CSF Sampling and Patients

The CSF patients involved in this study were all followed by the Rotterdam Multiple Sclerosis Center and the department of Neurology at Erasmus University Medical Center (Rotterdam, The Netherlands). The Medical Ethical Committee of Erasmus University Medical Centre in Rotterdam, The Netherlands, approved the study protocol and all study patients gave written consent. All CSF samples were specifically collected from patients that were not under any drug treatment.

All CSF samples were taken from patients via lumbar puncture. Immediately after sampling, the CSF samples were centrifuged to remove cells and cellular elements (10 minutes at 3000 rpm). Subsequently, a fraction of the CSF samples were used for diagnosis purpose and the remaining amounts were aliquoted and stored at −80°C.

The CSF samples were classified into two groups. The first group consisted of CSF samples collected from patients diagnosed with MScl. The second group of CSF samples was taken from patients who were diagnosed with clinically isolated syndrome of demyelination (CIS), which represents an early stage of MScl. It is worthwhile to mention that all patients diagnosed with CIS have later developed MScl. The overview of the available CSF samples for NMR and GC-MS is presented in Table 1, while clinical information is described in File S1. It is important to mention that the set of samples analysed by NMR and GC-MS only partly overlap (Table 1).

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Table 1. The number of samples included in a training and independent test set.

https://doi.org/10.1371/journal.pone.0038163.t001

NMR Samples Preparation and Data Acquisition

The CSF samples of the CIS and MScl classes were prepared as follows. An aliquot of 20 µL of the stored frozen human CSF sample (−80°C) was thawed at room temperature. Subsequently, 200 µL D₂O was added to biofluid in order to obtain sufficient sample volume for NMR measurements. We used 3-(Trimethylsilyl)propionic-2,2,3,3-d₄ acid sodium salt (TSP-d₄ 99 at.%D) as internal standard for chemical shift reference (δ 0.00 ppm) and metabolite quantification. For this and buffering, 70 µL of buffer solution was added to the 220 µL of human CSF sample. The buffer solution solvated in a mixture of water and D₂O consists of 2,85 mM TSP, 6.92 mM sodium azide (NaN₃) and 42.08 mM sodium phosphate dibasic dehydrate (Na₂HPO₄•2H₂O). The addition of mixture solution to 220 µL of CSF sample leads to a final concentration of 0.66 mM TSP-d₄ and corresponding concentrations of buffer solution components. The pH of the CSF NMR sample was adjusted to around 7 (7.0–7.1) by the buffering capacity of the phosphate in the buffer solution. The final CSF NMR sample (290 µL) was transferred to a SHIGEMI microcell tube for NMR measurements.

All spectra were recorded by using a standard pulse sequence (1D-NOESY; recycle delay-90°-t1-90°-t_m-90°) at a temperature of 25°C. The water suppression was achieved by presaturation during the relaxation delay (8 s) and mixing time (100 ms). All ¹H NMR spectra were acquired at 600 MHz Bruker NMR Spectrometer equipped with cryo-cooled probe. For each 1D ¹H NMR spectrum 256 scans were accumulated with a spectral width of 7200 Hz resulting in a total of 16K data points. The acquisition time for each scan was 2.2s. Prior to spectral analysis, all Free Induction Decays (FIDs) were multiplied with a 0.3 Hz line broadening function, Fourier transformed and manually phased. In addition, the TSP internal reference peak was set to 0 ppm. This initial processing was done using ACD/SpecManager software version 12.02 [21].

All 46 human CSF spectra were acquired and pre-treated as described above and subsequently, transferred to Matlab, version 7.6 (R2008b) (Mathworks, Natick, MA) for further analysis.

Preprocessing of NMR Spectra

The NMR spectral data of human CSF was pre-processed, which typically involves baseline correction, alignment, binning, normalization and scaling. Asymmetric Least Square method was used for baseline correction of NMR spectra [22]. Next, in order to remove variations in peak position, NMR spectra were aligned by using correlation optimized warping [23]. A further problem is the high dimensionality of the data (circa 15000 variables). To reduce the number of variables associated with the NMR spectra, we performed binning via adaptive intelligent binning [24]. Before binning data were normalized to total area. The chemical shift ranges of δ 0.75–4.15 and δ 8.65–8.85 were used for the binning procedure. The binning procedure led to 233 bins in total. In the final step of preprocessing data were scaled to unit variance.

