4

5

6

AIGAXPCOLFLRBN

INSCVOAG

C CIONEUSBWF

CJPMTA

NXRXBACMERTEKBCBS FGMAV

PCLKOPEPIFFCP

BHNZRALBARO

KDISMCDPGNTHO

NGDGEJNJMOBD

KDALFDXCENCSCMM

MMTCMKGUTX

RTNBEKPR

DBAXBMYMR

KPNUKMLTD S

MAYTOYWM

TARCOXYCHVXONMO

BCGPWM

BBHIHALSLBHMCSCOINT

CORCLUISHR

SSUNWHW

PNSMTXNIBMMS

FTAA IPWYBCCCHADDDO

WAEPSOUC

METRAITBE

LGTE T

AIG

AX

PC

OL

FLR

BN

IN

SC

VO

AG

C CI

ON

EU

SB

WF

CJP

MT

AN

XR

XB

AC

ME

RT

EK

BC

BS F

GM

AV

PC

LK

OP

EP

IFF

CP

BH

NZ

RA

LB

AR

OK

DIS

MC

DP

GN

TH

ON

GD

GE

JN

JM

OB

DK

DA

LF

DX

CE

NC

SC

MM

MM

TC

MK

GU

TX

RT

NB

EK

PR

DB

AX

BM

YM

RK

PN

UK

MLT

D SM

AY

TO

YW

MT

AR

CO

XY

CH

VX

ON

MO

BC

GP

WM

BB

HI

HA

LS

LB

HM

CS

CO

INT

CO

RC

LU

ISH

RS

SU

NW

HW

PN

SM

TX

NIB

MM

SF

TA

A IPW

YB

CC

CH

AD

DD

OW

AE

PS

OU

CM

ET

RA

ITB

EL

GT

E T

AIG AXP COL FLR BNI

NSC VO

AGC CI

ONE USB WFC JPM TAN XRX BAC MER TEK BC BS F

GM AVP CL KO

PEP IFF

CPB HNZ RAL BA

ROK DIS

MCD PG NT

HON GD GE JNJ MO BDK DAL FDX CEN CSC

MMM MTC MKG UTX

RTNBEK

PRD BAX BMY MRK PNU KM LTD S

MAY TOY

WMT ARC OXY CHV XON MOB CGP WMB

BHI HAL SLB HM

CSCOINTC

ORCLUIS

HRS SUNWHWP NSM TXN IBM

MSFTAA IP

WY BCC CHA DD

DOW AEP SO

UCM ETR AIT

BEL GTE

T

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

AA

AE

PA

GC

AIG

AIT

AR

CA

VP

AX

PB

AB

AC

BA

XB

CB

CC

BD

KB

EL

BH

IB

MY

BN

IB

SC

EN

CG

PC

HA

CH

V CI

CL

CO

LC

PB

CS

CC

SC

OD

AL

DD

DIS

DO

WE

KE

TR F

FD

XF

LR

GD

GE

GM

GT

EH

AL

HM

HN

ZH

ON

HR

SH

WP

IBM

IFF

INT

C IPJN

JJP

MK

MK

OLT

DM

AY

MC

DM

ER

MK

GM

MM

MO

MO

BM

RK

MS

FT

MT

CN

SC

NS

MN

TO

NE

OR

CL

OX

YP

EP

PG

PN

UP

RD

RA

LR

OK

RT

NB S

SLB

SO

SU

NW T

TA

NT

EK

TO

YT

XN

UC

MU

ISU

SB

UT

XV

OW

FC

WM

BW

MT

WY

XO

NX

RX

AA AEP AGC AIG AIT

ARC AVP AXP BA

BAC BAX BC

BCC BDK BEL BHI

BMY BNI BS

CEN CGP CHA CHV

CI CL

COL CPB CSC

CSCODAL DD DIS

DOW EK

ETR F

FDX FLR GD GE GM GTE HAL HM HNZ HON HRS HWP IBM IFF

INTCIP

JNJ JPM KM KO LTD MAY MCD MER MKG MMM

MO MOB MRK MSFTMTC NSC NSM

NT ONE

ORCLOXY PEP PG

PNU PRD RAL ROK RTNB

S SLB SO

SUNWT

TAN TEK TOY TXN UCM

UIS USB UTX VO

WFC WMB WMT WY XON XRX

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

123456

AIG AXP COL FLR BNI NSCVO AGCCI ONE USB WFC JPM TAN XRX BAC MER TEKBCBSF GM AVPCL KO PEP IFF CPB HNZ RAL BA ROK DIS MCDPGNT HONGDGE JNJ MO BDK DAL FDX CEN CSC MMM MTC MKG UTXRTNBEK PRD BAX BM

