To define a cutotype based on the skin microbiome, samples from each facial site were clustered using Jensen-Shannon distance (JSD) [78], respectively, which was calculated by taking the square root of the Jensen-Shannon divergence. The Jensen-Shannon divergence was an effective measure of divergence between distribution accounting for both the presence and abundances of microbes. Moreover, JSD was calculated according to this formula:

where

In this formula, pa and pb are the abundance distributions of samples a and b, and KLD is the Kullback-Leibler divergence.

As described in the enterotyping tutorial (http://enterotype.embl.de/enterotypes.html), clustering was performed via partitioning around medoid (PAM) by the pam function in cluster package [79] in R. The optimal number of clusters was determined by the Calinski-Harabasz (CH) index:

where k is the number of clusters, n is the number of data points, Bk is the between-cluster sum of squares (i.e., the squared distances between all points i and j, for which i and j are not in the same cluster) and Wk is the within-cluster sum of squares (i.e., the squared distances between all points i and j, for which i and j are in the same cluster). The CH index was calculated using clusterSim package [80] in R. Principal coordinates analysis (PCoA) was used to show cutotype results by the cmdscale function in R. The cutotype results were also verified based on Bray-Curtis (BC) distance using vegan package [76] in R. The JSD and BC of intra- and inter-cluster were shown by boxplots. We used the same method to define cutotype based on public data mentioned before for confirming the extensive existence of cutotype.

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