11 research outputs found
Robust Multiple Signal Classification via Probability Measure Transformation
In this paper, we introduce a new framework for robust multiple signal
classification (MUSIC). The proposed framework, called robust
measure-transformed (MT) MUSIC, is based on applying a transform to the
probability distribution of the received signals, i.e., transformation of the
probability measure defined on the observation space. In robust MT-MUSIC, the
sample covariance is replaced by the empirical MT-covariance. By judicious
choice of the transform we show that: 1) the resulting empirical MT-covariance
is B-robust, with bounded influence function that takes negligible values for
large norm outliers, and 2) under the assumption of spherically contoured noise
distribution, the noise subspace can be determined from the eigendecomposition
of the MT-covariance. Furthermore, we derive a new robust measure-transformed
minimum description length (MDL) criterion for estimating the number of
signals, and extend the MT-MUSIC framework to the case of coherent signals. The
proposed approach is illustrated in simulation examples that show its
advantages as compared to other robust MUSIC and MDL generalizations
On Measure Transformed Canonical Correlation Analysis
In this paper linear canonical correlation analysis (LCCA) is generalized by
applying a structured transform to the joint probability distribution of the
considered pair of random vectors, i.e., a transformation of the joint
probability measure defined on their joint observation space. This framework,
called measure transformed canonical correlation analysis (MTCCA), applies LCCA
to the data after transformation of the joint probability measure. We show that
judicious choice of the transform leads to a modified canonical correlation
analysis, which, in contrast to LCCA, is capable of detecting non-linear
relationships between the considered pair of random vectors. Unlike kernel
canonical correlation analysis, where the transformation is applied to the
random vectors, in MTCCA the transformation is applied to their joint
probability distribution. This results in performance advantages and reduced
implementation complexity. The proposed approach is illustrated for graphical
model selection in simulated data having non-linear dependencies, and for
measuring long-term associations between companies traded in the NASDAQ and
NYSE stock markets