Y MRK PNUKMLTDS MAY TOY WMT ARC OXY CHV XON MOB CGP WMB BHI HAL SLB HM CSCO INTC ORCL UIS HRS

SUNW HWP NSM TXN IBM MSFTAAIP WY BCC CHADD DOWAEPSO UCM ETRAIT BEL GTET

1

2

3

4

5

6

AIGAXPCOLFLRBN

INSCVOAG

C CIONEUSBWF

CJPMTA

NXRXBACMERTEKBCBS FGMAV

PCLKOPEPIFFCP

BHNZRALBARO

KDISMCDPGNTHO

NGDGEJNJMOBD

KDALFDXCENCSCMM

MMTCMKGUTX

RTNBEKPR

DBAXBMYMR

KPNUKMLTD S

MAYTOYWM

TARCOXYCHVXONMO

BCGPWM

BBHIHALSLBHMCSCOINT

CORCLUISHR

SSUNWHW

PNSMTXNIBMMS

FTAA IPWYBCCCHADDDO

WAEPSOUC

METRAITBE

LGTE T

AIG

AX

PC

OL

FLR

BN

IN

SC

VO

AG

C CI

ON

EU

SB

WF

CJP

MT

AN

XR

XB

AC

ME

RT

EK

BC

BS F

GM

AV

PC

LK

OP

EP

IFF

CP

BH

NZ

RA

LB

AR

OK

DIS

MC

DP

GN

TH

ON

GD

GE

JN

JM

OB

DK

DA

LF

DX

CE

NC

SC

MM

MM

TC

MK

GU

TX

RT

NB

EK

PR

DB

AX

BM

YM

RK

PN

UK

MLT

D SM

AY

TO

YW

MT

AR

CO

XY

CH

VX

ON

MO

BC

GP

WM

BB

HI

HA

LS

LB

HM

CS

CO

INT

CO

RC

LU

ISH

RS

SU

NW

HW

PN

SM

TX

NIB

MM

SF

TA

A IPW

YB

CC

CH

AD

DD

OW

AE

PS

OU

CM

ET

RA

ITB

EL

GT

E T

AIG AXP COL FLR BNI

NSC VO

AGC CI

ONE USB WFC JPM TAN XRX BAC MER TEK BC BS F

GM AVP CL KO

PEP IFF

CPB HNZ RAL BA

ROK DIS

MCD PG NT

HON GD GE JNJ MO BDK DAL FDX CEN CSC

MMM MTC MKG UTX

RTNBEK

PRD BAX BMY MRK PNU KM LTD S

MAY TOY

WMT ARC OXY CHV XON MOB CGP WMB

BHI HAL SLB HM

CSCOINTC

ORCLUIS

HRS SUNWHWP NSM TXN IBM

MSFTAA IP

WY BCC CHA DD

DOW AEP SO

UCM ETR AIT

BEL GTE

T

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

FHN

AFL

ALL

AIG

AOC

BSET

BK

CTX

ARB

JPM

CB

CI

CINF CMA

RHDC

EK

FRE

FNM

FITB FLTWQ

GCI

HDLM

HUM

HBAN

KBH

KEY

LNC

L

MMC

MI

MAS

BAC

NTRS

WFC

NYT

MO

PHM

PNC C

PGR

RAD STT

TRV

STI

TXT

TMK

TSN

UNH UNM

VMC

MBI

WAMUQ

ACE

XL

LEHMQ

LEN

XRAY

ABK

COF

MTG

USB SNV

HIG

AXP

AMGN

AMR

ADP

VZ HRB CTL

CMCSA

CAR MS

RRD

EFX FDX

BEN

GE

GENZ

DTV

GAP

HOG

HTMXQ

HAS IGT

IPG

LUK

MAT

MCD

MHP

MDT MDP

NWL

OMC

PAYX

SCHW

SCI

LUV

S

T

STJ

SYK

UIS

VAR

DIS

WPO

XRX

CBS

CEPH

FTR

CMCSKBSX

