Ten samples of G. lucidum fruiting body and ten G. lucidum spores samples were originated from Taishan, China. The fruiting body of G. lucidum was cross-sectioned into thin slices. From each sample, multiple spectra were taken from five different positions: top surface, middle area, bottom surface, outer stipe and inner stipe. In total, 80 spectra from G. lucidum fruiting body samples and 30 spectra from G. lucidum spores samples were collected.

A Fourier transform infrared (FTIR) spectrometer (Perkin-Elmer Spectrum 100 model) with an attenuated total reflectance (ATR) accessory was used to record the absorbance spectra of the G. lucidum fruiting body and spores directly without any processing. The ATR-FTIR spectra of all the G. lucidum samples were recorded in the mid-IR region of 4000 - 400 cm⁻¹ at resolution of 4 cm⁻¹ with 20 scans for each spectrum. Each spectrum with high signal-to-noise signal of about 50 was obtained by an average of these 20 scans. Background spectra were always recorded before running the sample spectra in order to obtain absorbance spectra with smooth baseline and with minimum detection of absorption bands of water vapor and carbon dioxide present in the optical path of the infrared beam in the spectrometer. Strong absorption bands in the absorbance spectra of the G. lucidum samples were accurately obtained by applying sufficient pressure on the sample onto the ZnSe crystal using a diamond tip in the ATR set-up [5] .

ATR-FTIR spectra are affected by both the concentration of the chemical constituents and the physical properties of the analyzed product. The physical effects, such as baseline variation, light scattering, path length differences, etc., account for the majority of the variance among spectra while the variance due to chemical composition is considered to be small. Therefore mathematical pretreatments are essential to reduce the variation due to physical effects so as to enhance the contribution of the chemical composition [7] [8] .

The spectra were first smoothed using the Savitzky-Golay algorithm [9] by spanning a 10-point window, and then were reduced by taking every sixth point to speed up subsequent manipulation. To remove the regions of the spectra with low signal-to-noise ratios arising from the lower system response, only the wavenumbers ranging from 4000 to 450 cm⁻¹ with 593 spectra points were used in the analysis. To remove slope variation and to correct light scatter due to different particle sizes, the standard normal variate (SNV) method [10] was used to standardize each spectrum by setting its mean intensity to zero and the variance to one. After pretreatment, the mean spectra from fruiting body and spores of G. lucidum have similar patterns as shown in Figure 1, which indicates similar chemical composition. Some small between-class differences were observed in the region of 1800 - 1050 cm⁻¹, 3000 - 2700 cm⁻¹ and 3700 - 3500 cm⁻¹, which may indicate different levels of the chemical components contained in fruiting body and spores of G. lucidum.

1) Principal component discriminant analysis (PCDA) and partial least squares discriminant analysis (PLSDA)

Multivariate statistical methods including principal component analysis (PCA), partial least squares (PLS) and linear discriminant analysis (LDA) [11] - [13] were employed on whole spectral region to investigate the differences of spectra from spores and fruiting body of G. lucidum.

Simple and direct implementation of LDA in high-dimensional spectroscopic data setting provides poor classification results and the interpretation of the results is challenging due to singularity problem and highly-correlated spectral features. To solve this problem, many traditional approaches to this problem involve performing feature selection to reduce the variable dimension before classification. PCA and PLS were used to reduce the dimension of the original spectral data matrix with little loss of information. Then LDA focuses on finding a linear combination of the new variables, provided either by PCA or PLS, to construct canonical variate which best separates the two groups. Using pretreated spectral data described in Section 2.3, classification rules were derived using principal component discriminant analysis (PCDA) [14] - [16] and partial least squares discriminant analysis (PLSDA) [15] - [17] . The PCDA involves an initial PCA on the pre-treated spectra followed by a LDA performed on the first k PCs’ scores. The PLSDA involves a PLS regression on the pre-treated spectra followed by a LDA on the first k PLS components’ scores. Both PCDA and PLSDA were carried out with k ranging from 2 to 20.

2) Penalized discriminant analysis (PDA)

Though the spectroscopic data are highly correlated due to the presence of a large number of overlapping broad peaks, in many applications, only a small subset of variables (wavelengths/wavenumbers) contain sufficient information for discrimination. Hence there is interest in determining if a small subset of spectral wavenumbers containsas much information as the full spectrum does.

