  In this work we present a clustering technique called \textit{multi-level
conformal clustering (MLCC)}. The technique is hierarchical in nature because
it can be performed at multiple significance levels which yields greater
insight into the data than performing it at just one level. We describe the
theoretical underpinnings of MLCC, compare and contrast it with the
hierarchical clustering algorithm, and then apply it to real world datasets to
assess its performance. There are several advantages to using MLCC over more
classical clustering techniques: Once a significance level has been set, MLCC
is able to automatically select the number of clusters. Furthermore, thanks to
the conformal prediction framework the resulting clustering model has a clear
statistical meaning without any assumptions about the distribution of the data.
This statistical robustness also allows us to perform clustering and anomaly
detection simultaneously. Moreover, due to the flexibility of the conformal
prediction framework, our algorithm can be used on top of many other machine
learning algorithms.