TROW

GILD

AM

BWS

BC CHRS

DLX

LIZ

LUB HST

NC

THC

PBY

PCH

R SKY

SLM

GGWPQ

SPG

JNY

BBT

HCP

ADCT

ADBE

AAPL ADSK BMC

CSCO

CA

CSC

GLW

DELL

FISV HRS HPQ

IBM

INTC

MSFT

MOLX

NRTLQ

NOVL

ORCL

PMTC

JAVA

SYMC

EMC

ERTS

QCOM

APH CPWR TLAB COMS

ABT

AGN

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50

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FHN ABT ADCT ADBE AMD AFL APD ACV AGN AYE HON ALL ALTR AA FO ABX AEP AXP AM AMGN HES WYE AIG AMR APC ADI AOC APA AAPL AMAT ADM ASH ADP ADSK AVY AVP BHI BLL CEG BCR BSET BAX BDX VZ BMS BJS BK BDK HRB BMC BA OMX BGG BMY BWS BF/B BC BNI CPB CAH PGN CAT CTL CTX ARB CHRS JPM CVX CB CI CINF CTAS CCTYQCSCO CLX CMS KO CCE CL CMCSACMA CA CSC CAG CNW CBE CTB TAP GLW CR CCK CSX CAR CMI DHR TGT MS DE DELL DLX DTE VVI DDS D RRD DOV DOW DUK RHDC DD EK ETN ECL PKI EP EMR ETR EFX EQT XOM FDO FDX FRE FNM FITB FISV FLTWQMEE FMC F FRX FWLT FPL BEN GCI GPS GE GD GIS GPC GENZ GM DTV GR GT GWW GAP HAL HDLM HOG HRS HTMXQHAS HLS HNZ HP HSY HPQ HD CNP HUM HBAN IBM ITW IR INTC IFF IGT IPG IP JEC JCI JNJ KSU KBH K KEY KMB KR LEG LUK LLY LTD LNC LLTC LIZ L LPX LOW LSI LUB HST MMC MI MAS MAT MDR MCD MHP MWV MDT CVS MRK MDP MSFT MU MIL MMM MOLX MOT MUR MYL NBR NC BAC THC NSM NAV NWL NEM GAS NKE NI NBL JWN NSC NTRS NOC NRTLQWFC NOVL NU XEL NUE NYT OXY ODP FE OMC OKE ORCL PCAR PCG PLL PH PMTC PAYX JCP PPL PBY PEP PFE EXC MO PHM PNW PBI BCO PNC PCH PPG PX PCP COST C PG PGR PEG STR RAD ROK RDC R SLE SCG EIX SGP SLB SCHW SCI SHW SIAL SKY SII SJM SNA LUV S SPW STT SWK T SO STJ TRV SYK SLM SUN JAVA STI SVU SYMC SYY RSH TE TIN TER TXN TXT TMO TNB TIF TKR TJX TMK TYC TSN UNH UN AEE UNP UIS UNM MRO X UTX VAR VFC VMC WAG WMT DIS WPO WY PAS WHR WMB WEC FL WOR XRX XLNX YRCW AES SPLS EMN EMC CCL ERTS MBI QCOM WAMUQCBS CEPH FTR ACE APH ESV EOG XL FAST M GGWPQKSS LEHMQLEN SPG TSO MCK TEX XRAY CMCSKBSX LMT BBY CPWR DRI JNY TLAB FCX COMS ABK AZO COF KLAC MTG SWY BBT USB SNV ITT HIG TROW HCP GILD

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1

395 stocks on US market 1996-2009 (routers)

