Multi-blocks methods

Transcript

1. Data Common Structure Groups Study Partial Analyses To go further Example
   Multiple Factor Analysis
   Julie Josse
   Applied Mathematics Department, Agrocampus Ouest
   Stat 300
   Stanford, July 2015
   1 / 58
   

   View Slide

2. Data Common Structure Groups Study Partial Analyses To go further Example
   Multiple Factor Analysis
   1 Data - Issues
   2 Common Structure
   3 Groups Study
   4 Partial Analyses
   5 Example
   2 / 58
   

   View Slide

3. Data Common Structure Groups Study Partial Analyses To go further Example
   Multi-blocks data set
   3
   Groups of variables (MFA)
   Groups of
   variables are
   quantitative and/
   or qualitative
   Objectives: - study the link between the sets of variables
   - balance the influence of each group of variables
   - give the classical graphs but also specific graphs:
   groups of variables - partial representation
   Examples: - Genomic: DNA, protein
   - Sensory analysis: sensorial, physico-chemical
   - Comparison of coding (quantitative / qualitative)
   • Sensory analysis: products - sensorial, physico-chemical
   • Survey: individuals - questionnaires themes (students health:
   addicted consumptions, psychological conditions, sleep, id)
   • Economy: countries - economic indicators each year
   • Biology: samples - Omics data (brain tumors: CGH, transcriptome;
   mouse: transcriptome, hepatic fatty acid measurements)
   ⇒ Generalized Canonical Correlation, Procrustes, Statis, etc.
   ⇒ MFA (Escofier & Pagès, 1998)
   ⇒ Continuous / categorical / contingency sets of variables
   3 / 58
   

   View Slide

4. Data Common Structure Groups Study Partial Analyses To go further Example
   Example: gliomas brain tumors
   The data
   
   Gliomas: Brain tumors, WHO classification
   - astrocytoma (A)……….……… x5
   - oligodendroglioma (O)……… x8
   - oligo-astrocytoma (OA)…… x6
   - glioblastoma (GBM)………… x24
   43 tumor samples
   (Bredel et al.,2005)
   - transcriptional modification (RNA), Microarrays
   - damage to DNA, CGH arrays
   • Transcriptional modification (RNA), microarrays: 489 variables
   • Damage to DNA (CGH array): 113 variables
   ‘-omics’ data
   1 j
   1
   J
   1
   1
   i
   I
   Tumors
   1 j
   2
   J
   2
   
   The data, the expectations
   
   
   4 / 58
   

   View Slide

5. Data Common Structure Groups Study Partial Analyses To go further Example
   Objectives
   • Study the similarities between individuals with respect to all
   the variables
   • Study the linear relationships between variables
   ⇒ taking into account the structure on the data (balance the
   influence of each group)
   • Find the common structure with respect to all the groups -
   highlight the specificities of each group
   • Compare the typologies obtained from each group of variables
   (separate analyses)
   5 / 58
   

   View Slide

6. Data Common Structure Groups Study Partial Analyses To go further Example
   Principal component methods
   The core of principal component methods is PCA on particular
   matrices
   "Doing a data analysis, in good mathematics, is simply searching
   eigenvectors, all the science of it (the art) is just to find the right
   matrix to diagonalize"
   Benzécri
   MFA is a particular weighted PCA!
   6 / 58
   

   View Slide

7. Data Common Structure Groups Study Partial Analyses To go further Example
   Balancing the groups of variables
   MFA is a weighted PCA:
   • compute the first eigenvalue λj
   1
   of each group of variables
   • perform a global PCA on the weighted data table:
   
   
   X1
   λ1
   1
   ;
   X2
   λ2
   1
   ; ...;
   XJ
   λJ
   1
   
   
   ⇒ Same idea as in PCA when variables are standardized: variables
   are weighted to compute distances between individuals i and i
   8 variables
   highly
   correlated
   2 var
   i
   i′
   7 / 58
   

   View Slide

8. Data Common Structure Groups Study Partial Analyses To go further Example
   Balancing the groups of variables
   Transcriptome Genome
   λ1 162 12
   λ2 35 10
   λ3 21 5
   This weighting allows that:
   • Same weight for all the variables of one group: the structure of
   the group is preserved
   • For each group the variance of the main dimension of
   variability (first eigenvalue) is equal to 1
   • No group can generate by itself the first global dimension
   • A multidimensional group will contribute to the construction
   of more dimensions than a one-dimensional group
   8 / 58
   

