C is a weight vector for maximizing the safety margin s, (W_{tau }) is a weight matrix for minimizing the norm of the torque, and (W_C) is a weight matrix for evaluating the continuity of the torque.
Then, the objective function to be minimized is written as (4) where W is a weight matrix, s is the scaling parameter and is the translation vector.
where B is a matrix containing the basis functions obtained from the training data set, and w is a weight matrix.
where (textbf {P}_{w}=textbf {I}-textbf {D}_{w}^{-frac {1}{2}}textbf {W}_{w}textbf {D}_{w}^{-frac {1}{2}}) the normalized Laplacian matrix, I is a unit matrix, and D w =d i a g(W w ·1) is a weight matrix whose diagonal elements are (textbf {D}_{w}^{ii}=sum _{j=1}^{n^{(t)}}w_{textit {ij}}^{(w)}), and t r denotes the trace function.
({{mathbf {W}}_{i}} in mathbb {C}^{M times left ({M - 1} right)}) is a weight matrix for the artificial noise, and the columns of ({mathbf {W}} buildrel Delta over = left [ {{{mathbf {w}}_{i}} {{mathbf {W}}_{i}}} right ]) constitute an orthogonal basis.
NMF partitions data V using two non-negative matrices W and H, V∼WH where W is a weight matrix that indicates how much each gene contributes to each metagene pattern, and H contains the expression profiles of the metagenes.
Here W is a weight matrix.
3. Weighted quadratic statistic: where W is a weight matrix.
This problem can be solved analytically by a closed-form solution: (17) W * = 1 || X T FY || 2 X T FY, where F is a weight matrix with F ij = | f j neg |, ∀ i ∈ f j pos and F ij = − | f j pos |, ∀ i ∈ f j neg.
Here B ∈ ℝ q × K is a basis matrix for the second term, and W ∈ ℝ q × N is a weight matrix such that elements of W are with nonzero values if the labels of corresponding proteins are known, otherwise elements of W are 0. Specifically, we have (9) W i j = 0. 01, if Y i is known and Y i j = 1, 1, if Y i is known and Y i j = 0, 0, if Y i is unknown.
