TY - GEN
T1 - Linear spectral unmixing via matrix factorization
T2 - 38th Annual IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2018
AU - Lin, Chia Hsiang
AU - Bioucas Dias, José M.
PY - 2018/10/31
Y1 - 2018/10/31
N2 - In hyperspectral unmixing and in many other areas (e.g., chemometrics, topic modeling, archetypal analysis) simplex-structured matrix factorization (SSMF) plays an essential role as suggested by years of research efforts devoted to this theme. Specifically, SSMF factorizes a data matrix into two matrix factors with one factor (i.e., the abundances) constrained to have its columns lying in the unit simplex. SSMF criteria include the well-known Craig's seminal minimum-volume enclosing simplex (MVES), originally proposed for blind hyperspectral unmixing, and the recently introduced maximum-volume inscribed ellipsoid (MVIE). The identifiability analysis of those criteria is essential to understand their fundamental behavior and also to devise effective SSMF algorithms tailored to the specificities of the different application scenarios. Our analysis is motivated by a simple fact taking place in most remotely sensed hyperspectral mixtures: in most pixels, only a subset of the materials is present. This is to say that the abundances exhibit a form of sparsity and thus lie in the boundary of the data simplex. We then derive some elegant sufficient condition, showing that as long as data points are locally well spread, perfect SSMF identifiability of both criteria can be guaranteed.
AB - In hyperspectral unmixing and in many other areas (e.g., chemometrics, topic modeling, archetypal analysis) simplex-structured matrix factorization (SSMF) plays an essential role as suggested by years of research efforts devoted to this theme. Specifically, SSMF factorizes a data matrix into two matrix factors with one factor (i.e., the abundances) constrained to have its columns lying in the unit simplex. SSMF criteria include the well-known Craig's seminal minimum-volume enclosing simplex (MVES), originally proposed for blind hyperspectral unmixing, and the recently introduced maximum-volume inscribed ellipsoid (MVIE). The identifiability analysis of those criteria is essential to understand their fundamental behavior and also to devise effective SSMF algorithms tailored to the specificities of the different application scenarios. Our analysis is motivated by a simple fact taking place in most remotely sensed hyperspectral mixtures: in most pixels, only a subset of the materials is present. This is to say that the abundances exhibit a form of sparsity and thus lie in the boundary of the data simplex. We then derive some elegant sufficient condition, showing that as long as data points are locally well spread, perfect SSMF identifiability of both criteria can be guaranteed.
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U2 - 10.1109/IGARSS.2018.8518462
DO - 10.1109/IGARSS.2018.8518462
M3 - Conference contribution
AN - SCOPUS:85061769006
T3 - International Geoscience and Remote Sensing Symposium (IGARSS)
SP - 6155
EP - 6158
BT - 2018 IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2018 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 22 July 2018 through 27 July 2018
ER -