   View Slide

9. Data Common Structure Groups Study Partial Analyses To go further Example
   Individuals and variables representations
   q
   −2 −1 0 1 2 3
   −3 −2 −1 0 1 2
   Individual factor map
   Dim 1 (20.99 %)
   Dim 2 (13.51 %)
   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
   q
   q
   q
   q
   q
   q
   q
   q
   q
   AA3
   AO1
   AO2
   AO3
   AOA1
   AOA2
   AOA3
   AOA4
   AOA6
   AOA7
   GBM1
   GBM11
   GBM15
   GBM16
   GBM21
   GBM22
   GBM23
   GBM24
   GBM25
   GBM26
   GBM27
   GBM28
   GBM29
   GBM3
   GBM30
   GBM31
   GBM4
   GBM5
   GBM6
   GBM9
   GNN1
   GS1
   GS2
   JPA2
   JPA3
   LGG1
   O1
   O2
   O3
   O4
   O5
   sGBM1
   sGBM3
   A
   GBM
   O
   OA q
   −1.0 −0.5 0.0 0.5 1.0
   −1.0 −0.5 0.0 0.5 1.0
   Correlation circle
   Dim 1 (20.99 %)
   Dim 2 (13.51 %)
   EXT1
   KIAA0934
   SVIL
   MGC39606
   ADARB2
   PARD3
   SPAG6
   AKR1C1
   CCDC3
   AKR1C2
   FLJ40873
   GYPA
   VASP
   ACAD8
   NPD014
   USP6NL
   CACNB2
   CLCA3
   COX7A1
   CEAL1
   FLJ38944
   LOC56931
   KIAA1543
   HBXIP
   ZNF226
   EDG1
   SORT1
   LOC283070
   DCLRE1B
   ZNF549
   KLRC3
   MGC4728
   DDEF1
   DMN
   KCNJ1
   MGC18216
   PSG5
   FBXO32
   FLJ12586
   SBP1
   MGC42367
   OSR1
   D21S2089E
   HNRNPG.T
   AP4B1
   ZNF160
   LRBA
   LILRA1
   EGLN2 LU
   GPSM2
   APOC1
   IGF1R
   TLL2
   CA11
   MGC39581
   KCNK6
   TFDP2
   ZNF233
   COX6A2
   UBE4B
   NDUFB11
   FLJ12572
   RBP7
   IGSF3
   BLVRB
   PSG1
   MYBPC2
   MSN
   H08563
   BGN
   TNFRSF12A
   CAPG
   MYCBP2
   EMP3 RTN3
   RGS16
   ITGA5
   PPP3CB
   LOC541471
   H78560
   ASPA
   TIMP1
   AA398420
   IMAGE.33267
   SOCS3
   PDPN
   CHI3L2
   MASP1
   PLP2
   S100A11
   SETD5
   T97457
   UBA52
   DLL3
   TSPYL1
   FAM84B
   RALY
   LOC613212
   CLIC1
   VEGF
   AA281932
   COL1A1
   CD47
   IFI30
   ATP6V1C1
   PSD3
   RUNX1
   LHFPL2 C9orf48
   CA12
   EDNRB
   PPP3CA
   LGALS3
   STEAP3
   IGFBP3
   KLRC3.1
   KLRC2
   KLRC1
   NPL
   ARPP.19
   PDE2A
   COL4A2
   TIMP3
   PLAUR
   PNCK
   WDR7
   X37864
   NNMT
   TBC1D7
   MRC2
   ABCA5
   TCF7L1
   CD58
   MST1
   DECR2
   AA131320
   LOC57228
   MST150
   PEG3
   TMEM49
   FABP3
   SLC16A3
   SERPINH1
   ADM
   NMNAT2
   GABBR1
   VAMP2
   CSPG2
   WASF1
   CBX6
   RAB27B
   COL3A1
   KIAA1644
   NLGN1
   C16orf5
   LOC400451
   AEBP1
   COL1A2
   COL6A2
   HEY1
   HSPG2
   RPS19BP1
   SUV39H1
   RFXAP
   TNC DKFZp313A2432
   STC1
   PDXP
   MOAP1
   MAPKBP1
   ID4 CACNB3
   SERPING1
   RND3
   HMOX1
   MTHFD2
   R70506
   APOC2
   ANXA1
   AA489629
   H86813
   SCAMP5
   RPS3A
   PLAU
   R61377
   NEFH
   STMN1
   FBXL16
   C1R
   WWTR1
   EPHB1
   ANXA5 AA906888
   AI262682
   LOC146795
   SOX4
   COL9A2
   SERPINA3
   AA029415
   PRKCZ
   FLJ35740
   FN1
   LOC388610
   AI871056
   FGF13
   STXBP1
   AI357047
   SP100
   HCLS1
   MGC26694
   LSP1
   PRKAR1B
   YWHAG
   CLTB
   AI335002
   A2BP1
   HLA.A
   SNCG
   IGFBP5
   PYCR1
   ABCC3
   L3MBTL4
   DPYD
   H20822
   AI822135
   LMO7
   ADFP KCNMA1
   PCDHGC3
   MSTP9
   AA479357
   LTF
   ZNF217
   AA490257
   LOC389831
   AA975768
   NOTCH1
   MB RAB30
   FCGR2B
   C4A FLJ38984
   PYGL
   SNRPN
   KNS2
   GBP1 IL32
   LY96
   AA181288
   IGF2BP3
   CALM1
   CASP1
   PDLIM7
   DEF6
   W93688
   USP3
   X38595
   H87106
   CDKN1A
   PHLDA1
   GOT1
   EFHB GYPC
   MYC
   CDC20B
   TNFAIP3
   POSTN
   PLOD2
   CDKN2D
   AA669383 CLSTN3
   MDK
   MVP
   CCL2
   FAM46A
   PLA2G2A
   KCNQ2
   CKMT1A
   H24428
   KIAA0963
   NSF
   RAB11FIP4
   CD53
   AA873230
   URP2
   CAMK2A
   APCS
   HPRT1
   LAMA4
   ITPKA
   HK2
   RBP4
   DDIT4
   OSBPL1A
   CAMKK2
   L1CAM
   PYHIN1
   H91845
   SLC35A2
   FCGRT
   AI005038
   PTPRZ1
   ADCY1
   HAMP
   CD44
   FAS
   NUAK1
   DNASE1L1
   GPNMB
   HBA1
   T62491 FBXO2
   VSNL1
   SPINT2
   C8orf4
   NCF2 PRSS3
   PLTP CAP2
   LAMB1
   EDG3
   INPP5F
   PDE4DIP
   MMP2
   S100A10
   LAPTM5
   PRRX1
   IL1RAP
   HLA.G
   TSPAN4
   ITGA9
   CCR1 MAL2
   DSCR1L1
   C6orf12
   DDN
   CBLN2
   GBP2 PRKCB1
   F13A1 S100A1
   R52960
   BCL2A1
   YWHAH
   FREQ
   UGCG
   SERPINI1
   NLK
   ANK3
   AI002301
   NCF1
   CA11.1
   NY.SAR.48
   AA598555
   CYBA
   ID3
   TAP1
   TGFBI
   AI263051
   TOMM40
   C1orf187
   IQSEC1
   DES
   NPC2
   AIF1
   HLA.F
   AI350724
   PRSS1
   SAA2
   CYR61 T51726
   SYNGR3
   ITGA3
   CHN1
   AA702986 FBXW7
   AA598631
   LUM
   PCP4
   SRPX
   IGHG1
   FAM84A
   H41096
   HPCA
   CTHRC1
   AA401952
   DYNLT1
   GAS1
   RAB20
   ESM1
   AA424849
   NR4A1 EPB49
   MDFI
   LYN
   TXNDC
   PALLD
   R70684
   CAV1
   ZFHX1B
   H10054
   NDST1
   SPARC
   SCN2B
   SYT7
   MED11
   PARP14
   MICAL2
   TncRNA
   BNIP2
   FZD7
   GADD45B
   FBL
   LOC283130
   STK17A
   PRKCG
   HLA.DRB1
   PRG1
   N98591
   PPP1R14A
   SLC15A2
   NPTX1
   MGP
   ⇒ What can be added to interpret?
   9 / 58
   

