Finding natural or biological centroids
Intuitively, we often want to find natural centroid sequences, i.e. those we would pick if we could visualize the data and the boundaries between clusters were clear, as below.

In practice, this is problematic for several reasons. Often, sequences are not neatly separated into groups, so that boundaries are ambiguous. It is difficult (arguably, impossible) to define clustering criteria that always generate clusters that are intuitively natural. This problem has been extensively studied in computer science, see e.g. this Wikipedia article.

Recentering
One approach to generating natural clusters using UCLUST is to use recentering, as illustrated in the figure below. The size of a dot indicates the number of identical sequences.

First, UCLUST is run using a length sort (e.g. cluster_fast). This ensures that fragments do not become centroids, but has the problem that the longest sequences (blue dots in figure above). tend to have more errors so tend to be outliers compared to the natural centroids. This tends to split a natural OTU into two or more clusters. This is addressed by constructing consensus sequences for each cluster, which tends to find the dominant sequence in the neighborhood. In the above figure, the dominant sequence is the due to the abundant sequence S indicated by the large orange dot, and the consensus sequences of the lower two clusters will converge on S. The consensus sequence of the top cluster will move closer to the orange dot.

Since consensus sequences of neighboring clusters may be identical or closer than the desired distance threshold, a second clustering pass is required to remove this redundancy. An abundance sort is usually preferred for this pass so that biologically correct / biologically more significant sequences are chosen as centroids.

After these two passes, the orange sequence above will become the centroid of an OTU which accounts for all the sequences in the figure. In this example, the three OTUs formed by the original outlier sequences are merged after this recentering process. This is typical of what happens in practice with 16S reads: the number of clusters is significantly reduced by recentering.

Recentering example
The following commands implement a recentering strategy.

usearch -cluster_fast reads.fasta -consout cons.fasta -id 0.97 -sizeout
usearch -sortbysize cons.fasta -output cons_bysize.fasta
usearch -cluster_smallmem cons_bysize.fasta -id 0.97 -centroids otus.fasta

With these commands, it is not guaranteed that all the original reads are at least 97% identical to a sequence in otus.fasta. If desired, this can be addressed by searching the reads against otus.fasta as a database and clustering any reads that do not match. However, it is reasonable to discard those reads as they are likely to be spurious (PCR or sequencing artifacts).