RoBoost-PLSR : Robust PLS regression method inspired from boosting principles

(1)

RoBoost-PLSR :

Robust PLS regression method inspired from

boosting principles

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p. 2

RoBoost-PLS : robust PLS regression method inspired from boosting principles

Summary

1. Introduction

a. Robustness

b. Robust PLS methods

2. Theory

a. RoBoost-PLS regression

b. Pros and Cons

3. Materials and Methods

a. Methods

b. Data

4. Results and discussions

5. Conclusion

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p. 3

1. Introduction

a. Robustness

(4)

p. 4

X0

1. Introduction

a. Robustness

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p. 5

1. Introduction

X1

X0

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p. 6

X1

X0

1. Introduction

a. Robustness

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p. 7

X1

X0

1. Introduction

a. Robustness

(8)

p. 8

Main hypothesis in Robust methods :

- Robust methods assume that the largest mass of data is X0 .

- The learning database is polluted

Main difficulties in Robust methods :

- Find a good measurement to highlight the outliers (especially when estimating

leverage points)

a. Robustness

1. Introduction

(9)

p. 9

Wakelinc et Macfie, « A Robust PLS Procedure »

Cummins , « Iteratively reweighted partial least squares: A performance analysis

by monte carlo simulation »

Pell, « Multiple Outlier Detection for Multivariate Calibration Using Robust

Statistical Techniques »

Griep et al., « Comparison of Semirobust and Robust Partial Least Squares

Procedures »

Serneels et al., « Partial Robust M-Regression »;

Gil et Romera, « On Robust Partial Least Squares (PLS) Methods »

Møller, Frese, et Bro, « Robust Methods for Multivariate Data Analysis »

Hubert et Branden, « Robust Methods for Partial Least Squares Regression ».

b. Robust PLS methods in literature

1. Introduction

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p. 10

PRM (Partial Robust M-regression) :

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

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p. 11

PRM (Partial Robust M-regression) :

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

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p. 12

PRM (Partial Robust M-regression) :

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

(13)

p. 13

PRM (Partial Robust M-regression) :

PLS regression model

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

(14)

p. 14

PRM (Partial Robust M-regression) :

PLS regression model

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

(15)

p. 15

PRM (Partial Robust M-regression) :

PLS regression model

Leverage and Y-residuals

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

(16)

p. 16

PRM (Partial Robust M-regression) :

PLS regression model

Leverage and Y-residuals

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

(17)

p. 17

PRM (Partial Robust M-regression) :

PLS regression model

Leverage and Y-residuals

Weight estimation

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

(18)

p. 18

PRM (Partial Robust M-regression) :

PLS regression model

Leverage and Y-residuals

Weight estimation

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Calculation of a PLS model with a defined

x latent variables then weighting according to the

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p. 19

PRM (Partial Robust M-regression) :

PLS regression model

Leverage and Y-residuals

Weight estimation

Weighting X and Y

matrices

b. Robust PLS methods in literature

1. Introduction

Until convergence

of model

Calculation of a PLS model with a defined

x latent variables then weighting according to the

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p. 20

a. RoBoost-PLS

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p. 21

Weighted PLSR model

with 1 LV

a. RoBoost-PLS

2. Theory

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p. 22

Weighted PLSR model

with 1 LV

a. RoBoost-PLS

2. Theory

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p. 23

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

a. RoBoost-PLS

2. Theory

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p. 24

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

a. RoBoost-PLS

2. Theory

(25)

p. 25

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

Weight estimation

a. RoBoost-PLS

2. Theory

(26)

p. 26

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

Weight estimation

a. RoBoost-PLS

2. Theory

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p. 27

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

Weight estimation

Until convergence

of model

a. RoBoost-PLS

2. Theory

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p. 28

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

Weight estimation

Until convergence

of model

a. RoBoost-PLS

2. Theory

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p. 29

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

Weight estimation

Until convergence

of model

a. RoBoost-PLS

2. Theory

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p. 30

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

Weight estimation

X = X-residuals and

Y = Y-residuals

Until convergence

of model

a. RoBoost-PLS

2. Theory

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p. 31

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

Weight estimation

X = X-residuals and

Y = Y-residuals

Until convergence

of model

a. RoBoost-PLS

2. Theory

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p. 32

Weighted PLSR model

with 1 LV

Leverage, Y-residuals,

X-residuals

Weight estimation

X = X-residuals and

Y = Y-residuals

Until convergence

of model

up to x latent variables

a. RoBoost-PLS

2. Theory

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p. 33

- Facilitates the weighting of

leverage point

- Apprehends X-residuals

Pros

- B-coef not observable

- Scores : non-orthogonal

Cons

b. Pros and Cons

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p. 34

- Facilitates the weighting of

leverage point

- Apprehends X-residuals

Pros

- B-coef not observable

- Scores : non-orthogonal

Cons

b. Pros and Cons

2. Theory

The distance to the center of the scores

is easy to define for one dimension

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p. 35

4 different methods :

PLSR with outliers in the training set

PLSR without outliers in the training set

PRM with outliers in the training set

RoBoost-PLSR with outliers in the training set

a. Methods

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p. 36

4 different methods :

PLSR with outliers in the training set

PLSR without outliers in the training set

PRM with outliers in the training set

RoBoost-PLSR with outliers in the training set

Reference

a. Methods

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Simulated data set

3. Materials and methods

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Real data set

3. Materials and methods

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p. 39

4. Results and discussions

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4. Results and discussions

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4. Results and discussions

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4. Results and discussions

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4. Results and discussions

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4. Results and discussions

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4. Results and discussions

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4. Results and discussions

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4. Results and discussions

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5. Conclusion

The results highlighted the good predictive capacity of the RoBoost-PLSR method,