In our experiments, the number of mixtures of UBM (or GMM) is 1024, and total variability space T is a rectangular matrix of low rank with dimension 1024*56 by 400.
where m is the language- and channel-independent mean supervector (which can be taken to be the UBM supervector), T is a rectangular matrix of low rank and the i-vector w is a random vector having a standard normal distribution.
Note that if d are n-dimensional vectors (n ≥ k), and s are m-dimensional, then didiT are square symmetric matrices, and the memory M is a rectangular matrix of dimensions nxnm.
∀ n ∈ Z 0 + and E 1 = ( I ⋮ 0 ) is a rectangular matrix with a number of rows equalizing that of the columns less one which loses the last value of the regressor of the preceding sample.
After N is known, the data need only be multiplied by a matrix B ′ = D ′ − 1 / 2 V ′ T in a similar fashion to Equation (4), where D ′ is a smaller N × N diagonal matrix containing only the N largest eigenvalues in D and V ′ is a rectangular matrix containing only the N columns of V corresponding to those eigenvalues.
More specifically, if denotes the SVD of the matrix, where are (rotation) unitary matrices and is a rectangular matrix whose diagonal elements are the ordered singular values of the matrix, the SVD design requires (2).
To do this, we searched for a rank- R matrix L that best represents the Q matrix in a least square sense, min L ∈ℝ MN × R ‖ Q− LL⊤‖ F, where R ≪ NM, L∈ℝ MN × R is a rectangular matrix with low row-rank and LL⊤ is called the rank- R approximation of Q.
Let be a rectangular matrix.
The grids were configured in a rectangular matrix of 4×8, 8×8, or 12×8.
where z is supposed to be the estimate of x Q, H = h 1 H h 2 H ⋮ h Q H (5). is a rectangular filtering matrix of size Q×M, h q, q=1,2,…,Q are complex-valued filters of length M, xfd=H x is the filtered desired signal, and vrn=H v is the residual noise.
where H ′ = h 1 ′H h 2 ′H ⋮ h Q ′H (55). is a rectangular filtering matrix of size Q×M, h q ′, q = 1, 2, …, Q are complex-valued filters of length M, x fd ′ = H ′ x d is the filtered desired signal, x ri ′ = H ′ x i is the residual interference, and v rn ′ = H ′ v is the residual noise.
