## 2 Materials and Methods
### FNAC Metabolomic Analyses Allowed Preoperative Diagnosis of Thyroid Nodules
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{Characteristics} & & & **All** & **Benign** & **Malignant** \\  & & & **\% (nb)** & **\% (nb)** & **\% (nb)** \\ \cline{3-6}  & & & **78** & **56** & **22** \\ \hline \multirow{4}{*}{Histology} & Benign & NNN & 30.4 (17) & 50 (17) & 0 \\  & Adenoma & 30.4 (17) & 50 (17) & 0 \\ \cline{2-6}  & & Classical variant & 15.4 (12) & 0 & 54.5 (12) \\  & & Follicular variant & 6.4 (5) & 0 & 22.7 (5) \\  & Malignant & Sclerosisant variant & 2.6 (2) & 0 & 9.1 (2) \\  & (PTC) & Onocytic variant & 1.3 (1) & 0 & 4.5 (1) \\  & & Tall cell variant & 1.3 (1) & 0 & 4.5 (1) \\  & & Solid variant & 1.3 (1) & 0 & 4.5 (1) \\ \hline \hline \end{tabular} Data are % (nb), or mean (\(\pm\)standard deviation). Abbreviations: F, female; NNN, non-neoplastic nodule; PTC, papillary thyroid carcinoma. Bethesda classification: II (benign lesion); III (atypia of undetermined significance, AUS); IV (FN, follicular neoplasm; HCN, Hürtle cell neoplasm; sFN, suspicious for follicular neoplasm); V (suspicious for malignancy); VI (malignant).  
\end{table} 
Table 1: _Cont._Metabolomic Profiling with 15 Features from FNAC Samples Allowed Preoperative Diagnosis of Thyroid Nodules  
We then wanted to reduce the number of metabolites to get the most parsimonious signature, using the SAE model with a step-by-step top-down procedure (Supplementary Figure S2). We obtained a short list of the top 15 ions of the SAE model. After logarithmic normalization, these 15 ions made it possible to accurately discriminate nearly all benign from malignant TNs. The performance of the SAE model is illustrated by the latent space for benign versus malignant samples (Figure 3A), and by a separation of the two curves of the kernel density estimation of the prediction probability (Figure 3B). Only two samples, one in each category, were misclassified by the SAE model. The misclassified samples (IB25 and IM12) are marked in Figure 3A. Using these top 15 ions, the SAE model yielded an accuracy of 0.957 (0.842-1), an AUC of 0.945 (0.833-1), a precision of 0.957 (0.864-1), a recall of 0.945 (0.833-1) and an F1 score of 0.947 (0.842-1) (Figure 3C, Tables 2 and 3). Remarkably, the performance of the SAE model was maintained throughout the 12-fold cross-validation analysis, with only minor variations between the individual cross-validations. Figure 2: Metabolomic analyses were feasible on liquid-based cytology of thyroid nodules. Representation of liquid chromatography spectra of a benign sample (blue upper panels), a malignant sample (dark-red middle panels), and a control (dark lower panels) in the positive (left panels) and negative mode (right panels), respectively. The light-red rectangles highlight the absence of hydrophilic metabolites (between 2 and 10 min of retention time) found in the positive and negative modes, in both benign and malignant nodules. Within a large background, there is no clear difference in the chromatography spectra between benign and malignant nodules. The chosen spectra are representative of the sample set for each class. The x-axis represents the retention time, and the y-axis represents the relative intensity of the peaks. Figure 3: A supervised autoencoder can accurately distinguish benign from malignant thyroid nodules using a liquid-based FNAC signature of 15 metabolites. A deep neural network (the SAE) was used to perform statistical analysis on the dataset [9]. From the initial database, it was possible to identify 15 relevant and statistically significant metabolites using the SAE. This 15-metabolite signature was used thereafter. (**A**) Distinct clustering of benign (blue dot) and malignant samples (orange dot) in the two dimensions of the latent space. The samples that were misclassified are annotated and encircled in red. (**B**) shows the kernel density estimation of the prediction probability in benign (blue) and malignant classes (orange). The kernel density is presented as a function of the prediction probability score.