720 research outputs found
Learning with Algebraic Invariances, and the Invariant Kernel Trick
When solving data analysis problems it is important to integrate prior
knowledge and/or structural invariances. This paper contributes by a novel
framework for incorporating algebraic invariance structure into kernels. In
particular, we show that algebraic properties such as sign symmetries in data,
phase independence, scaling etc. can be included easily by essentially
performing the kernel trick twice. We demonstrate the usefulness of our theory
in simulations on selected applications such as sign-invariant spectral
clustering and underdetermined ICA
Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods
Hyperspectral images show similar statistical properties to natural grayscale
or color photographic images. However, the classification of hyperspectral
images is more challenging because of the very high dimensionality of the
pixels and the small number of labeled examples typically available for
learning. These peculiarities lead to particular signal processing problems,
mainly characterized by indetermination and complex manifolds. The framework of
statistical learning has gained popularity in the last decade. New methods have
been presented to account for the spatial homogeneity of images, to include
user's interaction via active learning, to take advantage of the manifold
structure with semisupervised learning, to extract and encode invariances, or
to adapt classifiers and image representations to unseen yet similar scenes.
This tutuorial reviews the main advances for hyperspectral remote sensing image
classification through illustrative examples.Comment: IEEE Signal Processing Magazine, 201
Semi-Supervised Kernel PCA
We present three generalisations of Kernel Principal Components Analysis
(KPCA) which incorporate knowledge of the class labels of a subset of the data
points. The first, MV-KPCA, penalises within class variances similar to Fisher
discriminant analysis. The second, LSKPCA is a hybrid of least squares
regression and kernel PCA. The final LR-KPCA is an iteratively reweighted
version of the previous which achieves a sigmoid loss function on the labeled
points. We provide a theoretical risk bound as well as illustrative experiments
on real and toy data sets
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