  The usage of chemical imaging technologies is becoming a routine
accompaniment to traditional methods in pathology. Significant technological
advances have developed these next generation techniques to provide rich,
spatially resolved, multidimensional chemical images. The rise of digital
pathology has significantly enhanced the synergy of these imaging modalities
with optical microscopy and immunohistochemistry, enhancing our understanding
of the biological mechanisms and progression of diseases. Techniques such as
imaging mass cytometry provide labelled multidimensional (multiplex) images of
specific components used in conjunction with digital pathology techniques.
These powerful techniques generate a wealth of high dimensional data that
create significant challenges in data analysis. Unsupervised methods such as
clustering are an attractive way to analyse these data, however, they require
the selection of parameters such as the number of clusters. Here we propose a
methodology to estimate the number of clusters in an automatic data-driven
manner using a deep sparse autoencoder to embed the data into a lower
dimensional space. We compute the density of regions in the embedded space, the
majority of which are empty, enabling the high density regions to be detected
as outliers and provide an estimate for the number of clusters. This framework
provides a fully unsupervised and data-driven method to analyse
multidimensional data. In this work we demonstrate our method using 45
multiplex imaging mass cytometry datasets. Moreover, our model is trained using
only one of the datasets and the learned embedding is applied to the remaining
44 images providing an efficient process for data analysis. Finally, we
demonstrate the high computational efficiency of our method which is two orders
of magnitude faster than estimating via computing the sum squared distances as
a function of cluster number.
