metabolomic data: combining wavelet representation with learning approaches

Metabolomic data: combining waveletrepresentation with learning approaches

Nathalie Villa-Vialaneixhttp://www.nathalievilla.org

In collaboration with Noslen Hernández (CENATAV, La

Havane, Cuba) & Philippe Besse

IUT de Carcassonne (UPVD)

& Institut de Mathématiques de Toulouse

Groupe de travail BioPuces, INRA de Castanet

May 19th, 2010

1 / 23Nathalie Villa-Vialaneix

N

Présentation générale

1 Presentation of the data

2 Wavelet preprocessing and normalization

3 Learning methods

4 Identification of relevant metabolites


N

Presentation of the data


Data have been provided by Alain Paris (INRA): they aremetabolomic spectra (H NMR) from mice urine and consist of950 variables (from 0.50 ppm to 9.99 ppm).

Peaks have been aligned and baseline has been removed.


N



Data have been provided by Alain Paris (INRA): they aremetabolomic spectra (H NMR) from mice urine and consist of950 variables (from 0.50 ppm to 9.99 ppm).

Peaks have been aligned and baseline has been removed.3 / 23

Nathalie Villa-VialaneixN


Biologic question

Study the effets of Hypochoeris radicata (HR) ingestion on themetabolism: HR flowers are responsible for a mortal disease forhorses, the “Australian stringhalt” (nervous system attack,trembling...)

Experiences have been made with 72 mice.


N


Biologic question

Study the effets of Hypochoeris radicata (HR) ingestion on themetabolism: HR flowers are responsible for a mortal disease forhorses, the “Australian stringhalt” (nervous system attack,trembling...)Experiences have been made with 72 mice.


N


Description of the experiments

Mice are divided into several groups according to:

genders : 36 males ; 36 females

daily HR doses ingested : 0 (control) : 24 mice ; 3% : 24 mice ;9% : 24 mice

3 sacrifice dates : 8th day : 24 mice ; 15th : 24 mice ; 21st : 24mice

⇒ 18 groups (but groups coming from sacrifice dates are irrelevantfor the biological question).


N


Day of measures

Urine was collected the following days:

Days 0 1 4 8 11 15 18 21Nb of obs. 68 68 68 66 46 44 19 18

For each mice, from 1 to 8 measures were done.Finally, 397 observations with 950 variables.


N


Day of measures


Days 0 1 4 8 11 15 18 21Nb of obs. 68 68 68 66 46 44 19 18

For each mice, from 1 to 8 measures were done.

Finally, 397 observations with 950 variables.


N


Day of measures


Days 0 1 4 8 11 15 18 21Nb of obs. 68 68 68 66 46 44 19 18

For each mice, from 1 to 8 measures were done.Finally, 397 observations with 950 variables.


N

Wavelet preprocessing and normalization

Basics about wavelets

For a given integer J, a spectrum f can be expressed at level J by:

f(x) =∑

k

αk 2−J/2Ψ(2−Jx − k) +J∑

j=1

∑k

βjk 2−j/2Φ(2−jx − k

)

f(x) =∑

k

αk 2−J/2Ψ(2−Jx − k)︸︷︷︸Trend based on father wavelet Ψ

+J∑

j=1

∑k


)︸︷︷︸Details of levels 1, . . . , J

based on mother wavelet Φ


N




f(x) =∑

k


+J∑

j=1

∑k


)

f(x) =∑

k


+J∑

j=1

∑k





N




f(x) =∑

k


+J∑

j=1

∑k





N


Example of a hierarchical decomposi-tion for a metabolomic spectrum

↓ ↘

... Details 1 to 8↓ ↘


N


Example of a hierarchical decomposi-tion for a metabolomic spectrum

... Details 1 to 8↓ ↘


N


Several strategies

Several wavelet basisHaar wavelets (easily interpretable because they are close todiscrete derivatives);

D4 Daubechies wavelets (smoother representation but notdirectly interpretable).

Several preprocessingsUse all wavelet coefficients as input data;

Use thresholded wavelet coefficients as input data (i.e., deletethe smallest coefficient with an automatic method called “softthresholding”);

Use only the detailed coefficients (and the detailed coefficientsof the shifted spectra) as input data.


N


Scaling of wavelet coefficients (ex: Haardetailed coefficients)

D.1 D.57 D.125 D.297 D.370 D.443 D2.41 D2.120 D2.304 D2.389 D2.474

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Before scaling

D.1 D.57 D.125 D.297 D.370 D.443 D2.41 D2.120 D2.304 D2.389 D2.474

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After scaling


N


Normalization issue

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PCA for the coef-ficients: the dayof measure for thecontrol group isemphasized onaxis 2 and 4


N


Normalization

Find median and variance of the coefficients for each day ofmeasure based on the control group.

Use these values for the normalization of all the observations(according to the day of measure).

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Before After


N


Normalization

Find median and variance of the coefficients for each day ofmeasure based on the control group.

Use these values for the normalization of all the observations(according to the day of measure).