   View Slide

10. Data Common Structure Groups Study Partial Analyses To go further Example
    Individuals and variables representations
    q
    −2 −1 0 1 2 3
    −3 −2 −1 0 1 2
    Individual factor map
    Dim 1 (20.99 %)
    Dim 2 (13.51 %)
    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
    q
    q
    q
    q
    q
    q
    q
    q
    q
    AA3
    AO1
    AO2
    AO3
    AOA1
    AOA2
    AOA3
    AOA4
    AOA6
    AOA7
    GBM1
    GBM11
    GBM15
    GBM16
    GBM21
    GBM22
    GBM23
    GBM24
    GBM25
    GBM26
    GBM27
    GBM28
    GBM29
    GBM3
    GBM30
    GBM31
    GBM4
    GBM5
    GBM6
    GBM9
    GNN1
    GS1
    GS2
    JPA2
    JPA3
    LGG1
    O1
    O2
    O3
    O4
    O5
    sGBM1
    sGBM3
    A
    GBM
    O
    OA
    A
    GBM
    O
    OA
    Figure 4: Multi-way glioma data set: Characteristics of oligodendrogliomas are linked to modifica
    the genomic status of genes located on 1p and 19q positions.
    ⇒ Do the means of the tumors coordinates per stage on each
    dimension significantly differ from each other?
    10 / 58
    

    View Slide

11. Data Common Structure Groups Study Partial Analyses To go further Example
    Groups study
    ⇒ Synthetic comparison of the groups
    ⇒ Are the relative positions of individuals globally similar from one
    group to another? Are the partial clouds similar?
    ⇒ Do the groups bring the same information?
    11 / 58
    

    View Slide

12. Data Common Structure Groups Study Partial Analyses To go further Example
    Principal component in MFA
    MFA = weighted PCA ⇒ first principal component of MFA
    maximizes
    J
    j=1 k∈Kj
    cov2
    
    
    x.k
    λj
    1
    , F1
    
    
    =
    J
    j=1
    Lg
    (F1, Kj
    )
    Lg
    (F1, Kj
    ) =<
    WKj
    λ1
    , F1F1
    >= trace(WKj
    F1F1
    )
    ⇒ F1 the most related to the groups in the Lg sense
    12 / 58
    

    View Slide

13. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the groups
    Group j has the coordinates (Lg
    (F1, Kj
    ), Lg
    (F2, Kj
    ))
    0.0 0.2 0.4 0.6 0.8 1.0
    0.0 0.2 0.4 0.6 0.8 1.0
    Groups representation
    Dim 1 (20.99 %)
    Dim 2 (13.51 %)
    CGH
    expr
    WHO
    • 2 groups are all the more
    close that they induce the
    same structure
    • The 1st dimension is
    common to all the groups
    • 2nd dimension mainly due
    to CGH
    0 ≤ Lg
    (F1, Kj
    ) =
    1
    λj
    1 k∈Kj
    cov2(x.k, F1
    )
    ≤λj
    1
    ≤ 1
    ⇒ Could you predict the results of the PCA for each group?
    13 / 58
    

    View Slide

14. Data Common Structure Groups Study Partial Analyses To go further Example
    The RV coefficient
    Xj(I×Kj )
    and Xm(I×Km)
    not directly comparable
    Wj(I×I)
    = Xj Xj
    and Wm(I×I)
    = XmXm
    can be compared
    Inner product matrices = relative position of the individuals
    Covariance between two groups:
    < Wj , Wm >=
    k∈Kj l∈Km
    cov2(x.k, x.l
    )
    Correlation between two groups (Escoufier, 1973):
    RV (Kj , Km
    ) =
    < Wj , Wm >
    Wj Wm
    0 ≤ RV ≤ 1
    RV = 0: variables of Kj are uncorrelated with variables of Km
    RV = 1: the two clouds of points are homothetic
    ⇒ Extension of the notion of correlation matrix
    14 / 58
    

    View Slide

15. Data Common Structure Groups Study Partial Analyses To go further Example
    Similarity between two groups
    Measure of similarity between groups Kj and Km:
    Lg
    (Kj , Km
    ) =
    k∈Kj l∈Km
    cov2
    x.k
    λk
    1
    ,
    x.l
    λl
    1
    Ramsay (1984): "Matrices may be similar or dissimilar in a many
    ways"
    Canonical correlation (Hotteling, 1936), Mantel (1967), Procrustes
    (Gower, 1971), dCov (Szekely et al., 2007), kernel based HSIC
    (Gretton et al., 2005), etc...
    15 / 58
    

    View Slide

16. Data Common Structure Groups Study Partial Analyses To go further Example
    Numeric indicators
    > res.mfa$group$Lg
    CGH expr WHO
    CGH 2.51 0.60 0.46
    expr 0.60 1.10 0.36
    WHO 0.46 0.36 0.50
    > res.mfa$group$RV
    CGH expr WHO
    CGH 1.00 0.36 0.41
    expr 0.36 1.00 0.48
    WHO 0.41 0.48 1.00
    Lg
    (Kj , Kj
    ) =
    Kj
    k=1
    (λj
    k
    )2
    (λj
    1
    )2
    = 1+
    Kj
    k=2
    (λj
    k
    )2
    (λj
    1
    )2
    • CGH gives richer description (Lg greater)
    • RV: a standardized Lg
    • CGH and expr are not linked (RV=0.36)
    Contribution of each group to each component of the MFA
    > res.mfa$group$contrib
    Dim.1 Dim.2 Dim.3
    CGH 45.8 93.3 78.1
    expr 54.2 6.7 21.9
    • Similar contribution of the 2 groups to
    the first dimension
    • Second dimension only due to CGH
    16 / 58
    

    View Slide

17. Data Common Structure Groups Study Partial Analyses To go further Example
    Partial analyses
    ⇒ Comparison of the groups through the individuals
    ⇒ Comparison of the typologies provided by each group in a
    common space
    ⇒ Are there individuals very particular with respect to one group?
    ⇒ Comparison of the separate PCA
    17 / 58
    

    View Slide

18. Data Common Structure Groups Study Partial Analyses To go further Example
    Projection of partial points
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    00000000
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    xxxxx
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    00000
    Projection of group 1
    Projection of group 2
    Projection of group 3
    Data
    MFA individuals configuration
    i
    i1
    i2
    i3
    i
    Mean point
    Partial point 3
    Partial point 2
    Partial point 1
    G1 G2 G3
    RK = ⊕ RKj
    18 / 58
    

    View Slide

19. Data Common Structure Groups Study Partial Analyses To go further Example
    Partial points
    opinion attitude
    individuals
    individual i
    What you think
    What you do
    behavioral conflict
    F1
    F2
    19 / 58
    

    View Slide

20. Data Common Structure Groups Study Partial Analyses To go further Example
    Partial points
    What you expected
    for the tutorial
    What you have learned
    during the tutorial
    Tutorial participants
    F
    F
    F
    F1
    1
    1
    1
    F
    F
    F
    F2
    2
    2
    2
    What you have learned
    during the tutorial
    What you expected
    for the tutorial
    What you have learned
    during the tutorial
    What you expected
    for the tutorial
    20 / 58
    

