Fig. 5

Individualized kNN analysis for the gut microbiome. a The distribution of 184 microbial stool samples over the ‘assemblage space’, which represents the Jaccard distance between the species assemblages as depicted through principal coordinates analysis, is non-homogeneous. For example, the Jaccard distances between the 15 points marked by the red rectangle are significantly larger compared with the distances between the 15 points marked by the green rectangle (inset). b Three examples of kNN profiles of samples with small values of \(\langle D_{(10)} \rangle\), i.e., the average Jaccard between the sample and its 10 nearest neighbors (0.45, 0.45, and 0.48, green curves) and three with high values of \(\langle D_{(10)} \rangle\) (0.74, 0.74, and 0.8, red curves). The kNN profiles of the samples from dense neighborhoods typically reach a minimum (best prediction) at small values of k. In contrast, the kNN predictions of samples from sparse neighborhoods typically require including many or even all the cohort samples. c The kNN gain \(\Delta\) of a predetermined value \(k=10\) is significantly higher for the samples with small \(\langle D_{(10)} \rangle\) values compared with those with large \(\langle D_{(10)} \rangle\) values. Box plots represent the first and third quartiles; middle line, median; red daggers, outliers. Boxes represent equal ranges of \(\langle D_{10} \rangle\) values. Asterisk, p value \(=0.02\), calculated using the Mann-Whitney U-test between the samples associated with the left and the right boxes