PMFG

JPM,BAC,WFC,PNC

JPM,BAC,WFC,CBK,JPM,WFC,PNC

BAC,WFC,PNC,STI

BK,JPM,NTRS,PNC

BK,WFC,PNC,STT

AXP,JPM,BAC,CJPM,WFC,C,LEN

BAC,WFC,C,TMK

CMA,BAC,WFC,STIWFC,PNC,STI,USB

AXP,JPM,BAC,COF

AXP,JPM,MS,C

AXP,GCI,BAC,C

BK,JPM,CB,NTRSCTX,JPM,C,LEN

CMA,BAC,WFC,TXT

CMA,MI,BAC,STI

CMA,WFC,STI,BBT

AIG,BAC,C,TMK

LNC,WFC,C,TMK

AXP,JPM,MS,BEN

AXP,JPM,GAP,COF

AXP,MS,C,CBS

AXP,GCI,BAC,NWL

AXP,GCI,MDP,C

AIG,FRE,BAC,CBK,CB,NTRS,TRVCTX,ARB,JPM,C

CTX,JPM,KBH,LENJPM,CB,MMC,NTRS

JPM,MS,C,SCI

CMA,EK,WFC,TXTCMA,WFC,SPG,BBT

CMA,KEY,STI,BBT

GCI,HDLM,BAC,C

ALL,LNC,WFC,TMK

AFL,LNC,C,TMK

HBAN,MI,BAC,STI

WFC,STI,BBT,SNV

AFL,LNC,TMK,UNM

ALL,LNC,TMK,HIG

ALL,L,WFC,TMK

AXP,JPM,BEN,TROW

AXP,MS,BEN,SCHW

AXP,MS,DIS,CBS

AXP,RRD,GCI,MDP

AIG,FRE,BAC,LEHMQ

BK,NTRS,TRV,TSN

CTX,JPM,KBH,VMC

CTX,KBH,PHM,LEN

BSET,ARB,JPM,C

HRB,JPM,MS,BEN

AOC,CB,MMC,NTRS

CB,NTRS,PGR,TRV

FHN,CMA,KEY,STICINF,CMA,KEY,BBT

CAR,MS,C,CBS

FRE,FNM,BAC,C

GCI,MDP,NYT,C

FITB,HBAN,MI,STI

KEY,STI,XL,BBT

WFC,SPG,BBT,HCP

FHN,CMA,KEY,WAMUQ

ALL,L,MO,TMK

AXP,JPM,GE,TROW

AXP,MS,MSFT,SCHWAXP,MS,MHP,DIS

AXP,RRD,GCI,WPO

AXP,FDX,BEN,SCHW

AXP,BEN,LUK,TROW

AXP,OMC,DIS,CBS

BSET,JPM,RHDC,C

CTX,KBH,MAS,PHM

CB,PGR,TRV,ACE

CINF,CMA,MBI,BBT

MS,BEN,SCHW,VAR

KEY,RAD,XL,BBT

CI,LNC,TMK,HIG

L,WFC,TMK,XRAY

WFC,SLM,BBT,HCP

PCH,SPG,BBT,HCP

AXP,JPM,GE,HOG

AXP,MS,MHP,S

AXP,MS,MSFT,UIS

AXP,EFX,FDX,BEN

AXP,BEN,LUK,XRX

AXP,ADP,GE,TROW

AXP,IPG,OMC,CBS

CI,LNC,TMK,UNH

CMA,MBI,ABK,BBT

CSCO,MS,MSFT,SCHW

PCH,PPG,SPG,BBTHST,PCH,SPG,HCP

AXP,ADP,GE,PFE

AXP,JPM,HOG,IGT

AXP,MS,S,T

AXP,TGT,GE,HOG

AXP,CMCSA,IPG,CBS

AXP,HTMXQ,MSFT,UIS

ADP,GE,PAYX,TROW

CI,HUM,TMK,UNH

CSCO,MS,MSFT,PMTC

CSCO,MS,DTV,SCHW

CSCO,IBM,MSFT,SCHW

CMA,MBI,ABK,MTG

BC,HST,PCH,SPG

HST,PBY,PCH,HCP

HST,GGWPQ,SPG,HCP

NC,PCH,PPG,SPG

PCH,PPG,WY,BBT

AXP,CMCSA,CBS,CMCSK

AXP,TGT,GE,HD

AXP,CTL,MS,T

AXP,GE,MDT,PFE

AMGN,ADP,GE,PFE

AM,BC,HST,PCHBC,LIZ,PCH,SPG

CSCO,IBM,INTC,MSFT

CSCO,CSC,IBM,SCHW

CMA,FLTWQ,MBI,MTG

NC,PCH,PPG,R

DLX,NC,PCH,SPG

MWV,PCH,PPG,WY

AXP,CTL,MS,FTR

AXP,VZ,CTL,T

AXP,TGT,HD,TIF

AXP,GE,HD,LUV

AXP,GE,MDT,SYK

