Metric distances derived from cosine similarity and Pearson and Spearman correlations
This work addresses a theoretical problem in data analysis and machine learning for researchers and practitioners, but it appears incremental as it builds on known transforms and metric-preserving functions.
The paper tackled the problem of transforming cosine similarity and Pearson/Spearman correlations into metric distances, introducing two classes of transformations: one that separates anti-correlated objects and another that groups correlated and anti-correlated objects, with the sine function serving as an example for the latter.
We investigate two classes of transformations of cosine similarity and Pearson and Spearman correlations into metric distances, utilising the simple tool of metric-preserving functions. The first class puts anti-correlated objects maximally far apart. Previously known transforms fall within this class. The second class collates correlated and anti-correlated objects. An example of such a transformation that yields a metric distance is the sine function when applied to centered data.