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Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data
The classification of high dimensional data with kernel methods is considered
in this article. Exploit- ing the emptiness property of high dimensional
spaces, a kernel based on the Mahalanobis distance is proposed. The computation
of the Mahalanobis distance requires the inversion of a covariance matrix. In
high dimensional spaces, the estimated covariance matrix is ill-conditioned and
its inversion is unstable or impossible. Using a parsimonious statistical
model, namely the High Dimensional Discriminant Analysis model, the specific
signal and noise subspaces are estimated for each considered class making the
inverse of the class specific covariance matrix explicit and stable, leading to
the definition of a parsimonious Mahalanobis kernel. A SVM based framework is
used for selecting the hyperparameters of the parsimonious Mahalanobis kernel
by optimizing the so-called radius-margin bound. Experimental results on three
high dimensional data sets show that the proposed kernel is suitable for
classifying high dimensional data, providing better classification accuracies
than the conventional Gaussian kernel
Generalized Kernel-based Visual Tracking
In this work we generalize the plain MS trackers and attempt to overcome
standard mean shift trackers' two limitations.
It is well known that modeling and maintaining a representation of a target
object is an important component of a successful visual tracker.
However, little work has been done on building a robust template model for
kernel-based MS tracking. In contrast to building a template from a single
frame, we train a robust object representation model from a large amount of
data. Tracking is viewed as a binary classification problem, and a
discriminative classification rule is learned to distinguish between the object
and background. We adopt a support vector machine (SVM) for training. The
tracker is then implemented by maximizing the classification score. An
iterative optimization scheme very similar to MS is derived for this purpose.Comment: 12 page
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