Sentence examples for mean weight vector from inspiring English sources

A complexity comparison is provided to show their advantages over existing methods, and a sufficient condition for the convergence of the mean weight vector is established.

Figure 10 shows the effect of changing the step size on the mean weight vector of the FXLMF algorithm, and as depicted in Fig. 5, the algorithm converges faster as we increase the step size using uniform noise.

FXLMF and LFXLMF almost have identical curves because we are using a small leakage factor γ. Figure 5 shows the effect of changing the step size on the mean weight vector of the FXLMF algorithm; when we increase the values of the step size, the algorithm converges faster to the larger mean of the weight.

Dashed line: IT model Fig. 11 Comparison over mean weight vector for LFXLMF algorithms using different leakage factors γ = [0.1, 0.250, 0.50, 1] and fixed step size μ = 0.001 using uniform noise at low SNR = 5 dB Fig. 12 MSE for the FXLMF and LFXLMF algorithm robustness using uniform noise at low SNR = 5 dB, fixed step size μ = 0.00125, and leakage factor γ = 0.50.

The mean weight vector (principal component) w mean c for each class is calculated using the first l weights that belong to the eigenvectors with the largest eigenvalues (l < k, where k is the total number of training sample images in all the classes combined, k c is the number of training samples in a class c, and l will be the dimension of w mean c ). w mean c = 1 k c ∑ u T. σ train c (8).

(3) The bound for the step-size of the proposed algorithm that guarantees convergence of the mean weight-vector, given by (12), shows that the mean-weight-vector stability depends on the Cramer-Rao bound.

Therefore, the convergence of the mean-weight-vector of the proposed algorithm depends on its mean-square stability.

Two algorithms FXLMF and LFXLMF were proposed in this work; an analytical study and mathematical derivations for the mean weight adaptive vector and the mean square error for both algorithms have been obtained.

Consequently, taking the expectation on both sides of (14), under A.1-A.3, the mean weight-error vector of the proposed algorithm evolves as E [ v n + 1 ] = E [ v n ] + μ α ̄ n E e n x n ∥ x n ∥ 2 + ( 1 - α ̄ n ) E e n 3 x n ∥ x n ∥ 2. (15).

Also, we see that a larger step size will increase the mean of the weight vector.

Moreover, to combat the noise enhancement problem, we can apply the minimum mean square error (MMSE) weight vector for the linear equalizer, i.e., w k = w M M S E k = Λ ̄ k ( 1, 1 ) + 1 S N R - 1 Λ ̄ k ( 2, 2 ) + 1 S N R - 1 ⋅ ⋅ ⋅ Λ ̄ k ( N P, N P ) + 1 S N R - 1 T (14).