3 research outputs found
MIG Median Detectors with Manifold Filter
In this paper, we propose a class of median-based matrix information geometry
(MIG) detectors with a manifold filter and apply them to signal detection in
nonhomogeneous environments. As customary, the sample data is assumed to be
modeled as Hermitian positive-definite (HPD) matrices, and the geometric median
of a set of HPD matrices is interpreted as an estimate of the clutter
covariance matrix (CCM). Then, the problem of signal detection can be
reformulated as discriminating two points on the manifold of HPD matrices, one
of which is the HPD matrix in the cell under test while the other represents
the CCM. By manifold filter, we map a set of HPD matrices to another set of HPD
matrices by weighting them, that consequently improves the discriminative power
by reducing the intra-class distances while increasing the inter-class
distances. Three MIG median detectors are designed by resorting to three
geometric measures on the matrix manifold, and the corresponding geometric
medians are shown to be robust to outliers. Numerical simulations show the
advantage of the proposed MIG median detectors in comparison with their
state-of-the-art counterparts as well as the conventional detectors in
nonhomogeneous environments.Comment: 22 pages, 12 figure
Target Detection within Nonhomogeneous Clutter via Total Bregman Divergence-Based Matrix Information Geometry Detectors
Information divergences are commonly used to measure the dissimilarity of two
elements on a statistical manifold. Differentiable manifolds endowed with
different divergences may possess different geometric properties, which can
result in totally different performances in many practical applications. In
this paper, we propose a total Bregman divergence-based matrix information
geometry (TBD-MIG) detector and apply it to detect targets emerged into
nonhomogeneous clutter. In particular, each sample data is assumed to be
modeled as a Hermitian positive-definite (HPD) matrix and the clutter
covariance matrix is estimated by the TBD mean of a set of secondary HPD
matrices. We then reformulate the problem of signal detection as discriminating
two points on the HPD matrix manifold. Three TBD-MIG detectors, referred to as
the total square loss, the total log-determinant and the total von Neumann MIG
detectors, are proposed, and they can achieve great performances due to their
power of discrimination and robustness to interferences. Simulations show the
advantage of the proposed TBD-MIG detectors in comparison with the geometric
detector using an affine invariant Riemannian metric as well as the adaptive
matched filter in nonhomogeneous clutter.Comment: 15 pages, 8 figure
BrePartition: Optimized High-Dimensional kNN Search with Bregman Distances
Bregman distances (also known as Bregman divergences) are widely used in
machine learning, speech recognition and signal processing, and kNN searches
with Bregman distances have become increasingly important with the rapid
advances of multimedia applications. Data in multimedia applications such as
images and videos are commonly transformed into space of hundreds of
dimensions. Such high-dimensional space has posed significant challenges for
existing kNN search algorithms with Bregman distances, which could only handle
data of medium dimensionality (typically less than 100). This paper addresses
the urgent problem of high-dimensional kNN search with Bregman distances. We
propose a novel partition-filter-refinement framework. Specifically, we propose
an optimized dimensionality partitioning scheme to solve several non-trivial
issues. First, an effective bound from each partitioned subspace to obtain
exact kNN results is derived. Second, we conduct an in-depth analysis of the
optimized number of partitions and devise an effective strategy for
partitioning. Third, we design an efficient integrated index structure for all
the subspaces together to accelerate the search processing. Moreover, we extend
our exact solution to an approximate version by a trade-off between the
accuracy and efficiency. Experimental results on four real-world datasets and
two synthetic datasets show the clear advantage of our method in comparison to
state-of-the-art algorithms