# NMR in Metabolomics: From Conventional Statistics to Machine Learning and Neural Network Approaches
## 4 Applications of Deep Learning Approaches for NMR-Based Metabolomics
### Biomedical
Their results, taking advantage of Kaplan-Meier curves for prognosis and of a PCA-based kNN analysis, allowed distinguishing relapse-free and metastatic cancer groups, with the advantage of obtaining information about the risks in the early stage of the colorectal cancer disease. [PERSON] et al. [130], by using two-dimensional NMR correlational spectroscopy on the longitudinal (T\({}_{1}\)) and transversal components (T\({}_{2}\)) of the magnetization relaxation time during its equilibrium recovery, were able to perform a molecular phenotyping of blood with the employment of supervised learning models, including neural networks. In detail, by means of a fast two-dimensional Laplace inversion [117], they obtained T\({}_{1}\)-T\({}_{2}\) correlation spectra on a single drop of blood (<5 uL) in a few minutes (Figure 26) with a benchtop-sized NMR spectrometer. Then, they converted the NMR correlational maps for deep image analysis, achieving useful insights for medical decision making by the application of machine learning techniques. In particular, after an initial dimensionality reduction by unsupervised analysis, supervised neural network models were applied to train and predict the data that, at the end, were compared with the diagnostic prediction made by  
Figure 25: (**A**) Example of \({}^{1}\)H NMR spectrum for DLKP lung carcinoma cells. Labeled peak corresponds to (a) CH\({}_{3}\), (b) CH\({}_{2}\), (c) CH\({}_{2}\)CH=CH, (d) CH\({}_{2}\)COO, (e) =CHCH\({}_{2}\)CH=, and (f) HC=CH/CHOCOR. The highlighted intervals at 0.60–1.04 and 1.24–3.56 ppm were used for statistical analysis. (**B**) PCA score plot including data from all four cell lines. (**C**) Residual mean squares error vs. nodes number in the hidden layers, for the 3-layers (full symbols), and in the second (empty triangles) and third (empty circles) layer for the 4-layers networks. Figure reprinted from Ref. [127] under the terms of the Creative Commons Attribution License. humans. The results showed that ML approaches outperformed the human being and took a much shorter time. Therefore, the authors demonstrated the clinical efficacy of this technique by analyzing human blood in different physiological and pathological conditions, such as oxidation states [130]. Concerning the analysis of different physiological conditions, Figure 26 reports the T\({}_{1}\)-T\({}_{2}\) correlational maps of blood cells at oxygenated (a), oxidized (b), and deoxygenated (c) states. Three peaks with different relaxation times values were observed and assigned to the different microenvironments that water experiences in the considered samples of red blood cells. For the obtained maps, the coordinate for the bulk water peak (slowest component) is shown at the upper left of the map indicating T\({}_{2}\) and T\({}_{1}\) relaxations (in ms) and T\({}_{1}\)/T\({}_{2}\)-ratio, respectively. Instead, the coordinates of the fastest components, due to hydration and bound water molecules [131], are reported close to the corresponding correlation peak (Figure 26).