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Before After 12 / 23Nathalie Villa-Vialaneix

N


PCA after normalization

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N

Learning methods

Motivations

Purpose: Validation of the impact of HR ingestion on metabolismby predicting from the spectra the total HR dose ingested. Ifthe prediction is accurate, the impact is not an artefact of the dataand the biological dependency is validated.

Compared methods :

random forest (R package randomForest)

ridge regression (R package glmnet)

LASSO (R package glmnet)

Elasticnet (R package glmnet)

Partial Least Squares (PLS) (R package mixOmics)

sparse PLS (R package mixOmics)


N

Learning methods

Motivations

Purpose: Validation of the impact of HR ingestion on metabolismby predicting from the spectra the total HR dose ingested. Ifthe prediction is accurate, the impact is not an artefact of the dataand the biological dependency is validated.Compared methods :

random forest (R package randomForest)

ridge regression (R package glmnet)

LASSO (R package glmnet)

Elasticnet (R package glmnet)

Partial Least Squares (PLS) (R package mixOmics)

sparse PLS (R package mixOmics)


N

Learning methods

Methodology

Split the data into train and test sets that are balanced according tothe groups;

Preprocess (or not), scale and normalize the data with wavelets;

Learn each of the 6 methods (for each of the 7 kinds ofpreprocessing) on the train set with a cross-validation strategy totune the parameters;

Calculate the mean squared error on the test set.

Repeat the previous scheme 250 times.


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Learning methods

Mean performances in test

Methods Original Daubechies Daubechies Daubechies Haar Haar Haar- Details - Full - Threshold - Details - Full - Threshold

ELN 0.5 16.29 (1.03) 15.38 (0.9) 14.33 (1.07) 42.94 (52.25) 15.39 (1.04) 14.49 (1.03) 30.98 (16.43)ELN 0.25 16.12 (1.03) 15.28 (0.9) 14.35 (0.94) 44.62 (61.3) 15.2 (1) 14.47 (0.98) 32.54 (17.31)ELN 0.1 15.81 (0.98) 15.14 (0.77) 14.38 (0.84) 42.58 (53.83) 15.15 (0.87) 14.58 (0.92) 35.41 (19.43)ELN 0.75 16.31 (1.1) 15.48 (0.9) 14.43 (1.1) 42.62 (51.59) 15.44 (1.06) 14.5 (1.01) 30.31 (15.92)Lasso 16.37 (1.27) 15.56 (1.01) 14.45 (1.14) 41.82 (50.86) 15.56 (1.1) 14.49 (1.01) 30.8 (17.01)Ridge 16.82 (0.83) 16.22 (0.67) 15.56 (0.74) 41.75 (25.09) 16.16 (0.7) 15.66 (0.8) 37.58 (16.07)PLS 16.83 (1.1) 16.25 (0.79) 15.61 (0.87) 81.56 (116.21) 16.09 (0.87) 15.87 (0.91) 42.6 (25.14)RF 16.69 (0.91) 16.33 (1.36) 16.2 (1.16) 18.91 (1.66) 16.24 (1.06) 16.11 (1.09) 18.8 (1.32)SPLS 5 19.71 (1.63) 19.25 (1.25) 16.55 (1.18) 36.54 (31.88) 19.1 (1.63) 17.24 (1.4) 34.25 (24.99)SPLS 10 19.25 (1.65) 19.22 (1.23) 16.74 (1.15) 79.35 (110.56) 18.66 (1.36) 17.14 (1.25) 42.46 (23.76)SPLS 20 18.41 (1.5) 18.81 (1.18) 17.55 (1.2) 76.05 (104.74) 18.55 (1.2) 17.11 (1.13) 42.38 (23.74)


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Learning methods

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Learning methods

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Mean R2 on test sets is equal to 89.0% (minimum is 83.1% andmaximum is 92.8%). 18 / 23


Identification of relevant metabolites

Identification issue

The full learning process is the following:

Spectra→Wavelet preprocess→ Learning→ HR dose prediction

Hence, due to the preprocessing step, the coefficients selectedby ELN are not directly related to metabolites (or to localizationon the spectra).

19 / 23Nathalie Villa-VialaneixN


Adaptation of the importance measure

for Each of the 950 variables, v, of the original data set doRandomize the observations of the variable vCompute the full Daubechies wavelet representationwith the randomized observations for vScale and normalize according to the true values mean,median or variancefor Each test set, i do

Calculate new predictions with false values of vand corresponding mse: msev ,i

Calculate decrease in accuracy for test set: DAi =1 − msei

msev ,iend forAverage over i, DAi , to obtain Importance of v

end for20 / 23



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Identification of important metabolites

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Some havealready been identified: the most important is scyllo-inositol; oneof the orange is probably valine; one of the light yellow is probablytrimethylamine. The others are new.


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What next?

Identification of the metabolites, study of the correlation betweenthe ones found and the ones previously emphasized.Questions? Propositions?


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metabolomic data: combining wavelet representation with learning approaches

Science

data data

data presentation

mice urine

experiments mice

metabolomic data

data description

wavelet preprocessing

level j