GC-MS Samples Preparation and Data Acquisition

The GC-MS method applied here is a non-targeted GC-MS method which uses a derivatization step that has frequently been applied for metabolomics studies [25]. With this method it is possible to analyse simultaneously various classes of (polar) metabolites, e.g. amino acids, organic acids, fatty acids, sugars.

Human CSF samples (100 µL) were deproteinized by adding 400 µL methanol and subsequently centrifuged for 10 min at 10000 rpm. The supernatant was dried under N₂ followed by derivatization with methyl-N-(trimethylsilyl)-trifluoroacetamide (MSTFA) in pyridine similar to Koek et al. [25]. During the different steps in the sample work-up, i.e. prior to deproteinization, derivatization and injection, different (deuterated) internal standards were added at a level of circa 20 ng/µL. The end volume was 135 µl and 1 µl aliquots of the derivatized samples were injected in splitless mode on a HP5-MS 30 m×0.25 mm×0.25 mm capillary column (Agilent Technologies, Palo Alto, CA) using a temperature gradient from 70°C to 320°C at a rate of 5°C/min. GC-MS analysis was performed using an Agilent 6890 gas chromatograph coupled to an Agilent 5973 quadrupole mass spectrometer. Detection was carried out using MS detection in electron impact mode and full scan monitoring mode (m/z 15−800). The electron impact for the generation of ions was 70 eV.

A total of 38 human CSF samples were analysed by GC-MS. The samples were randomly distributed over batches and each sample was injected once. A pooled CSF sample was prepared from the study samples for quality control (QC). Aliquots of this QC sample were analysed in sextuplicate in each batch according to the procedure described by van der Greef et al. [26].

Data preprocessing was performed by composing target lists of peaks detected in the samples based on retention time and mass spectra. Peaks were characterized by retention time and m/z ratio and identified by comparison with a spectral database. These peaks were integrated for all samples. The peak areas were subsequently normalized using internal standards and corrected for intra- and inter-batch effects using the QC samples according to the procedure described by Verheij et al. [27]. The final step of preprocessing was unit variance scaling.

Explorative Analysis

The first step of our data analysis strategy consists of a data exploration by means of Robust – Principal Component Analysis (R-PCA) [28] and PCA. R-PCA was employed on the autoscaled data to detect the outliers in both datasets. To extract and display the systematic variation in the two datasets PCA was also carried out on the autoscaled data.

Selection of Training Set and Independent Test Set

In order to validate the performance of the classifier an independent test set was used. Dividing the data into training and test sets is a widely accepted approach for this purpose [29], [30]. The commonly used leave-one-out cross-validation (LOOCV) is biased to assess the predictive ability of the classification model. External validation using test sets provides a means to establish a more reliable predictive performance of the classification model [31], [32], [33].

The training set and an independent test set were selected separately for NMR and GC-MS datasets using the Kennard-and-Stone algorithm [34] in such a way that the number of samples in the test set in every group (i.e. MScl or CIS, see Table 1) was equal to 25% of the total number of samples in a group). The training sets were used for all optimization steps and for developing a classifier, while the independent test was utilized to assess the predictive ability of the classification model. The Kennard-and-Stone algorithm is one of many possible approaches for data division [32], [35], [36]. The use of Kennard-and-Stone algorithm for data division is justified by the advantage of obtaining representative training set and the reproducibility of the selection. Nevertheless, since it is Euclidean based algorithm it might be influenced by noisy variables. Therefore, in addition the training and independent test sets were selected randomly. The results of presented fusion approach for random division is shown in Figure S3 and File S1.

The number of samples included in the training set and independent test set is shown in Table 1. Since the number of overlapping samples between NMR and GC-MS is relatively low (22) this puts limitations on the accuracy of the predictions when using a relatively small independent test. Therefore, as an additional check of the meaningfulness of the classification model, a permutation test with 10000 permutations was performed. Using a permutation test, we checked if the assessment of the classification of objects into the original classes is significantly better than any random classification in two arbitrary classes.

Supervised Analysis: Linear and Non-linear Approaches

The supervised analysis is carried out in order to extract class related information. Below, we briefly describe the overall strategy. First, the supervised data analysis involving linear methods is described followed by the proposed kernel based non-linear methods. In the next sections detailed information on specific technical aspects of the supervised data analysis strategy is provided.