    View Slide

21. Data Common Structure Groups Study Partial Analyses To go further Example
    Partial points
    What you expected
    for the tutorial
    What you have learned
    during the tutorial
    Tutorial participants
    F
    F
    F
    F1
    1
    1
    1
    F
    F
    F
    F2
    2
    2
    2
    What you have learned
    during the tutorial
    What you expected
    for the tutorial
    What you have learned
    during the tutorial
    What you expected
    for the tutorial
    Disappointed
    learner
    Happy learner
    20 / 58
    

    View Slide

22. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the partial points
    q
    −4 −2 0 2 4 6
    −6 −4 −2 0 2 4
    Individual factor map
    Dim 1 (20.99 %)
    Dim 2 (13.51 %)
    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
    q
    q
    q
    q
    q
    q
    q
    q
    q
    AA3
    AO1
    AO2
    AO3
    AOA1
    AOA2
    AOA3
    AOA4
    AOA6
    AOA7
    GBM1
    GBM11
    GBM15
    GBM16
    GBM21
    GBM22
    GBM23
    GBM24
    GBM25
    GBM26
    GBM27
    GBM28
    GBM29
    GBM3
    GBM30
    GBM31
    GBM4
    GBM5
    GBM6
    GBM9
    GNN1
    GS1
    GS2 JPA2
    JPA3
    LGG1
    O1
    O2
    O3
    O4
    O5
    sGBM1
    sGBM3
    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
    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
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    q
    A
    GBM
    O
    OA
    CGH
    expr
    q
    −1 0 1 2
    −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
    Individual factor map
    Dim 1 (20.99 %)
    Dim 2 (13.51 %)
    A
    GBM
    O
    OA
    CGH
    expr
    • an individual is at the barycentre of its partial points
    • an individual is all the more "homogeneous" that its
    superposed representations are close
    21 / 58
    

    View Slide

23. Data Common Structure Groups Study Partial Analyses To go further Example
    Identify particular individuals
    q
    −2 −1 0 1 2 3
    −3 −2 −1 0 1 2
    Individual factor map
    Dim 1 (20.99 %)
    Dim 2 (13.51 %)
    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
    q
    q
    q
    q
    q
    q
    q
    q
    q
    AA3
    AO1
    AO2
    AO3
    AOA1
    AOA2
    AOA3
    AOA4
    AOA6
    AOA7
    GBM1
    GBM11
    GBM15
    GBM16
    GBM21
    GBM22
    GBM23
    GBM24
    GBM25
    GBM26
    GBM27
    GBM28
    GBM29
    GBM3
    GBM30
    GBM31
    GBM4
    GBM5
    GBM6
    GBM9
    GNN1
    GS1
    GS2
    JPA2
    JPA3
    LGG1
    O1
    O2
    O3
    O4
    O5
    sGBM1
    sGBM3
    q
    q
    A
    GBM
    O
    OA
    CGH
    expr
    22 / 58
    

    View Slide

24. Data Common Structure Groups Study Partial Analyses To go further Example
    Numeric indicators
    I
    i=1
    J
    j=1
    (Fij q
    )2 =
    I
    i=1
    J
    j=1
    (Fiq
    )2 +
    I
    i=1
    J
    j=1
    (Fij q
    − Fiq
    )2
    Total inertia = Between indiv. inertia + Within indiv. inertia
    > res.mfa$inertia.ratio
    Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
    0.84 0.56 0.44 0.59 0.43
    • For the first dimension, the coordinates of each partial points
    are close (0.84 close to 1)
    • The within inertia can be decomposed by individuals
    res.mfa$ind$within.inertia
    23 / 58
    

    View Slide

25. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the partial components
    Do the separate analyses give similar dimensions as MFA?
    PCA
    i
    I
    1
    1 q Q
    1 q Q
    24 / 58
    

    View Slide

26. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the partial components
    q
    −1.0 −0.5 0.0 0.5 1.0
    −1.0 −0.5 0.0 0.5 1.0
    Partial axes
    Dim 1 (20.99 %)
    Dim 2 (13.51 %)
    Dim1.CGH
    Dim2.CGH
    Dim3.CGH
    Dim1.expr
    Dim2.expr
    Dim3.expr
    Dim1.WHO
    Dim2.WHO
    Dim3.WHO
    CGH
    expr
    WHO
    • The first dimension of
    each group is well
    projected
    • CGH has same
    dimensions as MFA
    25 / 58
    

    View Slide

27. Data Common Structure Groups Study Partial Analyses To go further Example
    Use of biological knowledge
    Genes can be grouped by gene ontology (GO) biological process
    GO:0006928
    cell motility
    ANXA1
    CALD1
    EGFR
    ENPP2
    FN1
    FPRL2
    LSP1
    MSN
    PDPN
    PLAUR
    PRSS3
    SAA2
    SPINT2
    TNFRSF12A
    VEGF
    WASF1
    YARS
    GO:0009966
    regulation of signal
    transduction
    CASP1
    EDG2
    F2R
    HCLS1
    HMOX1
    IGFBP3
    IQSEC1
    LYN
    MALT1
    TCF7L1
    TNFAIP3
    TRIO
    VEGF
    YWHAG
    YWHAH
    GO:0052276
    chromosome
    organisation and
    biogenesis
    CBX6
    NUSAP1
    PCOLN3
    PTTG1
    SUV39H1
    TCF7L1
    TSPYL1
    26 / 58
    

    View Slide

28. Data Common Structure Groups Study Partial Analyses To go further Example
    Use of biological knowledge
    • Biological processes considered as supplementary groups of
    variables
    ‘-omics’ data
    1 j
    1
    J
    1
    1
    i
    I
    1 j
    2
    J
    2
    M1 M2 M3 …..
    Modules
    
    Tumors
    Modules
    Modular approach
    => Integration of the modules as groups of supplementary variables
    27 / 58
    

    View Slide

29. Data Common Structure Groups Study Partial Analyses To go further Example
    Use of biological knowledge
    0.0 0.2 0.4 0.6 0.8 1.0
    0.0 0.2 0.4 0.6 0.8 1.0
    Groups representation
    Dim 1 (20.99 %)
    Dim 2 (13.51 %)
    CGH
    expr
    WHO
    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
    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
    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
    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
    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 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
    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
    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
    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
    q
    q
    q
    q
    qq
    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
    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
    Many biological processes
    induce the same structure
    on the individuals than
    MFA
    28 / 58
    

