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Fig. 2 | Genome Biology

Fig. 2

From: tmap: an integrative framework based on topological data analysis for population-scale microbiome stratification and association studies

Fig. 2

Schematic illustration of the Mapper and SAFE algorithms used by tmap. a The Mapper algorithm comprises five steps. First, data points of high-dimensional microbiome profiles (such as OTU table) are taken as input. Then, projection of the high-dimensional data points to a low-dimensional space (R as shown in the figure) is performed by using a filter function (such as PC1 of PCoA). The covering step partitions the low-dimensional space into overlapping covers to bin a subset of data points within them. After that, clustering is conducted to cluster data points within each cover into different clusters based on their distances in the original high-dimensional space. The last step constructs a TDA network from the result of clustering analysis, in which node represents a cluster of data points and link between nodes indicates common data points between clusters. b The SAFE algorithm comprises three steps. Starting with a TDA network, it maps the values of metadata or microbiome features into the network as node attributes (e.g., average age). Second, subnetwork enrichment analysis is performed for each node to analyze its significance of the observed enrichment pattern via network permutations. This analysis is performed for each target variable (metadata or microbiome features) respectively. The last step is the calculation of SAFE score (O) via log transformation and normalization of the significance level of the observed enrichment. More details of these two algorithms are provided in the “Methods” section

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