Human microbiome research is helped by the characterization of microbial networks, as these may reveal key microbes that can be targeted for beneficial health effects. Prevailing methods of microbial network characterization are based on measures of association, often applied to limited sampling points in time. Here, we demonstrate the potential of wavelet clustering, a technique that clusters time series based on similarities in their spectral characteristics. We illustrate this technique with synthetic time series and apply wavelet clustering to densely sampled human gut microbiome time series. We compare our results with hierarchical clustering based on temporal correlations in abundance, within and across individuals, and show that the cluster trees obtained by using either method are significantly different in terms of elements clustered together, branching structure and total branch length. By capitalizing on the dynamic nature of the human microbiome, wavelet clustering reveals community structures that remain obscured in correlation-based methods.