    View Slide

30. Data Common Structure Groups Study Partial Analyses To go further Example
    To go further
    • Mixed data: MFA with 1 group = 1 variable
    continuous variables: PCA is recovered; categorical variables:
    MCA is recovered
    mixed: FAMD
    • MFA used for methodological purposes:
    • comparison of coding (continuous or categorical)
    • comparison between preprocessing (standardized PCA and
    unstandardized PCA)
    • comparison of results from different analyses
    • Hierarchical Multiple Factor Analysis:
    Takes into account a hierarchy on the variables: variables are
    grouped and subgrouped (like in questionnaires structured in
    topics and subtopics)
    29 / 58
    

    View Slide

31. Data Common Structure Groups Study Partial Analyses To go further Example
    Clustering: MFA as a preprocessing
    i
    i’
    X1 X2
    MFA balances the influence of the groups when computing
    distances between individuals
    d2(i, i ) =
    J
    j=1
    1
    λj
    Kj
    k=1
    (xik − xi k
    )2
    AHC or k-means onto the first principal components (F.1, ..., F.Q)
    obtained from MFA allows to
    • take into account the groups structure in the clustering
    • make the clustering more robust by deleting the last dimensions
    30 / 58
    

    View Slide

32. Data Common Structure Groups Study Partial Analyses To go further Example
    Clustering
    AHC onto the first 5 principal components from MFA
    0.0 0.4 0.8
    Hierarchical clustering
    inertia gain
    O4
    AO2
    sGBM1
    AOA6
    AO1
    AO3
    GBM1
    LGG1
    AOA3
    O3
    O1
    GBM6
    O2
    O5
    AOA4
    GBM25
    GS1
    GBM29
    GBM31
    GBM15
    GBM26
    JPA2
    GBM9
    GBM21
    GBM22
    GBM23
    GBM27
    GBM11
    GBM4
    GBM5
    GBM30
    GBM28
    GS2
    sGBM3
    AOA1
    GNN1
    AOA2
    AOA7
    GBM24
    JPA3
    AA3
    GBM3
    GBM16
    0.0 0.2 0.4 0.6 0.8 1.0
    Cluster Dendrogram
    Individuals are sorted according to their coordinate on F.1
    31 / 58
    

    View Slide

33. Data Common Structure Groups Study Partial Analyses To go further Example
    Partition from the tree
    An empirical number of clusters is suggested
    0.0 0.4 0.8
    Hierarchical clustering
    inertia gain
    O4
    AO2
    sGBM1
    AOA6
    AO1
    AO3
    GBM1
    LGG1
    AOA3
    O3
    O1
    GBM6
    O2
    O5
    AOA4
    GBM25
    GS1
    GBM29
    GBM31
    GBM15
    GBM26
    JPA2
    GBM9
    GBM21
    GBM22
    GBM23
    GBM27
    GBM11
    GBM4
    GBM5
    GBM30
    GBM28
    GS2
    sGBM3
    AOA1
    GNN1
    AOA2
    AOA7
    GBM24
    JPA3
    AA3
    GBM3
    GBM16
    0.0 0.2 0.4 0.6 0.8 1.0
    Cluster Dendrogram
    32 / 58
    

    View Slide

34. Data Common Structure Groups Study Partial Analyses To go further Example
    Partition on the principal component map
    −2 −1 0 1 2 3
    −4 −2 0 2
    Factor map
    Dim 1 (20.99%)
    Dim 2 (13.51%)
    GBM3
    GBM27
    GBM4
    GBM16
    GBM5 GBM9
    GBM30
    GS2
    GBM11
    GBM21
    GBM28
    GBM29
    GBM31
    GBM22
    JPA3
    GBM15
    GBM23
    GBM24
    GBM25
    GS1
    GBM26
    JPA2
    AA3
    sGBM3
    AOA4
    sGBM1
    AOA2
    GBM1
    GBM6
    AO2
    GNN1
    LGG1AOA6
    AOA3
    AO1
    O2
    AOA1
    AOA7
    O5
    AO3
    O3
    O1
    O4
    cluster 1
    cluster 2
    cluster 3
    cluster 1
    cluster 2
    cluster 3
    Continuous vision (principal component) and discontinuous
    (clusters)
    33 / 58
    

    View Slide

35. Data Common Structure Groups Study Partial Analyses To go further Example
    Cluster description by variables
    v.test =
    ¯
    x − ¯
    x
    s2
    I
    I−I
    I−1
    H0
    : random sampling of I values from I
    with ¯
    x the mean of variable x in cluster , ¯
    x (s) the mean
    (standard deviation) of the variable x in the data set, I the cardinal
    of cluster
    $desc.var$quanti$‘1‘
    v.test Mean in category Overall mean sd in category Overall sd p.value
    TMEM49 4.488 -0.430 -1.424 0.722 1.277 0.000
    TNFRSF12A 4.433 -0.794 -1.838 0.789 1.357 0.000
    LGALS3 4.369 -0.222 -1.216 0.861 1.312 0.000
    S100A11 4.300 -0.737 -1.500 0.525 1.024 0.000
    BGN 4.273 2.105 1.106 0.697 1.348 0.000
    IFI30 4.264 0.987 0.026 0.979 1.300 0.000
    ....
    ....
    C9orf48 -4.411 -0.686 -0.037 0.540 0.848 0.000
    PSD3 -4.594 -1.684 -1.024 0.419 0.829 0.000
    AA398420 -4.635 0.324 1.134 0.635 1.007 0.000
    34 / 58
    

    View Slide

36. Data Common Structure Groups Study Partial Analyses To go further Example
    Cluster description by observations
    • parangon: the closest observations to the centroid of the cluster
    min
    i∈
    d(xi., C ) with C the centroid of cluster
    • specific observations: the furthest observations to the centroids
    of the other clusters (the observations sorted according to their
    distance from the highest to the smallest to the closest centroid)
    max
    i∈
    min
    =
    d(xi., C )
    desc.ind$para
    cluster: 1
    GBM11 GBM28 GBM5 GBM25 GBM31
    0.6649847 0.7001998 0.7973604 0.8869271 0.9674042
    ---------------------------------------------------------------
    desc.ind$dist
    cluster: 1
    GBM30 GS2 GBM21 GBM22 GBM27
    3.227968 3.096048 3.031256 2.904327 2.778950
    ---------------------------------------------------------------
    35 / 58
    

    View Slide

37. Data Common Structure Groups Study Partial Analyses To go further Example
    Cluster description
    • by the principal components (observations coordinates): same
    description than for continuous variables
    $desc.axes$quanti$‘1‘
    v.test Mean in category Overall mean sd in category Overall sd p.value
    Dim.2 2.919 0.511 0 0.465 1.010 0.004
    Dim.1 -4.458 -0.974 0 0.560 1.259 0.000
    • by categorical variables: chi-square and hypergeometric test
    $test.chi2
    p.value df
    type 8.433474e-06 6
    ⇒ Active and supplementary elements are used
    ⇒ Only significant results are presented
    36 / 58
    

