  We present an extension of sparse Canonical Correlation Analysis (CCA)
designed for finding multiple-to-multiple linear correlations within a single
set of variables. Unlike CCA, which finds correlations between two sets of data
where the rows are matched exactly but the columns represent separate sets of
variables, the method proposed here, Canonical Autocorrelation Analysis (CAA),
finds multivariate correlations within just one set of variables. This can be
useful when we look for hidden parsimonious structures in data, each involving
only a small subset of all features. In addition, the discovered correlations
are highly interpretable as they are formed by pairs of sparse linear
combinations of the original features. We show how CAA can be of use as a tool
for anomaly detection when the expected structure of correlations is not
followed by anomalous data. We illustrate the utility of CAA in two application
domains where single-class and unsupervised learning of correlation structures
are particularly relevant: breast cancer diagnosis and radiation threat
detection. When applied to the Wisconsin Breast Cancer data, single-class CAA
is competitive with supervised methods used in literature. On the radiation
threat detection task, unsupervised CAA performs significantly better than an
unsupervised alternative prevalent in the domain, while providing valuable
additional insights for threat analysis.
