Fast Data Driven Estimation of Cluster Number in Multiplex Images using Embedded Density Outliers

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 re-solved, 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 (i.e. clusters) 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.