    View Slide

38. Data Common Structure Groups Study Partial Analyses To go further Example
    Cluster description
    $‘1‘
    Cla/Mod Mod/Cla Global p.value v.test
    type=GBM 75 94.73684 55.81395 3.300966e-06 4.651145
    type=OA 0 0.00000 13.95349 2.207775e-02 -2.289028
    type=O 0 0.00000 18.60465 5.071916e-03 -2.802430
    $‘2‘
    Cla/Mod Mod/Cla Global p.value v.test
    type=A 60 37.5 11.62791 0.0398214 2.055597
    $‘3‘
    Cla/Mod Mod/Cla Global p.value v.test
    type=O 100.0 50.00 18.60465 8.875341e-05 3.919444
    type=GBM 12.5 18.75 55.81395 2.319983e-04 -3.681354
    37 / 58
    

    View Slide

39. Data Common Structure Groups Study Partial Analyses To go further Example
    Complementarity between hierarchical clustering and
    partitioning
    • Partitioning after AHC: the k-means algorithm is initialized
    from the centroids of the partition obtained from the tree
    • consolidate the partition
    • loss of the hierarchy
    • AHC with many individuals: time-consuming
    ⇒ partitioning before AHC
    • compute k-means with approximately 100 clusters
    • AHC on the weighted centroids obtained from the k-means
    ⇒ top of the tree is approximately the same
    38 / 58
    

    View Slide

40. Data Common Structure Groups Study Partial Analyses To go further Example
    Other methods: ade4
    Two-table analysis
    Available methods
    individuals
    variables
    variables
    Function name Analysis name
    between Between-class analysis
    within Within-class analysis
    discrimin Discriminant analysis
    coinertia Coinertia analysis
    cca Canonical correspondence analysis
    pcaiv PCA on Instrumental Variables
    pcaivortho Orthogonal PCAIV
    procuste Procustes analysis
    niche Niche (OMI) analysis
    St´
    ephane Dray (Univ. Lyon 1) CARME 2011, Rennes 22 / 31
    39 / 58
    

    View Slide

41. Data Common Structure Groups Study Partial Analyses To go further Example
    Other methods: ade4
    Other functions
    K-table
    variables
    individuals
    Function name Analysis name
    sepan K-table separate analyses
    pta Partial triadic analysis
    foucart Foucart analysis
    statis STATIS analysis
    mfa Multiple factor analysis
    mcoa Multiple coinertia analysis
    statico 2 K-table analysis
    St´
    ephane Dray (Univ. Lyon 1) CARME 2011, Rennes 26 / 31
    40 / 58
    

    View Slide

42. Data Common Structure Groups Study Partial Analyses To go further Example
    Other methods
    Predict one block with others:
    • Multi-block PLS regression
    • Multi-block PCA on instrumental variables..
    41 / 58
    

    View Slide

43. Data Common Structure Groups Study Partial Analyses To go further Example
    RV Tests
    Is there any (linear) relationship between the 2 sets? H0
    : ρV = 0
    Asymptotic tests: distributions normal, elliptical - rank (Robert et
    al, 1985, Cléroux, 1995, Cléroux & Ducharme, 1989) nRV ∼ λi Z2
    i
    ⇒ sensitive to the departure from the distribution and to n
    42 / 58
    

    View Slide

44. Data Common Structure Groups Study Partial Analyses To go further Example
    RV Tests
    Is there any (linear) relationship between the 2 sets? H0
    : ρV = 0
    Asymptotic tests: distributions normal, elliptical - rank (Robert et
    al, 1985, Cléroux, 1995, Cléroux & Ducharme, 1989) nRV ∼ λi Z2
    i
    ⇒ sensitive to the departure from the distribution and to n
    Permutation tests:
    permute one matrix’s rows - compute the RV for n! permutations
    p-value: proportion of the values greater than the observed one
    ⇒ computationally costly (“old fashion" argument?)
    42 / 58
    

    View Slide

45. Data Common Structure Groups Study Partial Analyses To go further Example
    RV Tests
    Is there any (linear) relationship between the 2 sets? H0
    : ρV = 0
    Asymptotic tests: distributions normal, elliptical - rank (Robert et
    al, 1985, Cléroux, 1995, Cléroux & Ducharme, 1989) nRV ∼ λi Z2
    i
    ⇒ sensitive to the departure from the distribution and to n
    Permutation tests:
    permute one matrix’s rows - compute the RV for n! permutations
    p-value: proportion of the values greater than the observed one
    ⇒ computationally costly (“old fashion" argument?)
    Approximation of the permutation distribution
    • sampling from the permutations - package ade4 (RV.rtest)
    • moment matching: Pearson family, Edgeworth expansion
    42 / 58
    

    View Slide

46. Data Common Structure Groups Study Partial Analyses To go further Example
    Moments matching
    The first three moments under H0 (Kazi-Aoual et al., 1995)
    EH0
    (RV ) =
    βx × βy
    n − 1
    βx
    =
    (tr(X X))2
    tr((X X)2)
    =
    ( λi
    )2
    λ2
    i
    .
    βx a measure of complexity 1 ≤ βx ≤ p
    RV large: n small and many orthogonal variables per group
    ⇒ Normal approximation:
    RVstd
    =
    RV − EH0
    (RV )
    VH0
    (RV )
    43 / 58
    

    View Slide

47. Data Common Structure Groups Study Partial Analyses To go further Example
    Moments matching
    Problem: the exact distribution of the RVstd is often skewed
    Histogram of the standardized RV
    Density
    −1 0 1 2 3 4
    0.0 0.1 0.2 0.3 0.4 0.5
    Normal
    Gamma
    Edgeworth
    ⇒ Pearson type III
    f(x) (skewness= γ):
    (2/γ)4/γ2
    Γ(4/γ2)
    2+γx
    γ
    (4−γ2)/γ2
    e−2(2+xγ)/γ2
    ⇒ package FactoMineR (coeffRV) (Josse et al., 2008)
    44 / 58
    