AMGN,GE,GENZ,PFE

BC,LIZ,PCH,JNY

CSCO,HPQ,IBM,INTCCSCO,DELL,INTC,MSFT

TGT,GE,HD,MCD

DLX,NC,THC,PCH

GE,MDT,MRK,PFE

BWS,LIZ,PCH,SPG BMS,MWV,PCH,PPG

IP,MWV,PCH,WY

DD,MWV,PPG,WY

CNW,PCH,PPG,R

AXP,AMR,HD,LUV

AXP,HAS,HD,TIF

AXP,MDT,STJ,SYK

AMGN,GE,GENZ,GILD

BMS,HLS,MWV,PCH

BMS,MWV,PPG,SJMBLL,BMS,PCH,PPGBWS,CHRS,LIZ,SPG

BWS,PCH,SKY,SPG

AMAT,CSCO,DELL,INTC

CSCO,DELL,MSFT,ERTSCSCO,HPQ,INTC,MOLX

CNW,PPG,R,YRCW

TGT,HD,COST,TIF

DOW,DD,MWV,PPGAA,DD,PPG,WY

GE,JNJ,MRK,PFE

IP,MWV,TIN,WYOMX,IP,PCH,WY

AA,DD,IR,PPG

AXP,HAS,HD,MAT

AXP,MDT,STJ,BSX

AMGN,GENZ,CEPH,GILD

ADBE,AMAT,CSCO,DELL

AMAT,CSCO,INTC,XLNX

AAPL,AMAT,DELL,INTC

BLL,BMS,CCK,PPG

BLL,PCH,PPG,VFC

OMX,IP,ODP,PCH

OMX,LPX,PCH,WY

CSCO,HPQ,MOLX,APHCSCO,FISV,INTC,MOLX

TGT,HD,COST,WMT

DOW,DD,PPG,EMN

GE,JNJ,PFE,PG

JNJ,LLY,MRK,PFE

LUB,PCH,SKY,SPG

ADBE,AMAT,CSCO,SYMC

AA,IR,PPG,X

AMAT,CSCO,XLNX,QCOM

AMAT,INTC,TXN,XLNX

CSCO,INTC,ORCL,XLNX

CSCO,HRS,MOLX,APH

TGT,HD,LOW,WMT

CAT,DD,IR,PPG

DD,PPG,PX,EMN

ABT,JNJ,LLY,PFE

CL,JNJ,PFE,PG

BMY,LLY,MRK,PFE

NKE,PCH,PPG,VFC

ABT,BAX,JNJ,PFE

ABT,CAH,LLY,PFE

AA,NUE,PPG,X

AMD,AMAT,INTC,TXN

AMAT,LLTC,TXN,XLNX

AGN,BMY,LLY,PFEBMY,MRK,PFE,SGP

CAT,DD,MMM,PPG

CAT,IR,PH,PPG

CSCO,INTC,ORCL,EMCCSCO,CA,ORCL,XLNX

CSCO,XLNX,QCOM,COMS

KO,CL,JNJ,PG

TGT,HD,LOW,KSS

APD,DD,PPG,PX

HD,LOW,WAG,WMT

IR,PPG,TKR,X

INTC,MOT,TXN,XLNX

FMC,PPG,PX,EMN

ABT,BAX,BDX,JNJ

APD,AVY,DD,PPG

APD,ECL,PPG,PX

AGN,FRX,LLY,PFE

AA,NUE,X,FCX

AMAT,LLTC,TXN,KLACALTR,AMAT,LLTC,XLNX

CAH,LLY,PFE,MCK

CAT,ETN,IR,PH

BMC,CSCO,CA,ORCL

CSCO,INTC,JAVA,EMC

ADSK,CSCO,ORCL,EMC

KO,CL,PG,UN

KO,JNJ,PEP,PG

TGT,HD,JCP,KSS

TGT,FDO,LOW,KSS

CSX,DD,MMM,PPG

HD,LOW,SPLS,KSS

ITW,IR,PH,PPG

ADI,LLTC,TXN,XLNX

LOW,CVS,WAG,WMT

WYE,MRK,PFE,SGP

NUE,PPG,X,WOR

APD,ECL,PPG,SIAL

AGN,FRX,LLY,MYL

AA,OXY,X,FCX

ADI,LLTC,NSM,TXNADI,LSI,TXN,XLNX

AMAT,TER,TXN,KLAC

BCR,BAX,BDX,JNJ

BMC,CSCO,CA,CPWR

CAH,VVI,LLY,MCK

CAT,CMI,ETN,IR

CSCO,INTC,JAVA,TLAB

CSCO,GLW,JAVA,EMC

KO,CCE,JNJ,PEP

CPB,KO,PG,UN

CL,KMB,PG,UN

CSX,DD,NSC,PPG

TGT,JCP,M,KSS

ECL,IFF,PPG,PX

HD,LOW,SPLS,FAST

BGG,ITW,IR,PH

EMR,ITW,IR,PPG

GPC,ITW,PH,PPG

