Fig 1.
Schematic diagram of the predictive model.
The character or number in each box gives the name of the layer or the number of units (dimensionality), respectively.
Fig 2.
Schematic diagram of an autoencoder.
xni corresponds to the ith element of the nth sample. b(j) is the bias in the jth layer. yn(xn;W) = f(W(4)f(W(3)f(W(2)f(W(1)xn + b(0)) + b(1)) + b(2)) + b(3)) is the output of an autoencoder for a given xn, where W = {W(4),W(3),W(2),W(1),b(0),b(1),b(2),b(3)}. f is a p-dimensional sigmoid function, f(a) = [1/(1 + exp(−a1)),… 1/(1 + exp(−ap))].
Fig 3.
Pretraining procedure for autoencoder.
The weights of a 5-layer autoencoder (right) are copied from two 3-layer autoencoders (left and middle).
Fig 4.
Mean reconstruction errors in cross validation.
A, error of autoencoder for sensory data with respect to the number of units KS B, error for mass spectra with respect to the number of units KM.
Fig 5.
Mean reconstruction errors in cross-validation.
Optimal KS (or KM), giving the minimum error for each DS (or DM) with reference to Fig 4. Error bars indicate standard deviations of testing sample sets. A, error of autoencoder for sensory data with respect to the number of neurons in the hidden layer and error of PCA for sensory data with respect to the number of principal components. B, error for mass spectra with respect to the number of neurons in the hidden layer (in autoencoder) and error with respect to the number of principal components (in PCA).
Table 1.
Number of neurons employed in 9-layer predictive model.
Table 2.
Constant coefficients used in updating rule.
Fig 6.
Examples of predictions by two models, which give a value close to the correlation coefficient for each method. 3024 (= 144 descriptors × 21 samples) data points are plotted in each Fig A, result for the 9-layer predictive model (R ≅ 0.76), B, result for the PLS model (R ≅ 0.61).
Fig 7.
Mean prediction errors of 121 chemical samples.
The six most significant six samples (the top 5%) are indicated with the sample number.
Fig 8.
Mean prediction error of dimethylpyrazine (No. 47).
The maximum error in the sample was found to have a sensory normalized value of about 0.3.
Fig 9.
Scatter plots of the result of PCA applied to the original sensory evaluation data.
A, first and second principal components. B, first and third principal components.