    View Slide

48. Data Common Structure Groups Study Partial Analyses To go further Example
    Back to the wine example!
    • 10 white wines from Val de Loire (5 Vouvray - 5 Sauvignon)
    • 27 continuous variables: sensory descriptors
    O.fruity
    O.passion
    O.citrus
    …
    Sweetness
    Acidity
    Bitterness
    Astringency
    Aroma.intensity
    Aroma.persistency
    Visual.intensity
    Odor.preferene
    Overall.preference
    Label
    S Michaud 4.3 2.4 5.7 … 3.5 5.9 4.1 1.4 7.1 6.7 5.0 6.0 5.0 Sauvignon
    S Renaudie 4.4 3.1 5.3 … 3.3 6.8 3.8 2.3 7.2 6.6 3.4 5.4 5.5 Sauvignon
    S Trotignon 5.1 4.0 5.3 … 3.0 6.1 4.1 2.4 6.1 6.1 3.0 5.0 5.5 Sauvignon
    S Buisse Domaine 4.3 2.4 3.6 … 3.9 5.6 2.5 3.0 4.9 5.1 4.1 5.3 4.6 Sauvignon
    S Buisse Cristal 5.6 3.1 3.5 … 3.4 6.6 5.0 3.1 6.1 5.1 3.6 6.1 5.0 Sauvignon
    V Aub Silex 3.9 0.7 3.3 … 7.9 4.4 3.0 2.4 5.9 5.6 4.0 5.0 5.5 Vouvray
    V Aub Marigny 2.1 0.7 1.0 … 3.5 6.4 5.0 4.0 6.3 6.7 6.0 5.1 4.1 Vouvray
    V Font Domaine 5.1 0.5 2.5 … 3.0 5.7 4.0 2.5 6.7 6.3 6.4 4.4 5.1 Vouvray
    V Font Brûlés 5.1 0.8 3.8 … 3.9 5.4 4.0 3.1 7.0 6.1 7.4 4.4 6.4 Vouvray
    V Font Coteaux 4.1 0.9 2.7 … 3.8 5.1 4.3 4.3 7.3 6.6 6.3 6.0 5.7 Vouvray
    45 / 58
    

    View Slide

49. Data Common Structure Groups Study Partial Analyses To go further Example
    Back to the wine example!
    • 3 panels (oenologists, naive consumers, our students!)
    • 60 preference scores: taste evaluation 1 - 10
    Categorical
    Continuous variables
    Student
    (15)
    wine 10
    …
    wine 2
    wine 1
    Label
    (1)
    Preference
    (60)
    Consu
    mer
    (15)
    Expert
    (27)
    • How are the products described by the panels?
    • Do the panels describe the products in a same way? Is there a
    specific description done by one panel?
    46 / 58
    

    View Slide

50. Data Common Structure Groups Study Partial Analyses To go further Example
    Practice with R
    1 Define groups of active and supplementary variables
    2 Scale or not the variables
    3 Perform MFA
    4 Choose the number of dimensions to interpret
    5 Simultaneously interpret the individuals and variables graphs
    6 Study the groups of variables
    7 Study the partial representations
    8 Use indicators to enrich the interpretation
    47 / 58
    

    View Slide

51. Data Common Structure Groups Study Partial Analyses To go further Example
    Practice with R
    library(FactoMineR)
    Expert <- read.table("http://factominer.free.fr/docs/Expert_wine.csv",
    header=TRUE, sep=";", row.names=1)
    Consu <- read.table(".../Consumer_wine.csv",header=T,sep=";",row.names=1)
    Stud <- read.table(".../Student_wine.csv",header=T,sep=";",row.names=1)
    Pref <- read.table(".../Preference_wine.csv",header=T,sep=";",row.names=1)
    palette(c("black","red","blue","orange","darkgreen","maroon","darkviolet"))
    complet <- cbind.data.frame(Expert[,1:28],Consu[,2:16],Stud[,2:16],Pref)
    res.mfa <- MFA(complet,group=c(1,27,15,15,60),type=c("n",rep("s",4)),
    num.group.sup=c(1,5),graph=FALSE,
    name.group=c("Label","Expert","Consumer","Student","Preference"))
    plot(res.mfa,choix="group",palette=palette())
    plot(res.mfa,choix="var",invisible="quanti.sup",hab="group",palette=palette())
    plot(res.mfa,choix="ind",partial="all",habillage="group",palette=palette())
    plot(res.mfa,choix="axes",habillage="group",palette=palette())
    dimdesc(res.mfa)
    write.infile(res.mfa,file="my_wine_results.csv") #to export a list
    48 / 58
    

    View Slide

52. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the individuals
    -2 -1 0 1 2 3
    -3 -2 -1 0 1
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    S Michaud
    S Renaudie
    S Trotignon
    S Buisse Domaine
    S Buisse Cristal
    V Aub Silex
    V Aub Marigny
    V Font Domaine
    V Font Brûlés
    V Font Coteaux
    Sauvignon
    Vouvray
    Sauvignon
    Vouvray
    • The two labels are
    well separated
    • Vouvray are
    sensorially more
    different
    • Several groups of
    wines, ...
    49 / 58
    

    View Slide

53. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the active variables
    -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
    -1.0 -0.5 0.0 0.5 1.0
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    Expert
    Consumer
    Student O.Intensity.before.shaking
    O.Intensity.after.shaking
    Expression
    O.fruity
    O.passion
    O.citrus
    O.candied.fruit
    O.vanilla
    O.wooded
    O.mushroom
    O.plante
    O.flower
    O.alcohol
    Typicity
    Attack.intensity
    Sweetness
    Acidity
    Bitterness
    Astringency
    Freshness
    Oxidation
    Smoothness
    A.intensity
    A.persistency
    Visual.intensity
    Grade
    Surface.feeling
    O.Intensity.before.shaking_C
    O.Intensity.after.shaking_C
    O.alcohol_C
    O.plante_C
    O.mushroom_C
    O.passion_C
    O.Typicity_C
    A.intensity_C
    Sweetness_C
    Acidity_C
    Bitterness_C
    Astringency_C
    A.alcohol_C
    Balance_C
    Typical_C
    O.Intensity.before.shaking_S
    O.Intensity.after.shaking_S
    O.alcohol_S
    O.plante_S
    O.mushroom_S
    O.passion_S
    O.Typicity_S A.intensity_S
    Sweetness_S
    Acidity_S
    Bitterness_S
    Astringency_S
    A.alcohol_S
    Balance_S
    Typical_S
    50 / 58
    

    View Slide

54. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the active variables
    -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
    -1.0 -0.5 0.0 0.5 1.0
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    Expert
    Consumer
    Student
    O.passion
    Sweetness
    Acidity
    O.passion_C
    Sweetness_C
    Acidity_C
    O.passion_S
    Sweetness_S
    Acidity_S
    50 / 58
    

