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Abstract:
Introduction: Factorization into independent components (ICA)
has become a standard procedure in fMRI data analysis. Here we
present an alternative factorization using non-negative matrix
factorization (NMF). NMF can be seen as a form of blind source separation with non-negativity constraints. In contrast to ICA, the
components obtained by NMF are not designed to be independent
and may potentially overlap which may provide greater
realism. It also allows various metrics for defining similarity. NM
factorizations are generated by an iterative process and the resulting
factorizations are not necessarily unique. Here, we apply
NMF to matrices containing pairwise similarities between fMRI
time courses with similarity defined by spectral coherence. We
hypothesized that different spectral bands may lead to distinct
decompositions. To test this hypothesis we applied NMF using a
range of different starting values. Non-robust results would falsify
this hypothesis.
Methods and Results: Functional resting state MRI/EPI data
were acquired of 22 normal volunteers on a 3T MRI scanner
(Siemens Trio) using TR = 2.3 sec, TE = 30ms, 3 ·3mm2 in-plane
resolution, 3mm slice thickness, 1mm gap between slices. Data
were acquired for 6.5 minutes during which subjects were asked
to fixate on a fixation point. All data sets were initially registered
to an AC/CP coordinate system where the data were resampled
to an isotropic voxel grid with a resolution of (3mm)3. We
manually defined a mask containing about 40,000 voxels covering
the entire cerebrum. We then computed a similarity matrix V
containing spectral coherence at 0.08Hz and 0.04Hz between
fMRI time series computed pairwise within this mask and averaged
across the 22 subjects. These two matrices were factorized
using NMF so that V=W H+ e, where W is a matrix of 6 basis
vectors, H is a matrix of weights and e residual errors. We used
the ALS algorithm with 15 different starting values. We analyzed
the variation across different starting values and differences between
the spectral bands. Results are shown in the figures.
Conclusion: In contrast to ICA, NMF allows investigation of a
range of metrics defining components and allows component
overlap. NMF may thus prove to be a valuable alternative. As hypothesized, we found striking differences between spectral
bands. The standard error across repetitions was small, indicating
that consistent results can be obtained.