Penalized discriminant analysis (PDA) [18] [19] involves a sparse linear combination of all spectral features by imposing an norm penalty on the discriminant vector. The PDA extends LDA to the high-dimensional setting to deal with ill-posed problem without filtering out any spectral feature. Using pretreated spectral data with number of spectra points p = 593, classification rules were derived by a PDA using Fisher’s criteria [20] . It generates discriminant vector v in Fisher’s discriminant problem which involves a sparse linear combination of p number of spectral features by shrinking some coefficients towards zero and setting others equal to zero. The PDA investigated here can be expressed in the following optimization problem:

where is the sample estimate of between-class covariance matrix and is the sample estimate of within-

class covariance matrix, λ is non-negative tuning parameter. A diagonal estimate for the within-class covariance matrix is used here because it has been shown to give good results in the high dimensional setting [21] . Each feature of the discriminant vector v is additionally penalized by its sample within-group standard deviation. The larger the value of λ, the larger the penalty on v and therefore the smaller the number of non-zero components, that is, the resulting discriminant vector v will be sparse in the spectral features. Classification accuracy was used to guide the choice of optimal parameter.

Leave-one-out cross-validation was used to train the algorithm by carrying out the PCDA, PLSDA and PDA classification rules on all the data except one sample which was then tested. This was repeated until all samples have been tested and an overall model accuracy was determined. To ensure that the wavelengths selected by PDA model are not training set specific, the PDA model was also validated with 70% of the data being treated as training data and 30% as test data. To ensure the statistical robustness, this process was repeated 50 times with different random splits of training and test sets, and the average misclassification rates were presented to assess the classification performance.

All the algorithms for computations and analyses were implemented in R statistical programming language [22] .

Figure 1 shows the typical ATR-FTIR spectrum of G. lucidum after pretreatment in the region of 4000 - 450 cm⁻¹ with major peaks of the absorption bands labeled on the mean spectrum. The spectral wavenumbers and their corresponding assignments of the absorption bands in the ATR-FTIR spectrum of G. lucidum were given in Table 1 based on literature [7] [23] - [26] .

Polysaccharide, triterpene, sterols, amino acids, proteins, fatty acids have been known as the most biologically active substances in G. lucidum spores [27] [28] . The bioactive polysaccharides in the forms of glucomannan and arabinan isolated from G. lucidum spores, identified by the absorption band at 1064 cm⁻¹, 1035 cm⁻¹ respectively (listed in Table 1), have been demonstrated to exhibit strong immunomodulation and anti-tumor activities including preventing oncogenesis and tumor metastasis [23] [24] . Furthermore, synergistic effect of polysaccharides and other bioactive components such as triterpene and sterols compounds isolated from spores G. lucidum, identified in the absorption band at 1415 cm⁻¹, 1377 cm⁻¹ and 1145 cm⁻¹ (given in Table 1), have shown to possess high bioactivities and proved effective as cytotoxic, antiviral and antiinflamatory agents [25] [27] . In the regions like ~1630 cm⁻¹, 1733 - 1710 cm⁻¹, 2957 - 2852 cm⁻¹, spectra receive contributions from the compounds, such as protein, fatty acids and lipids of G. lucidum spores [25] [27] .

For PCDA and PLSDA model using the full spectrum region, the number of PCs or PLS components chosen is crucial to the discrimination performance. The discrimination results of cross-validation were used to optimize the number of PCs or PLS components. For PCDA model, the first seven PCs were used to construct the discrimination model and the leave-one-out cross-validation analysis gave a discrimination accuracy of 97%. With the relationship between the spectra variables and the responses taken into account for latent variable design, the PLSDA model used a fewer optimal number of latent variables (only three PLS components) when constructing the canonical variate and the leave-one-out cross-validation achieved a discrimination accuracy of 99%. In Figure 2 the 3D scatter plot of the first three PLS components illustrated a very clear separation between spores and fruiting body of G. lucidum in a 3D space.

PDA model seeks to find an optimal parameter λ with lowest error rate. Figure 3 shows the relationship among the tuning parameter λ, the number of the selected non-zero features (representing the sparsity level of the discriminant vector) and the corresponding error rate of PDA model. It illustrates that the sparsity level of the solution varies smoothly with λ, with larger values of λ resulting in very sparse solutions. When is less than 0.11, larger values of λ result in sparser solutions and lower error rate. The drop is observed at around 50 non-zero features. When λ is more than 0.11, larger λ gives higher error rate. The penalized LDA model with optimal tuning parameters of λ = 0.11 and 53 (out of 593) selected wavelengths points gives classification accuracy of 99% for discrimination between spectra of spores and fruiting body of G. lucidum. The contributions of this wavelength selection method are essential. It leads to a model having a small number of selected wavelength regions, yet comparable or better classification ability than full-spectrum model. Out of 50 random splits of data, the number of times the wavelength was selected shows how important is the wavelength to the discrimination. The selected wavelengths recorded in Figure 4 are concentrated in the regions of 3700 - 3500 cm⁻¹, 3000 - 2800 cm⁻¹, ~1700 cm⁻¹, ~1400 cm⁻¹, ~1000 cm⁻¹, which are consistent with the spectral variation in Figure 1. The selected wavelengths show us which parts of the spectrum are important to the discrimination.

