MICROWAVE DIELECTRIC SPECTRA AND THE COMPOSITION OF FOODS: PRINCIPAL COMPONENT ANALYSIS VERSUS ARTIFICIAL NEURAL NETWORKS.

Transcription

1 MICROWAVE DIELECTRIC SPECTRA AND THE COMPOSITION OF FOODS: PRINCIPAL COMPONENT ANALYSIS VERSUS ARTIFICIAL NEURAL NETWORKS.

2 Michael Kent, Frank Daschner, Reinhard Knöchel Christian Albrechts University of Kiel, Germany.

3 Complex dielectric permittivity e* f = e f - je f Dispersion, energy storage Loss factor, energy dissipation

4 Dielectric spectra for Chicken at 30 C: 2 hours in 2% polyphosphate e',e" outlier mean 10 x s.d. replicates 0 1.0E E E E+11 frequency (Hz)

5 Multivariate analysis

6 Principal Component Analysis (PCA) Y j = c 1j X 1 + c 2j X c pj X p.

7 45.00 PC PC2 e' at 12GHz e' at 6GHz

8 Principal Component Analysis (PCA) Y j = c 1j X 1 + c 2j X c pj X p X values are collinear,

9 Principal Component Analysis (PCA) Y j = c 1j X 1 + c 2j X c pj X p X values are collinear, Y values are orthogonal.

10 Principal Component Analysis (PCA) Y j = c 1j X 1 + c 2j X c pj X p X values are collinear, Y values are orthogonal. Data reduction: n values of Y replace p>n values of X

11 Principal Component Analysis (PCA) Y j = c 1j X 1 + c 2j X c pj X p X values are collinear, Y values are orthogonal. Data reduction: n values of Y replace p>n values of X Principal component Regression (PCR)

12 Principal Component Analysis (PCA) Y j = c 1j X 1 + c 2j X c pj X p X values are collinear, Y values are orthogonal. Data reduction: n values of Y replace p>n values of X Principal component Regression (PCR) k responses y, n Principal Components Y y k = a k + 1 n b ki Y i

13 Partial Least Squares Regression (PLSR)

14 Partial Least Squares Regression (PLSR) Similar to PCR but y values included in optimisation process.

15 Partial Least Squares Regression (PLSR) Similar to PCR but y values included in optimisation process. Constructs linear combinations of inputs incorporating y

16 Partial Least Squares Regression (PLSR) Similar to PCR but y values included in optimisation process. Construct linear combinations of inputs incorporating y Finds directions with maximum variance and correlation with the output

17 Partial Least Squares Regression (PLSR) Similar to PCR but y values included in optimisation process. Construct linear combinations of inputs incorporating y Finds directions with maximum variance and correlation with the output Partial least squares regression operates like principal component regression

18 Principal Components Regression Regress on n < p principal components of X

19 Principal Components Regression Regress on n < p principal components of X Partial Least Squares Regression Regress on n < p directions of X weighted by y

20 Artificial Neural Networks (ANN)

21 Artificial Neural Networks (ANN) y = f(x,w)

22 Artificial Neural Networks (ANN) X variables measured y = f(x,w)

23 Artificial Neural Networks (ANN) y = f(x,w) X variables measured W weighting vector or activation function

24 Artificial Neural Networks (ANN) Activation function of neurons

25 Artificial Neural Networks (ANN) Activation function of neurons: linear-emulates PCR

26 Artificial Neural Networks (ANN) Activation function of neurons: linear-emulates PCR non-linear- more general

27 Artificial Neural Networks (ANN) Activation function of neurons: linear-emulates PCR non-linear- more general- sigmoid, tansig or logsig tansig(n)=2/(1+exp(-2n))-2

28

29 Samples and data used

30 chicken 1 calibration 144 samples measured in 1994; 72 controls, 72 treated. validation 72 samples measured in chicken 2 calibration pooled data -106 validation samples. validation 110 randomly selected samples. prawns calibration 152 samples validation 16 samples prepared at a later date pork calibration 167 various types of treated pork, canned, bacon, ham and fresh validation 18 unknown samples prepared at a later date; 4 leg meat, 4 streaky bacon, 4 ham and 6

31 Some results

32 R 2 PCR RMSE C RMSE Chicken 1 Water Protein Added Water Chicken 2 Water Protein Added Water Prawns Water Fat Protein NaCl Phosphate Added Water Pork Water Fat Ash Protein NaCl Added Water V

33 R 2 PCR PLSR RMSE RMSE R 2 RMSE C V C RMSE Chicken 1 Water Protein Added Water Chicken 2 Water Protein Added Water Prawns Water Fat Protein NaCl Phosphate Added Water Pork Water Fat Ash Protein NaCl Added Water V

34 R 2 PCR PLSR ANN (linear) RMSE RMSE R 2 RMSE RMSE R 2 RMS C V C V E C Chicken 1 Water Protein Added Water Chicken 2 Water Protein Added Water Prawns Water Fat Protein NaCl Phosphate Added Water Pork Water Fat Ash Protein NaCl Added Water RMS E V

35 PCR PLSR ANN (linear) ANN(non-linear) R 2 RMSE C RMSE V R 2 RMSE C RMSE V R 2 RMS E C RMS E V R 2 RMSE C RMSE V Chicken 1 Water Protein Added Water Chicken 2 Water Protein Added Water Prawns Water Fat Protein NaCl Phosphate Added Water Pork Water Fat Ash Protein NaCl Added Water

36 PCR PLSR ANN (linear) ANN(non-linear) R 2 RMSE C RMSE V R 2 RMSE C RMSE V R 2 RMS E C RMS E V R 2 RMSE C RMSE V Chicken 1 Water Protein Added Water Chicken 2 Water Protein Added Water Prawns Water Fat Protein NaCl Phosphate Added Water Pork Water Fat Ash Protein NaCl Added Water

37 Comparison of PCR and ANN

38 Predicted Moisture Content (%) Predicted Fat Content (%) leg streaky ham unknown Predicted Ash Content (%) Moisture Content (%) Fat Content (%) Ash Content (%) Predicted Protein Content (%) Predicted Salt Content (%) Predicted Added Water (%) Protein Content (%) Salt Content (%) Calculated Added Water (%)

39 Predicted Moisture Content (%) Predicted Fat Content (%) leg streaky ham unknown Predicted Ash Content (%) Moisture Content (%) Fat Content (%) Ash Content (%) Predicted Protein Content (%) Predicted Salt Content (%) Predicted Added Water (%) Protein Content (%) Salt Content (%) Calculated Added Water (%)

40 Acknowledgements Some of the data used in this paper was taken from work supported by the UK Food Standards Agency. The authors are grateful for permission to use it. Further data was obtained from a project supported by the Commission of the European Communities, Agriculture and Fisheries (FAIR) specific RTD programme FAIR CT Added Water in Foods. It does not necessarily reflect the Commission s views and in no way anticipates its future policy in this area.