The unified matrix representation for precise merging is presented and the approximate merging curve is further derived based on matrix operation.
Some of the analytical expressions were derived based on the matrix representation, and they were utilized for analysis.
We measured the RF distance to the collection of input trees (RF-distance) and the parsimony score of a best found supertree based on the matrix representation of the input trees.
We first determined the neighbors for each seed voxel by solving the sparse representation equations and then constructed a sparse similarity matrix based on the representation coefficient matrix to cluster the seed region into separate clusters.
In this work, a method to directly design two-dimensional pulses using the small-tip angle approximation is introduced based on a direct matrix representation.
For all the data sets, the MRP supertrees had the lowest (best) parsimony score based on a binary matrix representation of the input trees (Table 1).
A class of parametric transforms that are based on unified representation of transform matrices in the form of sparse matrix products is described.
Based on the four matrix representations Y (1), Y (2), Y (3) and Y (4), the parameter matrices A t (θ t,ϕ t ), A r (θ r,ϕ r ), G(θ r,ϕ r,γ,η) and B(f d ) can be estimated using quadrilinear alternating least square (QALS) to fit PARAFAC model.
Thus, the similarity matrix constructed based on these representation coefficients could be used for data clustering (Elhamifar and Vidal 2013; Vidal 2011).
Then, a similarity matrix was constructed based on these representation coefficients (Fig. 1d), and spectral clustering was applied to generate individual parcellation for each subject (Fig. 1e f).