    View Slide

55. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the groups
    0.0 0.2 0.4 0.6 0.8 1.0
    0.0 0.2 0.4 0.6 0.8 1.0
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    Expert
    Consumer
    Student
    Preference
    Label
    • 2 groups are all the
    more close that they
    induce the same
    structure
    • The 1st dimension is
    common to all the
    panels
    • 2nd dimension mainly
    due to the experts
    • Preference linked to
    sensory description
    51 / 58
    

    View Slide

56. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the partial points
    -4 -2 0 2 4
    -3 -2 -1 0 1 2
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    S Michaud
    S Renaudie
    S Trotignon
    S Buisse Domaine
    S Buisse Cristal
    V Aub Silex
    V Aub Marigny
    V Font Domaine
    V Font Brûlés
    V Font Coteaux
    Sauvignon
    Vouvray
    Expert
    Consumer
    Student
    52 / 58
    

    View Slide

57. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of the partial dimensions
    -1.5 -1.0 -0.5 0.0 0.5 1.0
    -1.0 -0.5 0.0 0.5 1.0
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    Dim1.Expert
    Dim2.Expert
    Dim1.Consumer
    Dim2.Consumer
    Dim1.Student
    Dim2.Student
    Dim1.Preference Dim2.Preference
    Dim1.Label
    Expert
    Consumer
    Student
    Preference
    Label
    • The two first
    dimensions of each
    group are well projected
    • Consumer has same
    dimensions as MFA
    53 / 58
    

    View Slide

58. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of supplementary continuous variables
    -1.0 -0.5 0.0 0.5 1.0
    -1.0 -0.5 0.0 0.5 1.0
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    ⇒ Preferences do not participated to the construction of the
    dimensions
    ⇒ Preferences are linked to sensory description
    54 / 58
    

    View Slide

59. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of supplementary continuous variables
    -2 -1 0 1 2 3
    -3 -2 -1 0 1
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    S Michaud
    S Renaudie
    S Trotignon
    S Buisse Domaine
    S Buisse Cristal
    V Aub Silex
    V Aub Marigny
    V Font Domaine
    V Font Brûlés
    V Font Coteaux
    Sauvignon
    Vouvray
    Sauvignon
    Vouvray
    -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
    -1.0 -0.5 0.0 0.5 1.0
    Dim 1 (42.52 %)
    Dim 2 (24.42 %)
    Expert
    Consumer
    Student
    O.passion
    Sweetness
    Acidity
    O.passion_C
    Sweetness_C
    Acidity_C
    O.passion_S
    Sweetness_S
    Acidity_S
    54 / 58
    

    View Slide

60. Data Common Structure Groups Study Partial Analyses To go further Example
    Representation of supplementary continuous variables
    ⇒ Main information: the favourite is Vouvray Aubuisières Silex
    54 / 58
    

    View Slide

61. Data Common Structure Groups Study Partial Analyses To go further Example
    Helps to interpret
    • Contribution of each group of variables to each component of
    the MFA
    > res.mfa$group$contrib
    Dim.1 Dim.2 Dim.3
    Expert 30.5 46.0 33.7
    Consumer 33.2 23.1 31.2
    Student 36.3 30.9 35.1
    • Similar contribution of the 3 groups
    to the first dimension
    • Second dimension mainly due to the
    expert
    • Correlation between the global cloud and each partial cloud
    > res.mfa$group$correlation
    Dim.1 Dim.2 Dim.3
    Expert 0.95 0.95 0.96
    Consumer 0.95 0.83 0.87
    Student 0.99 0.99 0.84
    First components are highly linked to
    the 3 groups: the 3 clouds of points
    are nearly homothetic
    55 / 58
    

    View Slide

62. Data Common Structure Groups Study Partial Analyses To go further Example
    Similarity measures between groups
    > res.mfa$group$Lg
    Expert Consumer Student Preference Label MFA
    Expert 1.45 0.94 1.17 1.01 0.89 1.33
    Consumer 0.94 1.25 1.04 1.11 0.28 1.21
    Student 1.17 1.04 1.29 1.03 0.62 1.31
    Preference 1.01 1.11 1.03 1.47 0.37 1.18
    Label 0.89 0.28 0.62 0.37 1.00 0.67
    MFA 1.33 1.21 1.31 1.18 0.67 1.44
    > res.mfa$group$RV
    Expert Consumer Student Preference Label MFA
    Expert 1.00 0.70 0.85 0.69 0.74 0.92
    Consumer 0.70 1.00 0.82 0.82 0.25 0.90
    Student 0.85 0.82 1.00 0.75 0.55 0.96
    Preference 0.69 0.82 0.75 1.00 0.31 0.81
    Label 0.74 0.25 0.55 0.31 1.00 0.56
    MFA 0.92 0.90 0.96 0.81 0.56 1.00
    • Expert gives a richer description (Lg greater)
    • Groups Student and Expert are linked (RV = 0.85)
    • Group Student is the closest to the overall (RV = 0.96)
    56 / 58
    

    View Slide

63. Data Common Structure Groups Study Partial Analyses To go further Example
    Partition from the tree
    An empirical number of clusters is suggested (minq
    Wq−Wq+1
    Wq−1−Wq
    )
    0.0 0.5 1.0 1.5 2.0
    Hierarchical Clustering
    inertia gain
    V Aub Silex
    S Trotignon
    S Renaudie
    S Michaud
    S Buisse Domaine
    S Buisse Cristal
    V Font Brûlés
    V Font Domaine
    V Aub Marigny
    V Font Coteaux
    0.0 0.5 1.0 1.5 2.0
    Hierarchical Classification
    57 / 58
    

    View Slide

64. Data Common Structure Groups Study Partial Analyses To go further Example
    Partition on the principal component map
    -2 -1 0 1 2 3 4
    -3 -2 -1 0 1 2
    Dim 1 (42.52%)
    Dim 2 (24.42%)
    V Aub Silex
    S Trotignon
    S Buisse Domaine
    S Renaudie
    S Michaud
    S Buisse Cristal
    V Font Brûlés
    V Font Domaine
    V Aub Marigny
    V Font Coteaux
    cluster 1
    cluster 2
    cluster 3
    cluster 4
    cluster 5
    -2 -1 0 1 2 3 4
    -3 -2 -1 0 1 2
    Dim 1 (42.52%)
    Dim 2 (24.42%)
    V Aub Silex
    S Trotignon
    S Buisse Domaine
    S Renaudie
    S Michaud
    S Buisse Cristal
    V Font Brûlés
    V Font Domaine
    V Aub Marigny
    V Font Coteaux
    cluster 1
    cluster 2
    cluster 3
    cluster 4
    cluster 5
    Continuous vision (principal component) and discontinuous
    (clusters)
    58 / 58
    

    View Slide