AA,JEC,OXY,X

AMAT,MU,TER,TXN

CPB,KO,HNZ,UN

CAT,CMI,DE,IR

CSCO,GLW,NRTLQ,JAVA

ADCT,CSCO,INTC,TLAB

KO,CCE,PEP,PAS

CLX,CL,KMB,PG

BNI,CSX,NSC,PPG

CMI,ETN,IR,PCAR

TGT,DDS,JCP,M

TGT,JWN,M,KSS

DHR,EMR,ITW,IR

CBE,EMR,ITW,PPG

DOV,EMR,IR,PPG

GPC,ITW,PPG,SHW

HD,LOW,FAST,AZO ABX,OXY,X,FCX

ADCT,CSCO,INTC,NOVL

AA,ADM,JEC,OXY

ABX,NEM,OXY,FCX

BNI,CSX,NSC,UNP

CPB,KO,HNZ,SYY

CAT,CMI,DE,TEX

AVP,CLX,CL,PG

CBE,ITW,PPG,TNBCMI,IR,NAV,PCAR

DHR,EMR,ITW,TMO

TGT,DDS,FL,M

TGT,LTD,JWN,M

DOV,EMR,IR,ROK

CR,DOV,EMR,PPG

DOV,IR,PPG,SWK

ETN,IR,JCI,PCAR

HD,LOW,BBY,AZO MEE,JEC,OXY,X

ACV,AVP,CL,PG

CPB,HNZ,SLE,SYY

CR,DOV,EMR,TYC

CR,DOV,BCO,PPG

CR,EMR,PBI,PPG

CSX,KSU,NSC,UNP

DHR,PKI,EMR,TMO

TGT,LTD,TJX,M

DOV,IR,ROK,ITTDOV,IR,SPW,SWKDOV,GWW,PPG,SWK

MEE,JEC,OXY,STR

MEE,FWLT,JEC,XHD,LOW,RSH,BBY

F,IR,JCI,PCAR

IR,PPG,SNA,SWK

LTD,JWN,M,DRI

CPB,GIS,HNZ,SLE

TGT,GPS,LTD,TJX

DOV,IR,PLL,ITTPKI,EMR,MIL,TMO

F,GM,IR,JCICTAS,F,IR,PCAR

HNZ,SLE,SVU,SYY

CCTYQ,HD,RSH,BBY

FO,IR,PPG,SNA

JEC,MUR,OXY,STR

BDK,PPG,SNA,SWK

FO,IR,PPG,UTX

BDK,PPG,SWK,WHR

CPB,GIS,HNZ,K

HNZ,KR,SVU,SYY

MUR,NBL,OXY,STR

BDK,LEG,PPG,WHR

CPB,HNZ,HSY,K

HON,IR,PPG,UTX

KR,SVU,SYY,SWY

APA,MUR,NBL,OXY

EQT,NBL,OXY,STR

HON,GT,IR,PPGHON,IR,UTX,CCL

HON,BA,PPG,UTX

APC,APA,MUR,NBL

HES,APA,MUR,OXY

APA,HP,NBL,OXY

CPB,CAG,HNZ,HSY

EP,EQT,NBL,STR

EQT,OXY,OKE,STR

HON,BA,GD,PPG

HON,BA,PCP,UTX

HES,MUR,OXY,MRO

APC,APA,NBL,EOGAPA,HP,NBL,SII

BA,GR,PPG,UTX

EP,NBL,STR,WMB

EQT,OKE,STR,AEE

CTB,GT,IR,PPG

HON,BA,GD,NOC

HES,MUR,SUN,MRO

HES,CVX,OXY,MRO

APA,HP,RDC,SII

EP,STR,WMB,AES

ASH,MUR,OXY,MRO

OKE,PEG,STR,AEE

BA,GD,NOC,LMT

CVX,XOM,OXY,MRO

HP,NBR,RDC,SIIMUR,SUN,MRO,TSO

GAS,OKE,PEG,AEE

HP,MDR,NBR,RDC

NBR,RDC,SII,ESV

GAS,PEG,TE,AEE

BJS,NBR,SII,ESV

EXC,PEG,TE,AEE

BHI,RDC,SII,ESV

BHI,RDC,SLB,SII

PPL,EXC,PEG,AEE

BHI,HAL,SLB,SII

D,PPL,PEG,AEE

CEG,D,PPL,PEG

D,NU,PPL,AEED,FPL,PEG,AEEPGN,D,FPL,AEE

ETR,FPL,PEG,AEE

AEP,PGN,D,AEE

PGN,DTE,FPL,AEE

ETR,PEG,EIX,AEE

AEP,PGN,D,DUK

AEP,PGN,FE,AEE

AEP,CMS,D,AEE

PGN,DTE,SO,AEE

PCG,PEG,EIX,AEE

AYE,AEP,CMS,D

AEP,D,DUK,CNP

PGN,NI,FE,AEE

PGN,PNW,SO,AEE

