Data selection with set-membership affine projection algorithm

Data Censoring with Set-Membership Affine Projection Algorithm

“…By reviewing [27], we approximate γ 1 in the ST-SM-AP algorithm for online censoring in flowing big data problems in this section. In streaming data (and when we have data abundance), it is helpful to attain a satisfactory solution by adopting a predetermined portion of data rather than processing all of the acquired data.…”

“…Hence, by considering this distribution, we can evaluate threshold γ 1 . Defining the noiseless error signal by e(k) = x T (k)[w o −w(k)] T , we know that e(k) is uncorrelated with n(k); thus, we get [27].…”

“…Using Equation (11) to obtain E[ e 2 (k)], we require γ 1 ; thus, we first assume that E[e(k)] = 0, Var[e(k)] = σ 2 n , and the distribution of e(k) is the zero-mean Gaussian with variance σ 2 n . Therefore, for a given p, the initial approximation of γ 1 can be obtained by [27].…”

“…Thus, we can compute the variance of e(k) by Equation (10); the distribution of the error would be a zero-mean Gaussian with variance σ 2 e = Var[e(k)] = E[ e 2 (k)] + σ 2 n . Therefore, the improved estimate for γ 1 can be attained by [27].…”

“…Hence, to defeat the limitations and obtain the preferred outcome, we must be able to define the informative incoming data. In this work, by reviewing [27], we utilized the sought-after probability of updating coefficients to approximate the threshold parameter in the single-threshold set-membership affine projection (ST-SM-AP) algorithm to censor non-informative data.…”