The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem. This algorithm appears to perform extremely well and is extremely fast even when the given covariance matrix has a very large dimension. The effectiveness of the algorithm is assessed through simulation studies and by applications to three real benchmark datasets that are considered. A local convergence analysis of the algorithm is also presented.
The organization of the neocortical projection to the inferior colliculus (IC) was studied in 36 rats using retrograde transport of horseradish peroxidase (HRP) or horseradish peroxidase conjugated with lectin (WGA-HRP). Projection to the external and dorsal cortices originates in the temporal neocortical areas Te 1, Te 2 and Te 3 and in the parietal area Par 2. The corticocollicular projection is predominantly ipsilateral with a weak contralateral contribution. Projection to the rostromedial and rostrolateral part of the external cortex (EC) of the IC arises mainly from the areas Par 2 and Te 1. The participation of the cortical areas Te 2 and Te 3 in this projection is only small. The fibres to the caudobasal part of the external cortex descend from the caudal parts of areas Te 1, Te 2, and Te 3. The corticocollicular projections to the dorsal part of the IC are more numerous than the projections to the EC and originate in all temporal areas, i.e. in area Te 1, Te 2 and Te 3. However, the topographical organization of the corticocollicular projection is more pronounced in the part which projects to the EC. We suggest that the topographical organization of the projections to the EC corresponds with the map of auditory space in the EC. The source of corticocollicular fibres are exclusively neurones of lamina V of all cortical areas sending their fibres to the IC.