The most straightforward approach in data analysis is to first use a linear method. Therefore, the linear method by means of the cross model validation (CMV) PLS-DA is applied [37]. In this technique, two cross validation procedures are included in the variable selection procedure based on jack-knifing. This approach enables removal of irrelevant variables and optimizes the model for accurate prediction of group memberships. This technique was first applied to individual datasets and then the selected variables were fused and analysed by the linear classifier.

Next, if the considered classification problem is suspected to be non-linear (e.g. when prediction accuracy of linear model is low), more sophisticated algorithms can be applied. Here, a non-linear technique based on kernel methods was utilised. The strategy is shown in Figure 1. The steps 1 and 2 were carried out on the training set. The first step consists of a variable selection method, which aims to obtain meaningful information from each individual data set. We used SVM-RFE for the non-linear kernel as variable selection method [19]. For both datasets the radial basis function (rbf), i.e. a Gaussian function, is used to map the original input data into a feature space [38] (see also File S1 Kernel transformations part). The choice of kernel function is performed both by means of visual inspection of PCA score plot and using the root mean square error of cross validation (RMSECV).

RMSECV  =  Here, Y is a real class label, while is the predicted class label; n indicates the number of observations.

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Figure 1. Conceptual flowchart of kernel-based data fusion.

X₁ and X₂ are two blocks of data. *Note that all optimized parameters, i.e. number of variables, sigma for the rbf kernel, coefficients µ and nr. of LV’s are kept during the model reconstruction using all available samples. The particular steps are described in sections data analysis.

https://doi.org/10.1371/journal.pone.0038163.g001

The kernel parameter sigma (σ) is optimized by LOOCV. More specifically, in each iteration, one object from the training set is removed and a model is constructed on the remaining objects for different values of σ. This is repeated until each object has been removed once. The RMSECV is calculated for each iteration. The optimal σ value is selected based on the first minimum in the RMSECV. SVM-RFE is performed for both datasets separately. Only the selected variables are then used in the subsequent steps. In the final part of step 1 (see Figure 1), the data with only significant variables are analysed by K-PLS-DA, which is an alternative to the SVM technique. This part is employed to tune the kernel parameters and to estimate the classification accuracy of the separate datasets. The optimal model complexity (i.e. number of latent variables (LV’s)) was selected based on RMSECV. Note that the selected variables per dataset can be concatenated in classical mid-level fusion and analysed with K-PLS-DA. [8] In our procedure, SVM-RFE was selected as variable selection and K-PLS-DA as classification method. The use of SVM-RFE it justified by the fact that it is a well-established method, able to find significant variables in non-linear space. The binary classifier (PLS-DA) is a popular alternative to SVM. Our choice was guided by the fact that SVM offers sparse solutions based on a limited number of observations, i.e. the support vectors. Since the obtained hyperplane can be based on outlying objects, this brings a question about the robustness of SVM [38]. The main benefits of K-PLS-DA are its efficiency and simplicity. In addition, it has convenient visualisation options in the latent variable space. Nevertheless, as it will be shown latter, in terms of prediction K-PLS-DA and SVM perform similarly (see Data fusion by MKL).In the second step (see Figure 1), the kernels of the individual datasets are concatenated by linear combination of their kernel matrixes. In step 3 the combined kernels are analyzed with K-PLS-DA. The accuracy of the K-PLS-DA model is validated by the independent test set and by the permutation test. In order to obtain more robust classification model in the final step (number 4) the K-PLS-DA model is reconstructed using all available samples (i.e. both training and test sets) and all previously optimized parameters, namely number of variables, sigma for rbf kernel, coefficients µ and nr. of LV’s (see later). Moreover in this step variable importance in kernel space is evaluated and visualized.

Variable Selection by SVM- RFE

The first step of our approach (Figure 1) consists of extracting the most relevant information from the datasets by using SVM- RFE variable selection. SVM is a powerful, supervised method and since this technique is extensively discussed in the literature we do not focus on its description [39]. SVM- RFE is an application of RFE in the SVM algorithm and was introduced by Guyon [19]. RFE is a backward elimination algorithm that ranks variables on the basis of the smallest change in a cost function minimized in the SVM algorithm. In the specific case of a non-linear kernel, used in this manuscript, the cost function to be minimized takes the form:(1)Here, H is a matrix with elements y_iy_jK(x_i,x_j), K is a kernel function, y_j and y_j denotes the class labels, α’s are the Lagrangian multipliers and 1 is a vector of ones. The algorithm begins by using all training data to train SVM. The matrix H is than recomputed for every variable being removed, while the α’s values remain unchanged. The elimination of the input variable “i” causes the change in cost function, J. The change in the cost function is calculated according to equation 2:(2)Here, H(-i) indicates the matrix H calculated when the input component “i” is removed. All the ΔJ(i) is calculated and the values are sorted accordingly. A subset of variables corresponding to the end of the sorted list of ΔJ (i.e. those with small ΔJ) is then removed. In our case, the subset is formed by only one variable in each iteration.

