  We introduce a novel type of computationally efficient artificial neural
network (ANN) called the rank similarity filter (RSF). RSFs can be used to both
transform and classify nonlinearly separable datasets with many data points and
dimensions. The weights of RSF are set using the rank orders of features in a
data point, or optionally the 'confusion' adjusted ranks between features
(determined from their distributions in the dataset). The activation strength
of a filter determines its similarity to other points in the dataset, a measure
related to cosine similarity. The activation of many RSFs maps samples into a
new nonlinear space suitable for linear classification (the rank similarity
transform (RST)). We additionally used this method to create the nonlinear rank
similarity classifier (RSC), which is a fast and accurate multiclass
classifier, and the nonlinear rank similarity probabilistic classifier (RSPC),
which is an extension to the multilabel case. We evaluated the classifiers on
multiple datasets and RSC was competitive with existing classifiers but with
superior computational efficiency. Open-source code for RST, RSC and RSPC was
written in Python using the popular scikit-learn framework to make it easily
accessible. In future extensions the algorithm can be applied to specialised
hardware suitable for the parallelization of an ANN (GPU) and a Spiking Neural
Network (neuromorphic computing) with corresponding performance gains. This
makes RSF a promising solution to the problem of efficient analysis of
nonlinearly separable data.
