  The wealth of data being gathered about humans and their surroundings drives
new machine learning applications in various fields. Consequently, more and
more often, classifiers are trained using not only numerical data but also
complex data objects. For example, multi-omics analyses attempt to combine
numerical descriptions with distributions, time series data, discrete
sequences, and graphs. Such integration of data from different domains requires
either omitting some of the data, creating separate models for different
formats, or simplifying some of the data to adhere to a shared scale and
format, all of which can hinder predictive performance. In this paper, we
propose a classification method capable of handling datasets with features of
arbitrary data types while retaining each feature's characteristic. The
proposed algorithm, called Random Similarity Forest, uses multiple
domain-specific distance measures to combine the predictive performance of
Random Forests with the flexibility of Similarity Forests. We show that Random
Similarity Forests are on par with Random Forests on numerical data and
outperform them on datasets from complex or mixed data domains. Our results
highlight the applicability of Random Similarity Forests to noisy, multi-source
datasets that are becoming ubiquitous in high-impact life science projects.
