Fig. 1

Overview of the TEMPTED algorithm for analyzing multi-subject multi-feature temporal microbiome data. a Simulated microbiome count data (see Additional file 1) is transformed into relative abundance and plotted for four representative microbes and three groups of hosts. Microbe 1 has a unique temporal pattern for group 1, microbe 2 has a temporal pattern shared by groups 2 and 3, microbe 3’s temporal pattern is shared by all groups, and microbes 4–100 have no temporal patterns. Sampling time points are uniformly distributed and used as is without binning. b The observed multi-subject multi-feature temporal data are formatted into a temporal tensor with three modes representing subject, feature (microbe), and time, respectively. TEMPTED reduces the dimension of the temporal tensor by decomposing it into a small number of components, each containing a subject loading vector, a feature loading vector, and a temporal loading function. c–e TEMPTED loadings of the first three components from the simulated data. The first component captures the bell-shaped trend of microbe 1 and separates group 1 from groups 2 and 3. The second component captures the increasing trend of microbe 2 and separates group 2 from groups 1 and 3. The third component captures the m-shaped trend of microbe 3 and does not separate any groups. Microbes 4–100 have low feature loadings in all components