In order to select an optimal set of variables LOOCV approach is used. We used RFE with cross-validation since it increases the likelihood that relevant variables are selected. Averaging over cross-validation iterations ensures that the variables that were significant in each run are selected. This gives a better estimation of the important variables than performing variable selection only once using all training samples. Moreover, using a variable selection procedure with cross-validation, overly optimistic results (solely valid for the training models) can be avoided. In LOOCV in each iteration, one object of the training set is left out and a ranking is obtained. Next, the total ranking is obtained by sorting the variables based on the amount of times it is selected in the LOOCV. All variables that appear twice or more in the “top ten” of the rankings are selected. Although the number ten is somewhat arbitrary, exploration of other options (e.g. “top fifteen” or median +1 of the amount it is selected in the LOOCV) did not affect the outcome.

Data Fusion by Multiple Kernel Learning

The second step of our approach (step 2, Figure 1) aims to combine the kernels. This is done by means of Multiple Kernel Learning (MKL), which was pioneered by Lanckriet et al. [40]and Bach et al. [41] as extension of single kernel to integrate multiple kernels in SVM. They integrated multiple kernels in classification problems. The essence of MKL is to combine kernel matrices into a single kernel using basic algebraic operations such as addition or multiplication. For example, given two (positive semi-definitive) kernels K₁ and K₂ it is possible to define the new kernel K, which is a parameterized linear combination of K₁ and K₂. In particular, given a set of kernels K it is possible to combine them by linear combination according to equation 3:(3)Here m is a number of kernels and coefficients µ are non-negative to assure positive semi-definiteness of K: µ_i ≥0. Note that the dimensions of the kernels have to be equal (i.e. the number of samples in the datasets has to match). The coefficients µ_i in equation 3 can be tuned to weight the importance of the different kernels. The weights can be obtained in multiple ways, i.e. by applying different regularization method such as the L₁ or L₂-norm. L₁ regularization on the kernel coefficients corresponds to the requirement that the sum of µ_i equals one (||µ_i||₁ = 1). L₁ regularization can lead to sparse optimal solution and diminishing one of the platforms. In the current problem of deriving metabolite profiles from NMR and GC-MS datasets both datasets are relevant and complementary (the sets of measured metabolites are partially different). In order to avoid the possibility of shrinking the importance of any platform the L₂-norm was used as regularization parameter. In the L₂-norm approach, different constraint on the coefficients are used, i.e. the sum of squares of µ_i equals one (||µ_i||₂ = 1). The L₂-norm yields a non-sparse solution and it distributes the coefficients over multiple kernels [20]. Using the L₂-norm MKL we try to find the best separation between classes by solving the objective as follows:

(4)The weights µ_i were optimized by LOOCV performed on the training set. The optimal weights were selected based on the minimal error of the root mean square error of cross-validation (RMSECV).

K-PLS-DA and Variables Visualisation

In the non-linear architecture presented in Figure 1, the fused kernels are analyzed with a classification method, K-PLS-DA (step 3). This means that PLS-DA is applied on to the combined kernel matrix.

The classification model is statistically validated, i.e. it is based on the prediction accuracy of the K-PLS-DA model, on the independent test and on the permutation test. Therefore, in the final fourth step of the approach shown in Figure 1 K-PLS-DA is first reconstructed using all available samples and next variables importance is established.

To represent the importance of the original variables, the pseudo samples principle, recently proposed by Krooshof et al. [16] and based on the non-linear plot principle described by Gower [42], was applied (step 4; Figure 1). As shown in Figure 2a, the matrix X (with n number of objects and p number of variables) is mapped by the kernel function K(x_i,x_j) (where x_i and x_j are samples from matrix X). The obtained kernel matrix K is a square matrix of size “n x n” (where n is a number of samples). The application of PLS-DA on the kernel matrix leads to a linear model, i.e. y = Kb+r, where y a vector of group memberships, b regression coefficients and r a model residual. It is possible to obtain predicted ŷ-values for all training samples of matrix X, but the information about the variables (i.e. metabolites) involved in the discrimination is lost. In our approach every original variable is represented as a set of pseudo samples. The pseudo samples are artificial samples constructed as follows: every pseudo sample contains a certain value (e.g. 1) for only one variable and zeros for all the others. It is possible to check the influence of these pseudo samples in a K-PLS-DA model by predicting their corresponding ŷ-values or projecting them into latent variable space.

