Abstract-Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: 1) the endmembers are the vertices of a simplex and 2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.Index Terms-Linear unmixing, simplex, spectral mixture model, unmixing hypespectral data, unsupervised endmember extraction, vertex component analysis (VCA).

Abstract-Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2) sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.Index Terms-Independent component analysis (ICA), independent factor analysis (IFA), mixture of Gaussians, unmixing hyperspectral data.

The spindle assembly checkpoint detects errors in kinetochore attachment to the spindle including insufficient microtubule occupancy and absence of tension across bi-oriented kinetochore pairs. Here, we analyse how the kinetochore localization of the Drosophila spindle checkpoint proteins Bub1, Mad2, Bub3 and BubR1, behave in response to alterations in microtubule binding or tension. To analyse the behaviour in the absence of tension, we treated S2 cells with low doses of taxol to disrupt microtubule dynamics and tension, but not kinetochore-microtubule occupancy. Under these conditions, we found that Mad2 and Bub1 do not accumulate at metaphase kinetochores whereas BubR1 does. Consistently, in mono-oriented chromosomes, both kinetochores accumulate BubR1 whereas Bub1 and Mad2 only localize at the unattached kinetochore. To study the effect of tension we analysed the kinetochore localization of spindle checkpoint proteins in relation to tension-sensitive kinetochore phosphorylation recognised by the 3F3/2 antibody. Using detergent-extracted S2 cells as a system in which kinetochore phosphorylation can be easily manipulated, we observed that BubR1 and Bub3 accumulation at kinetochores is dependent on the presence of phosphorylated 3F3/2 epitopes. However, Bub1 and Mad2 localize at kinetochores regardless of the 3F3/2 phosphorylation state. Altogether, our results suggest that spindle checkpoint proteins sense distinct aspects of kinetochore interaction with the spindle, with Mad2 and Bub1 monitoring microtubule occupancy while BubR1 and Bub3 monitor tension across attached kinetochores.

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