Motivation: High-throughput technologies play a more and more significant role in discovering prognostic molecular signatures and identifying novel drug targets. It is common to apply Machine Learning (ML) methods to classify high-dimensional gene expression data and to determine a subset of features (genes) that is important for decisions of a ML model. One feature subset of important genes corresponds to one dataset and it is essential to sustain the stability of feature sets across different datasets with the same clinical endpoint since the selected genes are candidates for prognostic biomarkers. The stability of feature selection can be improved by including information of molecular networks into ML methods. Gene expression data can be assigned to the vertices of a molecular network's graph and then classified by a Graph Convolutional Neural Network (GCNN). GCNN is a contemporary deep learning approach that can be applied to graph-structured data. Layer-wise Relevance Propagation (LRP) is a technique to explain decisions of deep learning methods. In our recent work we developed Graph Layer-wise Relevance Propagation (GLRP) --- a method that adapts LRP to a graph convolution and explains patient-specific decisions of GCNN. GLRP delivers individual molecular signatures as patient-specific subnetworks that are parts of a molecular network representing background knowledge about biological mechanisms. GLRP gives a possibility to deliver the subset of features corresponding to a dataset as well, so that the stability of feature selection performed by GLRP can be measured and compared to that of other methods.
Results: Utilizing two large breast cancer datasets, we analysed properties of feature sets selected by GLRP (GCNN+LRP) such as stability and permutation importance. We have implemented a graph convolutional layer of GCNN as a Keras layer so that the SHAP (SHapley Additive exPlanation) explanation method could be also applied to a Keras version of a GCNN model. We compare the stability of feature selection performed by GCNN+LRP to the stability of GCNN+SHAP and to other ML based feature selection methods. We conclude, that GCNN+LRP shows the highest stability among other feature selection methods including GCNN+SHAP. It was established that the permutation importance of features among GLRP subnetworks is lower than among GCNN+SHAP subnetworks, but in the context of the utilized molecular network, a GLRP subnetwork of an individual patient is on average substantially more connected (and interpretable) than a GCNN+SHAP subnetwork, which consists mainly of single vertices.
Thermal load forecasting in district heating networks using deep learning and advanced feature selection methods