It is possible that the superior performance of PDA model relative to the models using full wavelength is due to the fact that ATR-FTIR spectroscopic data consist of many overlapping absorption bands of which only a small proportion may be informative for explaining the response. Including those uninformative wavelength points in a model may introduce a great deal of noise and thus reduce the performance of the model.

The good discrimination results from all these models suggested that there may exist some inherent compositional differences between spores and fruiting body of G. lucidum.

Discrimination performance of the models may be explained by the correlation between spectral features and chemical constituents of G. lucidum spores. With non-zero features selected for discrimination, the discriminant vector of PDA model makes direct and valuable contribution to interpreting spectral features related to the medical

effect of G. lucidum spores. In Figure 5, the informative features selected are in the regions of 1150 - 980 cm⁻¹, 1700 cm⁻¹, 3000 - 2700 cm⁻¹ and 3700 - 3500 cm⁻¹ corresponding to some differences between the mean spectra of spores and fruiting body of G. lucidum. The non-zero regions with prominent absorption features around 1150 - 1050 cm⁻¹ are typical features of triterpenoids and polysaccharides due to the C-O vibrations, which are the major chemical constituents of G. lucidum. The other prominent absorption peak selected at around 1700 cm⁻¹ is consistent with a C=O stretching vibration in carbonyl compounds which may be characterized by the presence of high content of terpenoids and protein in G. lucidum. It is reported that G. lucidum spores possess a much higher content of triterpenoids on a weight basis when compared to G. lucidum fruiting body [29] . The selected features with sharp peak at around 3000 - 2700 cm⁻¹ are due to C-H stretching vibration. The non-zero regions of 3700 - 3500 cm⁻¹ are characteristic of carbohydrates proteins due to the O-H stretching vibration as shown in Table 1. The carbohydrate content in fruiting body of G. lucidum is much higher than that in spores [27] - [29] , which also explains the mean spectra differences between fruiting body and spores of G. lucidum in this region.

For the PCDA and PLSDA model, the PCDA or PLSDA loading of the original variables combines the loading from PCA or PLS and the loading from LDA when constructing a canonical variate. Therefore the PCDA loading and the PLSDA loading show the contribution at each wavelength to the linear diagnostic rule and thus can be related easily to the spectral features, which permits interpretation of its spectral basis. A comparison between PCDA loading and the PLSDA loading for discrimination between spores and fruiting body of G. lucidum can be seen in Figure 6. The loading features emphasized by the PLSDA model are very similar to those

emphasized by PCDA model, which are consistent with group differences between spores and fruiting body of G. lucidum as shown in Figure 7. When comparing the PDA coefficient in Figure 5 with PCDA and PLSDA loadings in Figure 6, we found that the non-zero regions with prominent absorption features from PDA model were also observed as the most prominent features by PCDA loadings and the PLSDA loadings. However, for the PLSDA and PCDA model, when the number of components used for the discrimination is getting bigger, the loadings from these two models may become more complex and thus the contribution of each wavelength to the classification becomes less interpretable when it is related to the spectral features. The major features of these loadings can also be explained by the assignments of the corresponding absorption bands in the ATR-FTIR spectrum listed in Table 1. The high consistency between the selected features by the discrimination models and chemical features of the ATR-FTIR spectrum may provide a quantitative explanation of the major chemical constituents of spores G. lucidum with respect to chemometrics.

G. lucidum contains approximately 400 different bioactive compounds [22] . Among these ingredients, triterpenoids, polysaccharides, sterols, proteins, nucleo-sides and fatty acid are found the major chemical constituents of G. lucidum [28] . These biologically active compounds have been demonstrated to play a significant role in prevention of oncogenesis and tumor metastasis [6] . The spores of G. lucidum possess a much higher amount of bioactive substances than the fruiting body of G. lucidum [28] . In particular, polysaccharides from G. lucidum

spores have immunomodulating properties. G. lucidum spores have been found to be effective in modulating the immune responses, and thus show efficacy of immunostimulatory and antitumor activities. Some comparative studies also reported that spores and fruiting body of G. lucidum showed different efficacy with regard to their antitumor effects and immunomodulatory activities [1] [29] .