4,376 research outputs found
Non-convex regularization in remote sensing
In this paper, we study the effect of different regularizers and their
implications in high dimensional image classification and sparse linear
unmixing. Although kernelization or sparse methods are globally accepted
solutions for processing data in high dimensions, we present here a study on
the impact of the form of regularization used and its parametrization. We
consider regularization via traditional squared (2) and sparsity-promoting (1)
norms, as well as more unconventional nonconvex regularizers (p and Log Sum
Penalty). We compare their properties and advantages on several classification
and linear unmixing tasks and provide advices on the choice of the best
regularizer for the problem at hand. Finally, we also provide a fully
functional toolbox for the community.Comment: 11 pages, 11 figure
Unsupervised spectral sub-feature learning for hyperspectral image classification
Spectral pixel classification is one of the principal techniques used in hyperspectral image (HSI) analysis. In this article, we propose an unsupervised feature learning method for classification of hyperspectral images. The proposed method learns a dictionary of sub-feature basis representations from the spectral domain, which allows effective use of the correlated spectral data. The learned dictionary is then used in encoding convolutional samples from the hyperspectral input pixels to an expanded but sparse feature space. Expanded hyperspectral feature representations enable linear separation between object classes present in an image. To evaluate the proposed method, we performed experiments on several commonly used HSI data sets acquired at different locations and by different sensors. Our experimental results show that the proposed method outperforms other pixel-wise classification methods that make use of unsupervised feature extraction approaches. Additionally, even though our approach does not use any prior knowledge, or labelled training data to learn features, it yields either advantageous, or comparable, results in terms of classification accuracy with respect to recent semi-supervised methods
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
Submodular meets Spectral: Greedy Algorithms for Subset Selection, Sparse Approximation and Dictionary Selection
We study the problem of selecting a subset of k random variables from a large
set, in order to obtain the best linear prediction of another variable of
interest. This problem can be viewed in the context of both feature selection
and sparse approximation. We analyze the performance of widely used greedy
heuristics, using insights from the maximization of submodular functions and
spectral analysis. We introduce the submodularity ratio as a key quantity to
help understand why greedy algorithms perform well even when the variables are
highly correlated. Using our techniques, we obtain the strongest known
approximation guarantees for this problem, both in terms of the submodularity
ratio and the smallest k-sparse eigenvalue of the covariance matrix. We further
demonstrate the wide applicability of our techniques by analyzing greedy
algorithms for the dictionary selection problem, and significantly improve the
previously known guarantees. Our theoretical analysis is complemented by
experiments on real-world and synthetic data sets; the experiments show that
the submodularity ratio is a stronger predictor of the performance of greedy
algorithms than other spectral parameters
- …