  Complex categorical data is often hierarchically coupled with heterogeneous
relationships between attributes and attribute values and the couplings between
objects. Such value-to-object couplings are heterogeneous with complementary
and inconsistent interactions and distributions. Limited research exists on
unlabeled categorical data representations, ignores the heterogeneous and
hierarchical couplings, underestimates data characteristics and complexities,
and overuses redundant information, etc. The deep representation learning of
unlabeled categorical data is challenging, overseeing such value-to-object
couplings, complementarity and inconsistency, and requiring large data,
disentanglement, and high computational power. This work introduces a shallow
but powerful UNsupervised heTerogeneous couplIng lEarning (UNTIE) approach for
representing coupled categorical data by untying the interactions between
couplings and revealing heterogeneous distributions embedded in each type of
couplings. UNTIE is efficiently optimized w.r.t. a kernel k-means objective
function for unsupervised representation learning of heterogeneous and
hierarchical value-to-object couplings. Theoretical analysis shows that UNTIE
can represent categorical data with maximal separability while effectively
represent heterogeneous couplings and disclose their roles in categorical data.
The UNTIE-learned representations make significant performance improvement
against the state-of-the-art categorical representations and deep
representation models on 25 categorical data sets with diversified
characteristics.
