Exploration of deep-learning based classification with human SNP image graphs

BackgroundWith the advancement of NGS platform, large numbers of human variations and SNPs are discovered in human genomes. It is essential to utilize these massive nucleotide variations for the discovery of disease genes and human phenotypic traits. There are new challenges in utilizing such large numbers of nucleotide variants for polygenic disease studies. In recent years, deep-learning based machine learning approaches have achieved great successes in many areas, especially image classifications. In this preliminary study, we are exploring the deep convolutional neural network algorithm in genome-wide SNP images for the classification of human populations.ResultsWe have processed the SNP information from more than 2,500 samples of 1000 genome project. Five major human races were used for classification categories. We first generated SNP image graphs of chromosome 22, which contained about one million SNPs. By using the residual network (ResNet 50) pipeline in CNN algorithm, we have successfully obtained classification models to classify the validation dataset. F1 scores of the trained CNN models are 95 to 99%, and validation with additional separate 150 samples indicates a 95.8% accuracy of the CNN model. Misclassification was often observed between the American and European categories, which could attribute to the ancestral origins. We further attempted to use SNP image graphs in reduced color representations or images generated by spiral shapes, which also provided good prediction accuracy. We then tried to use the SNP image graphs from chromosome 20, almost all CNN models failed to classify the human race category successfully, except the African samples.ConclusionsWe have developed a human race prediction model with deep convolutional neural network. It is feasible to use the SNP image graph for the classification of individual genomes.

Homomorphisms into Loop-Threshold Graphs

Many problems in extremal graph theory correspond to questions involving homomorphisms into a fixed image graph. Recently, there has been interest in maximizing the number of homomorphisms from graphs with a fixed number of vertices and edges into small image graphs. For the image graph $H_\text{ind}$, the graph on two adjacent vertices, one of which is looped, each homomorphism from $G$ to $H_\text{ind}$ corresponds to an independent set in $G$. It follows from the Kruskal-Katona theorem that the number of homomorphisms to $H_\text{ind}$ is maximized by the lex graph, whose edges form an initial segment of the lex order. A loop-threshold graph is a graph built recursively from a single vertex, which may be looped or unlooped, by successively adding either a looped dominating vertex or an unlooped isolated vertex at each stage. Thus, the graph $H_\text{ind}$ is a loop-threshold graph. We survey known results for maximizing the number of homomorphisms into small loop-threshold image graphs. The only extremal homomorphism problem with a loop-threshold image graph on at most three vertices not yet solved is $H_\text{ind}\cup E_1$, where extremal graphs are the union of a lex graph and an empty graph. The only question that remains is the size of the lex component of the extremal graph. While we cannot give an exact answer for every number of vertices and edges, we establish the significance of and give bounds on $\ell(m)$, the number of vertices in the lex component of the extremal graph with $m$ edges and at least $m+1$ vertices.