  Most data is multi-dimensional. Discovering whether any subset of dimensions,
or subspaces, of such data is significantly correlated is a core task in data
mining. To do so, we require a measure that quantifies how correlated a
subspace is. For practical use, such a measure should be universal in the sense
that it captures correlation in subspaces of any dimensionality and allows to
meaningfully compare correlation scores across different subspaces, regardless
how many dimensions they have and what specific statistical properties their
dimensions possess. Further, it would be nice if the measure can
non-parametrically and efficiently capture both linear and non-linear
correlations.
  In this paper, we propose UDS, a multivariate correlation measure that
fulfills all of these desiderata. In short, we define \uds based on cumulative
entropy and propose a principled normalization scheme to bring its scores
across different subspaces to the same domain, enabling universal correlation
assessment. UDS is purely non-parametric as we make no assumption on data
distributions nor types of correlation. To compute it on empirical data, we
introduce an efficient and non-parametric method. Extensive experiments show
that UDS outperforms state of the art.