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Figure 2. Representations of the a) kernel mapping of data matrix X into kernel space; b) pseudo samples principle in K-PLS-DA.

k indicates the range of pseudo sample values (uniformly distributed); *Note that there are “p” pseudo sample matrixes and “p” kernel pseudo samples matrixes. **The ŷ-values can be projected into latent variable space. ^#Note that for kernel pseudo samples the loading and b vector of K-PLS-DA model are used. ***These ŷ-values can be represented as “regression coefficients” shown later in Figure 4 or loading plot shown in Figure 5.

https://doi.org/10.1371/journal.pone.0038163.g002

The graphical representation of the pseudo samples principle is shown in Figure 2b. It is possible to construct for each original variable a series of pseudo samples containing different values. These different values permit to describe a complete trajectory for each variable. In that way, for every variable a matrix of size “k×p” (where k is the number of pseudo samples used to span the complete range of the original variable and p the number of original variables) is created. From now on, we call this set of pseudo samples describing a single original variable a pseudo samples matrix. For data matrix X (shown in Figure 2a) “p” pseudo samples matrices are created, each of size “k×p”. Once all pseudo samples matrices are constructed, one can apply the K-PLS-DA model to estimate the influence of the original variables. The pseudo samples are first mapped into the kernel space in relation to the original data matrix X using the same kernel function as derived for data matrix X (Figure 2a), i.e. K(x_i,ps_j) where x_i is an object of matrix X and ps_j is one pseudo sample. This leads to “p” kernel pseudo samples matrices (Figure 2b). Next the ŷ-values of pseudo samples can be estimated using regression vector “b” of K-PLS-DA model or they can be projected into LV space using loading vector of K-PLS-DA model. It has been shown that for linear kernel predicted ŷ-values of pseudo samples can be directly related to the regression coefficient of the original variables [17]. The projections of pseudo samples into the regression vector “b” of K-PLS-DA model from now on will be called “regression coefficient”; while the projection of the pseudo samples in the LV space will be referred to as a loading plot.

The first graphical representation (Figure 3a) permits one to investigate how the original variables evolve as a function of the studied response as well as their global and local importance in the model. As described above, the kernels pseudo samples (see Figure 2b) are projected into the K-PLS-DA model to visualize the importance and behaviour of the original variables. A schematic example is provided in Figure 3a. The “regression coefficients” of four variables trajectories are displayed, each one illustrating a different case. If the influence of a given variable to the model is linear the corresponding pseudo samples trajectory should form a straight line, as variable 1 in Figure 3a. Variable 2 behaves linearly in the low variable range but becomes non-linear in the high range as can be observed from the corresponding curvature. Variable 3 represents a more complex sigmoid shape. This variable has big importance in the model in the low range and in high range but less in intermediate range. Note that in the high range variable 3 shows a plateau, which indicates that after passing a certain concentration value its importance stays constant. Finally, the last variable shown in Figure 3a, variable 4, has very little influence on the model. Note that, if the optimal K-PLS-DA model complexity is one LV, information contained in the regression coefficient and the loading vector (obtained from K-PLS-DA model) is equivalent. Therefore it is possible to use the loading vector instead of the regression vector “b” for obtaining the predicted ŷ-values of pseudo samples (the y-axis of Figure 3a represent 1LV). This kind of plot in linear PLS-DA is called loading plot. Therefore, in the rest of paper it will also be called loading plot.

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Figure 3. Schematic example of: (a) “regression coefficients” of original variables trajectories plotted versus their range; (b) the maximum absolute value of “regression coefficients” of original variables trajectories shown in a.

https://doi.org/10.1371/journal.pone.0038163.g003

Another piece of information delivered from Figure 3a, is the change of variable value between studied groups. Positive predicted ŷ-values of pseudo samples indicates group A and a negative indicates group B. For instance the value of variable 1 increases from group A to group B, while the value of variable 2 decreases from group A to group B.

