To derive the partial derivative, we begin by substituting the determinant formulation into our volume penalization and arrive at the following calculation: therefore, the gradient of log vol(K) is given by where the eigenvector z d satisfies the equality Qz d = λ d z d and E ij is the indicator matrix for the entry ij.
The prior probabilities, i.e. the probability of belonging to class j, prior to observing the p variables in X, is denoted by π j = P(G= j)s where the discrete random variable G should not be confused with the indicator matrix G.
Towards that end, let (Delta _{t}' in {0,1}^{Ntimes N}) be the difference indicator matrix that only indicates the packets that are received at current time t, i.e., Delta_{t}'= Delta_{t} - S^{downarrow}Delta_{t-1}. (20).
Let H l be the cluster indicator matrix at iteration time l (l > 1).
Constant features as well as each feature corresponding to the consensus amino acid at a certain sequence position (usually the wild-type) were removed from the indicator matrix of the training data, as such features contain no additional information.
Neglecting constants and adding the L1-norm regularization for H, the modified formulation was as follows: (4) min H ≥ 0 - ∑ i = 1 N ∑ j = 1 N W i, j log H H T i, j - H H T i, j + ∑ i = 1 N ∑ z = 1 K β h i, z where the hyper-parameter β > 0 controlled the sparsity of H, and H ≥ 0 was the cluster indicator matrix.
We omit the indicator matrix Z used in original EMMA model, because in the CC data, Z is an identity matrix.
Furthermore, for a MIMO channel matrix, the rank is the indicator of how many data streams can be spatially multiplexed on the channel, and the data streams are represented by the singular values and the corresponding singular vectors.
where is the indicator function, defined as the th column of, is a diagonal matrix, and.
Let (Delta _{t}in mathbb {R}^{Ntimes N}) be an indicator matrix with binary elements {0,1} indicating the complete buffer contents of (bar {f}'_{t}) at time t.
