Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimensionality Reduction via Regression in Hyperspectral Imagery   This paper introduces a new unsupervised method for dimensionality reduction
via regression (DRR). The algorithm belongs to the family of invertible
transforms that generalize Principal Component Analysis (PCA) by using
curvilinear instead of linear features. DRR identifies the nonlinear features
through multivariate regression to ensure the reduction in redundancy between
he PCA coefficients, the reduction of the variance of the scores, and the
reduction in the reconstruction error. More importantly, unlike other nonlinear
dimensionality reduction methods, the invertibility, volume-preservation, and
straightforward out-of-sample extension, makes DRR interpretable and easy to
apply. The properties of DRR enable learning a more broader class of data
manifolds than the recently proposed Non-linear Principal Components Analysis
(NLPCA) and Principal Polynomial Analysis (PPA). We illustrate the performance
of the representation in reducing the dimensionality of remote sensing data. In
particular, we tackle two common problems: processing very high dimensional
spectral information such as in hyperspectral image sounding data, and dealing
with spatial-spectral image patches of multispectral images. Both settings pose
collinearity and ill-determination problems. Evaluation of the expressive power
of the features is assessed in terms of truncation error, estimating
atmospheric variables, and surface land cover classification error. Results
show that DRR outperforms linear PCA and recently proposed invertible
extensions based on neural networks (NLPCA) and univariate regressions (PPA).

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat