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Independent component analysis for brain FMRI does indeed select for maximal independence.

Calhoun VD, Potluru VK, Phlypo R, Silva RF, Pearlmutter BA, Caprihan A, Plis SM, Adalı T - PLoS ONE (2013)

Bottom Line: A recent paper by Daubechies et al. claims that two independent component analysis (ICA) algorithms, Infomax and FastICA, which are widely used for functional magnetic resonance imaging (fMRI) analysis, select for sparsity rather than independence.The argument was supported by a series of experiments on synthetic data.We show that these experiments fall short of proving this claim and that the ICA algorithms are indeed doing what they are designed to do: identify maximally independent sources.

View Article: PubMed Central - PubMed

Affiliation: Medical Image Analysis Lab, The Mind Research Network, Albuquerque, New Mexico, USA. vcalhoun@unm.edu

ABSTRACT
A recent paper by Daubechies et al. claims that two independent component analysis (ICA) algorithms, Infomax and FastICA, which are widely used for functional magnetic resonance imaging (fMRI) analysis, select for sparsity rather than independence. The argument was supported by a series of experiments on synthetic data. We show that these experiments fall short of proving this claim and that the ICA algorithms are indeed doing what they are designed to do: identify maximally independent sources.

Show MeSH
Sparsity measures for three different coordinate system origins ().Sparsity as measured with respect to different coordinate system origins (), as a function of the relative size of the active region. Remark that for a relative size of zero, only background samples are present and, thus, the mean of the mixture model coincides with the mean of the background (and the two sparsity measures correspond at this point). An analogous observation can be made for a relative size of one, now with respect to the activity (signal samples).
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pone-0073309-g003: Sparsity measures for three different coordinate system origins ().Sparsity as measured with respect to different coordinate system origins (), as a function of the relative size of the active region. Remark that for a relative size of zero, only background samples are present and, thus, the mean of the mixture model coincides with the mean of the background (and the two sparsity measures correspond at this point). An analogous observation can be made for a relative size of one, now with respect to the activity (signal samples).

Mentions: A legitimate question now is what about a signal of which all but 1 coefficient differ from a number, say, . Let that one coefficient equal zero. Is that signal sparse? Under the above definition, the signal would not be considered as sparse, since only a single coefficient could be coded as a zero without introducing a reconstruction error. However, if we would allow for coding a shift by , then coding coefficients as zero would result in a reconstruction error upper bounded by (and we would find with probability ). It is clear from this very simple example that it is important to appropriately choose the origin for the coordinate system () in which one foresees to evaluate the sparseness of the signal. For the model considered in Daubechies et al. [8], we plot the sparsity measure for three different choices of . Here, the ordinary sparsity measure (as understood in Daubechies et al. [8]) is taken with respect to , i.e., the mean of the “background distribution”, with sparsity decreasing as the active region size increases (see Figure 3). Note that for fMRI we typically use zero-mean samples when using ICA, thus measuring our sparsity with respect to the mean of the mixture model.


Independent component analysis for brain FMRI does indeed select for maximal independence.

Calhoun VD, Potluru VK, Phlypo R, Silva RF, Pearlmutter BA, Caprihan A, Plis SM, Adalı T - PLoS ONE (2013)

Sparsity measures for three different coordinate system origins ().Sparsity as measured with respect to different coordinate system origins (), as a function of the relative size of the active region. Remark that for a relative size of zero, only background samples are present and, thus, the mean of the mixture model coincides with the mean of the background (and the two sparsity measures correspond at this point). An analogous observation can be made for a relative size of one, now with respect to the activity (signal samples).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3757003&req=5

pone-0073309-g003: Sparsity measures for three different coordinate system origins ().Sparsity as measured with respect to different coordinate system origins (), as a function of the relative size of the active region. Remark that for a relative size of zero, only background samples are present and, thus, the mean of the mixture model coincides with the mean of the background (and the two sparsity measures correspond at this point). An analogous observation can be made for a relative size of one, now with respect to the activity (signal samples).
Mentions: A legitimate question now is what about a signal of which all but 1 coefficient differ from a number, say, . Let that one coefficient equal zero. Is that signal sparse? Under the above definition, the signal would not be considered as sparse, since only a single coefficient could be coded as a zero without introducing a reconstruction error. However, if we would allow for coding a shift by , then coding coefficients as zero would result in a reconstruction error upper bounded by (and we would find with probability ). It is clear from this very simple example that it is important to appropriately choose the origin for the coordinate system () in which one foresees to evaluate the sparseness of the signal. For the model considered in Daubechies et al. [8], we plot the sparsity measure for three different choices of . Here, the ordinary sparsity measure (as understood in Daubechies et al. [8]) is taken with respect to , i.e., the mean of the “background distribution”, with sparsity decreasing as the active region size increases (see Figure 3). Note that for fMRI we typically use zero-mean samples when using ICA, thus measuring our sparsity with respect to the mean of the mixture model.

Bottom Line: A recent paper by Daubechies et al. claims that two independent component analysis (ICA) algorithms, Infomax and FastICA, which are widely used for functional magnetic resonance imaging (fMRI) analysis, select for sparsity rather than independence.The argument was supported by a series of experiments on synthetic data.We show that these experiments fall short of proving this claim and that the ICA algorithms are indeed doing what they are designed to do: identify maximally independent sources.

View Article: PubMed Central - PubMed

Affiliation: Medical Image Analysis Lab, The Mind Research Network, Albuquerque, New Mexico, USA. vcalhoun@unm.edu

ABSTRACT
A recent paper by Daubechies et al. claims that two independent component analysis (ICA) algorithms, Infomax and FastICA, which are widely used for functional magnetic resonance imaging (fMRI) analysis, select for sparsity rather than independence. The argument was supported by a series of experiments on synthetic data. We show that these experiments fall short of proving this claim and that the ICA algorithms are indeed doing what they are designed to do: identify maximally independent sources.

Show MeSH