Figure 3b is an enhanced version of the figure presented in reference [17]. It allows direct visualisation of the importance of each variable on the K-PLS-DA model. Figure 3b is constructed as follows: the absolute value of the maximal “regression coefficients” (i.e. predicted values of pseudo samples) is used as the relative importance of each variable. Note that this approach can be used when the original variables are scaled to unit variance. Note further, an alternative to estimate/visualize the relative importance would be by taking the absolute value of the difference between maximum value and minimum value. The result can be graphically represented using the traditional regression plot obtained in any regression method [8]. Note that the importance of the variables can be also directly read off from Figure 3a, i.e. from the absolute max values along the horizontal axis. The 4 variables in Figure 3b correspond thus to the ones shown in Figure 3a.

Data

Every NMR spectrum of CIS and MScl groups was divided into 233 bins, corresponding to relative metabolites concentrations. These bins are equivalent to approximately 50 identified metabolites and some unidentified resonances. The GC-MS data consists of 66 metabolites and their corresponding relative concentrations. It is important to mention that 20 metabolites were measured by both NMR and GC-MS. Some metabolites are identified only by NMR (e.g. methanol) or only by GC-MS (e.g. urea) [43].

These two datasets are used as case study to represent the proposed architecture for non-linear data analysis and fusion. After variables selection by SVM-RFE the NMR data and GC-MS data are reduced to 47 bins and 29 metabolites, respectively. In case of NMR these 47 informative bins correspond to 20 identified metabolites and some unidentified resonances.

It is important to keep in mind that σ, i.e. the parameter controlling the smoothness of the function, has to be tuned correctly, since it impacts the model performance. The σ parameter used for rbf kernel function is optimized separately for NMR dataset and GC-MS dataset and again before kernel fusion. An overview of σ parameters optimized in particular steps in Figure 1 is summarized in Table 2.

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Table 2. Summary of σ parameter for rbf kernel function.

https://doi.org/10.1371/journal.pone.0038163.t002

Metabolites Identification

After selection and visualization of the most important variables, the corresponding metabolites were identified (NMR). Metabolite identification for NMR data was carried out by using the 600 MHz library of metabolite NMR spectra from the Chenomx NMR Suite 7. The library of metabolite spectra is obtained based on a database of pure compound spectra acquired using particular pulse sequence and acquisition parameters, the tn-noesy-presaturation pulse sequence with 4s acquisition time and 1s of recycle delay [44].

Linear Methods

The analysis of the data can be first performed per analytical method. This is particularly significant not only during exploratory phase but also during supervised analysis, where relevance of individual sets is investigated. Both datasets were first analyzed with R-PCA and PCA for presence of outliers and to detect potential trends. In total 4 NMR spectra and 3 GC-MS samples were detected as outliers and removed from further analysis. Since PCA score plots did not reflect any groupings and the variations did not separate according to groups CIS and MScl, the results of this analysis are not shown. Next, the linear method, CMV-PLS-DA, was employed on separate platforms and on fused datasets in mid-level fashion. In our case, the application of linear methods provided disappointing results for the separate datasets as well as for the datasets fused in the mid-level fashion. The degree of correct classification for a validation set obtained for the individual data-set analysis and for the concatenated sets can be seen in Table 3 and the corresponding figures are shown in Figure S2a−S2c.

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Table 3. An overview of prediction accuracy for the validation set using linear methods, non-linear methods and MKL.

https://doi.org/10.1371/journal.pone.0038163.t003

Non-linear Analysis

Since linear methods did not lead to satisfactory results (see Table 3), we used more sophisticated methods (i.e. non-linear) to find differences in metabolic profiles of CSF of CIS and MScl groups. As pointed out previously (see Materials and Methods), our approach is based on four steps. The first one consists of a variable selection performed on each dataset. We used SVM-RFE in order to get good predictive group membership ability and a meaningful interpretation of the model. After the first step, we analysed the separate datasets by K-PLS-DA. After variable selection every dataset can be assessed in terms of complexity and prediction accuracy. The overall correct classification for independent test sets, left out during model optimization and construction, is 93% for NMR data and 85% for GC-MS data, respectively (Table 3). Both K-PLS-DA models were constructed for 2 latent variables (LV’s). These results suggest that both data sources hold relevant information concerning discriminating CIS and MScl groups. The overview of the prediction of each K-PLS-DA model is presented in Table 3.

