One of the main challenges in applying graph convolutional neural networks on gene-interaction data is the lack of understanding of the vector space  to which they belong and also the inherent difficulties involved in representing those interactions on a significantly lower dimension, viz Euclidean spaces. The challenge becomes more prevalent when dealing with various types of heterogeneous data. We introduce a systematic, generalized method, called iSOM-GSN, used to transform ``multi-omic'' data with higher dimensions onto a two-dimensional grid. Afterwards, we apply a convolutional neural network to predict disease states of various types. Based on the idea of Kohonen's self-organizing map, we generate a two-dimensional grid for each sample for a given set of genes that represent a gene similarity network.   We have tested the model to predict breast and prostate cancer using gene expression, DNA methylation and copy number alteration, yielding prediction accuracies in the 94-98% range for tumor stages of breast cancer and calculated Gleason scores of prostate cancer with just 11 input genes for both cases. The scheme not only outputs nearly perfect classification accuracy, but also provides an enhanced scheme for representation learning, visualization, dimensionality reduction, and interpretation of the results. Large scale projects such as "The Cancer Genome Atlas" (TCGA) generate a plethora of multidimensional data by applying high-resolution microarrays and next generation sequencing. This leads to diverse multi-dimensional data in which the need for devising dimensionality reduction and representation learning methods to integrate and analyze such data arises. An earlier study by Shen et al. proposed algorithms iCluster (Shen et al., 2009a) and iCluster+ (Shen et al., 2009b) , which made use of the latent variable model and principal component analysis (PCA) on multi-omic data and aimed to cluster cancer data into sub-types; even though it performed well, it did not use multi-omics data. In another study, (Lyu and Haque, 2018) attempted to apply heatmaps as a dimensionality reduction scheme on gene expression data to deduce biological insights and then classify cancer types from a Pan-cancer cohort. However, the accuracy obtained by using that method was limited to 97% on Pan-cancer data, lacking the benefits of integrated multi-omics data. In a recent study (Choy et al., 2019) used self-Organizing maps (SOMs) to embed gene expression data into a lower dimensional map, while the works of (Bustamam et al., 2018; Mallick et al., 2019; Paul and Shill, 2018; Loeffler-Wirth et al., 2019) generate clusters using SOMs on gene expression data with different aims. In addition, the work of (Hopp et al., 2018) combines gene expression and DNA methylation to identify subtypes of cancer similar to those of (Roy et al., 2018) , which identifies modules of co-expressing genes. On the other hand, the work of (Kartal et al., 2018) uses SOMs to create a generalized regression neural network, while the model proposed in (Yoshioka and Dozono, 2018; Shah and Luo, 2017) uses SOMs to classify documents based on a word-tovector model. Apart from dimensionality reduction methods, attempts have been made by applying supervised deep machine learning, such as deepDriver (Luo et al., 2019) , which predicts candidate driver genes based on mutation-based features and gene similarity networks. Although these works have been devised to use embedding and conventional machine learning approaches, the use deep neural networks on multi-omics data integration is still in its infancy. In addition, these methods lack Gleason Score Number of Samples Group  3+4  147  34  4+3  101  43  4+5,5+4  139  9   Table 1 : Distribution of the different Gleason groups considered for PRCA. in adequacy to generalize them multi-omics data to predic disease states. More specifically, none of these models combine the strength of SOMs for representation learning combined with the CNN for image classification as we do in this work. In this paper, a deep learning-based method is proposed, and is used to predict disease states by integrating multi-omic data. The method, which we call iSOM-GSN, leverages the power of SOMs to transform multi-omic data into a gene similarity network (GSN) by the use of gene expression data. Such data is then combined with other genomic features to improve prediction accuracy and help visualization. To our knowledge, this the first deep learning model that uses SOMs to transform multi-omic data into a GSN for representation learning, and uses CNNs for classification of disease states or other clinical features. The main contributions of this work can be summarized as follows: • A deep learning method for prediction of tumor aggressiveness and progression using iSOM-GSN. • A new strategy to derive gene similarity networks via self-organizing maps. • Use of iSOM-GSN to identify relevant biomarkers without handcrafted feature engineering. • An enhanced scheme to interpret and visualize multi-dimensional, multi-omics data. • An efficient model for graph representation learning. This paper presents a framework that uses a self-organizing map and a convolutional neural network used to conduct data integration, representation learning, dimensionality reduction, feature selection and classification simultaneously to harness the full potential of integrated high-dimensional large scale cancer genomic data. We have introduced a new way to create gene similarity networks, which can lead to novel gene interactions. We have also provided a scheme to visualize high-dimensional, multi-omics data onto a two-dimensional grid. In addition, we have devised an approach that could also be used to integrate other types of multi-omic data and predict any clinical aspects or states of diseases, such as laterality of the tumor, survivability, or cancer sub types, just to mention a few. This work can also be extended to classify Pan-cancer data. Omics can be considered as a vector and more than three types of data (i.e., beyond RGB images) can be incorporated for classification. Apart from integrating multi-omics data, the proposed approach can be considered as an unsupervised clustering algorithm, because of the competitive learning nature of SOMs. We can also apply iSOM-GSN on other domains, such as predicting music genre's for users based on their music preference. As a first step, we have applied the SOM to a Deezer dataset and the results are encouraging 14. Applications of iSOM-GSN can also be in drug response or re-purposing, prediction of passenger or oncogenes, revealing topics in citation networks, and other prediction tasks.
This paper presents a deep learning model that combines self-organizing maps and convolutional neural networks for representation learning of multi-omics data
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