PGN,NI,XEL,AEE

PGN,PNW,SCG,AEE

PGN,SCG,AEE,WECBF/B,PGN,AEE,WECBF/B,PGN,TAP,AEE

number of clusters 14

number of bubbles 392

number of cliques 1177

Bubble tree

0

2

4

6

8

10

12

14

PNC

USB

FITBMI

HBAN

STI

SNVEK

WFC

TXT

STT

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PN

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

FH

NA

BT

AD

CT

AD

BE

AM

DA

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0

0.1

0.2

0.3

0.4

0.5

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0.7

0.8

0.9

1

02468

1

0

1

2

1

4

PNC USBFITBMIHBANSTISNVEKWFC TXT STTCMA MBIMTGFLTW

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Dynamics window size

log-returns

exponential smoothing

T. Aste, W. Shaw and T. Di Matteo “Correlation structure and dynamics in volatile markets”, New Journal of Physics 12 (2010) 085009 1-21. T. Di Matteo, F. Pozzi, T. Aste, "The use of dynamical networks to detect the hierarchical organization of financial market sectors", Eur. Phys. J. B 73 (2010) 3–11.

Dynamics window size

log-returns

exponential smoothing

T. Aste, W. Shaw and T. Di Matteo “Correlation structure and dynamics in volatile markets”, New Journal of Physics 12 (2010) 085009 1-21. T. Di Matteo, F. Pozzi, T. Aste, "The use of dynamical networks to detect the hierarchical organization of financial market sectors", Eur. Phys. J. B 73 (2010) 3–11.

Dynamics window size

log-returns

exponential smoothing

T. Aste, W. Shaw and T. Di Matteo “Correlation structure and dynamics in volatile markets”, New Journal of Physics 12 (2010) 085009 1-21. T. Di Matteo, F. Pozzi, T. Aste, "The use of dynamical networks to detect the hierarchical organization of financial market sectors", Eur. Phys. J. B 73 (2010) 3–11.

Dynamics window size

log-returns

exponential smoothing

T. Aste, W. Shaw and T. Di Matteo “Correlation structure and dynamics in volatile markets”, New Journal of Physics 12 (2010) 085009 1-21. T. Di Matteo, F. Pozzi, T. Aste, "The use of dynamical networks to detect the hierarchical organization of financial market sectors", Eur. Phys. J. B 73 (2010) 3–11.