The most straightforward approach for data fusion is to analyse the two datasets together by simply concatenating the selected variables from two data sources together (mid-level fusion). It is expected that the two types of information from the NMR and GC-MS datasets should complement each other and improve the class separation. However, this mid-level fusion provides very similar results in terms of complexity of the K-PLS-DA model and correct classification (i.e. 2LV’s and 89% correct classification, see Table 3).

Data Fusion by Multiple Kernel Learning

Since the analysis of both sets as unique matrices does not provide a better separation of the groups, we decided to apply kernel-based fusion by MKL (Materials and Methods). Note that this kernel fusion architecture, as applied by us here, falls outside the range of the classical low-, mid-, or high-level fusion. It uses the specific property of the kernel matrix in the data fusion, i.e. its dimensions and its nature comparable to a similarity matrix.

The MKL approach used here is composed of optimizing weights for each kernel matrix. The optimized weights were equal 0.75 for NMR and 0.661 for GC-MS. This indicates that both datasets are almost equally important. After weighted kernel-based fusion, the newly formed kernel matrix can by analysed by PLS-DA. The kernel fusion leads to correct prediction of 100% on the independent test set (versus 89% for mid-level fusion, see Table 3). The K-PLS-DA model was constructed by using 1 LV. As an additional check, we performed a permutation test. The p-value for 10000 permutations was equal to 0.0013. The accuracy of K-PLS-DA was further compared to SVM. The correct prediction was as well 100% on the independent test set.

Since the model shows good predictive ability on the independent test set, we consider it as statistically validated and as shown in Figure 1 (step 4) the K-PLS-DA model is then reconstructed using all available samples. The resulting model can be graphically assessed using a score plot (here not shown). Obviously, this kind of plot is the normal visual representation of kernel method.

Variables Importance Visualization

As shown in Materials and Methods, it is possible to visualize the original variables in discriminating the groups. For that purpose the maximum absolute value of the predicted values of pseudo samples was calculated. The obtained values are shown in Figure 4. This figure demonstrates that there are several variables having very high importance. For instance, variables number 67 (sucrose), 76 (urea) and 50 (3-methyl-2-hydroxybutanoic acid) have the highest values of the predicted values of pseudo samples, demonstrating the relevance of these variables. There are just few variables seen as less significant, for example variable 57 (glycerol) or 63 (phenylalanine). The complete list of names of metabolites corresponding to variable number is given in Table S1.

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Figure 4. The maximum absolute value of “regression coefficients” of original variables.

https://doi.org/10.1371/journal.pone.0038163.g004

As was explained in Materials and Methods, to investigate the relation between individual variables and changes of metabolite concentration (i.e. elevation or reduction) the trajectory of predicted values of pseudo samples (representing individual variables) can be studied. Since the optimal model complexity is 1LV we used loading vector delivered from K-PLS-DA model to project the pseudo samples into LV1. The obtained trajectories are shown in Figure 5. Because presenting trajectories for all variables makes the plot unreadable, in Figure 5, only a few of them are given. Trajectories for all variables are given in Figure S1.

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Figure 5. Loading plot of pseudo samples trajectories for selected variables.

Numbers in the brackets correspond to variable numbers in Figure 4.

https://doi.org/10.1371/journal.pone.0038163.g005

Besides showing the importance of variables in discriminating, Figure 5 also reveals the linear or non-linear trend and/or monotonicity of the variables in certain concentration ranges. A variable which shows a non-linear trend is glutamine and is derived from NMR. Valine is characterized by linearity and monotonicity in its low range, and non-linearity in its high range. Urea and sucrose demonstrate linearity over the whole concentration range.

As mentioned before the change in metabolite concentrations across groups can be assessed. The horizontal axis in the Figure 5 represents the range of every original variable (scaled to its min to max value). The levels of lactate and of valine both increase, while the concentration of glutamine and citrate is reduced with disease progression. To make the change of metabolite concentrations more evident we included the direction of groups along vertical y-axis. More specifically, the negative values of the predicted values of pseudo samples correspond to CIS and the positive values to MScl.

At this point one should remember that some metabolites were measured both by NMR and GC-MS. It is therefore interesting to check how the corresponding variables compare with each other. For instance, pseudo sample trajectories for glutamine derived from NMR and GC-MS reveal very similar evolution upon disease progression. Correspondingly, pseudo sample for lactate, glucose and citrate measured by NMR and GC-MS display comparable trajectories along concentration range. This suggests that even after non-linear transformation the same variables measured by two different analytical methods are correlated and demonstrate their akin behaviour.