NDLI: Nonlinear Unmixing by Using Different Metrics in a Linear Unmixing Chain

Content Provider	IEEE Xplore Digital Library
Author	Heylen, R. Scheunders, P. Rangarajan, A. Gader, P.
Copyright Year	2008
Abstract	Several popular endmember extraction and unmixing algorithms are based on the geometrical interpretation of the linear mixing model, and assume the presence of pure pixels in the data. These endmembers can be identified by maximizing a simplex volume, or finding maximal distances in subsequent subspace projections, while unmixing can be considered a simplex projection problem. Since many of these algorithms can be written in terms of distance geometry, where mutual distances are the properties of interest instead of Euclidean coordinates, one can design an unmixing chain where other distance metrics are used. Many preprocessing steps such as (nonlinear) dimensionality reduction or data whitening, and several nonlinear unmixing models such as the Hapke and bilinear models, can be considered as transformations to a different data space, with a corresponding metric. In this paper, we show how one can use different metrics in geometry-based endmember extraction and unmixing algorithms, and demonstrate the results for some well-known metrics, such as the Mahalanobis distance, the Hapke model for intimate mixing, the polynomial post-nonlinear model, and graph-geodesic distances. This offers a flexible processing chain, where many models and preprocessing steps can be transparently incorporated through the use of the proper distance function.
Starting Page	2655
Ending Page	2664
Page Count	10
File Size	1099523
File Format	PDF
ISSN	19391404
Volume Number	8
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Kernel Data models Hyperspectral imaging Mathematical model Euclidean distance Algorithm design and analysis spectral analysis
Content Type	Text
Resource Type	Article
Subject	Atmospheric Science Computers in Earth Sciences

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