Dynamics window size

log-returns

exponential smoothing

T. Aste, W. Shaw and T. Di Matteo “Correlation structure and dynamics in volatile markets”, New Journal of Physics 12 (2010) 085009 1-21. T. Di Matteo, F. Pozzi, T. Aste, "The use of dynamical networks to detect the hierarchical organization of financial market sectors", Eur. Phys. J. B 73 (2010) 3–11.

401 firms on the US equity market from 01/01/96 to 01/01/2009 data over a window of 250 days with 20 days steps

1996 1998 2000 2002 2004 2006 2008 20100.1

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5

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FIG. 14: Number of clusters retrieved from the analysis of the Pearson’s cross-correlations between log-retrns of 395 stock

prices in the years 1996 and 2009 measured over a moving window of 365 days (1 year).

BMC SOFTWARE INC

CISCO SYSTEMS INC

CA INC

DELL INC

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INTERNATIONAL BUSINESS MACHINES CORP INTEL CORP

LINEAR TECHNOLOGY CORP

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MICRON TECHNOLOGY INC

MOTOROLA INC

14

Number of clusters

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FIG. 15: PMFG graphs from the analysis of the Pearson’s cross-correlations between log-retrns of 395 stock prices in the

years 1996 and 2009 measured over a window of 365 days (1 year). With yellow stars are indicated a subset of stocks belonging

to the technology sector with activities in electronics and informatics. With yellow stars are indicated a subset of stocks

belonging to the technology sector with activities in electronics and informatics. The green diamonds refer instead to a subset

of stocks belonging to the utility sector with industrial activity in the energy sub sector. The plots for the year 2000 are

reported in the main paper.

18

Financial and energy sectors

Variations in the hierarchy

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2

3

4

5

6

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12/1996!12/1997

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2

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4

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9

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12/1997!12/1998

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2

3

4

5

6

7

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2

3

4

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7

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12/2002!12/2003

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FIG. 16: Dendrograms representing the hierarchical organization from our clustering method obtained from the analysis of

the Pearson’s cross-correlations between log-retrns of 395 stock prices in the years 1996 and 2009 measured over a window of

365 days (1 year). The colors in the dendrogram;s lines represent the di!erent clusters. The vertical lines in the background

indicate a subset of stocks belonging to the technology sector with activities in electronics and informatics (yellow) or a subset

of stocks belonging to the utility sector with industrial activity in the energy sub sector (green). The plots for the year 2000

are reported in the main paper.

19

1996 1998 2000 2002 2004 2006 2008 2010

1

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2

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3.5

4

4.5

5

(a)

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Rela

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centr

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1996 1998 2000 2002 2004 2006 2008 20100.8

1

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t

Rela

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1996 1998 2000 2002 2004 2006 2008 20100.7

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0.85

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1

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1.1

(c)

t

Rela

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1996 1998 2000 2002 2004 2006 2008 20100.7

0.75

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0.85

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1

1.05

1.1

(d)

t

Rela

tive c

lose

ness

Loss of centrality of financial sector

Brain activity

Case study 3

Coexistence of local specialized activity and

cross-scale global organization in human brain

Henrik J. Jensen

Similarity measure evolution during a performance (moving window of 0.5 sec containing 256 data points)

PMFG 3-cliques on Maximal Planar Graphs have a unique property: They contain other cliques inside or/and they are contained inside the other cliques.

Communities This provides automatically a classification into communities organized into a nested hierarchy

FC2, FCz, Fz

Brain activity: EEG data

Communities & Scaling

Exponent

play normal

play mechanically

play creatively

Conclusions Filtering information out of complex data-sets

Define a similarity measure (and a dissimilarity measure)

Build a complex network that best

reflects the information in the similarity measure

Study the structure of the network to retrieve the

relevant information in the original datasets

Correlations and dependency measures can be filtered by means of a mapping into graphs

A convenient set of graphs is the embedded maximally filtered graphs (EMFG)

Meaningful hierarchical clustering into communities emerges naturally

Clusters are organized with both intra-cluster and inter-cluster hierarchical levels following the rank vertex � clique � bubble � cluster � graph

Both local clustering and global organization can be detected

Si l’ordre satisfait la raison, le désordre fait les délices de l’imagination Paul Claudel

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