Abstract
In this paper, we propose a novel online scheme named the adaptive proximal forward-backward splitting method to suppress the sum of'smooth' and'nonsmooth' convex functions, both of which are assumed time-varying. We derive a powerful algorithm for sparse system identification by defining each function as a certain average squared distance ('smooth') and a weighted ℓ1-norm ('nonsmooth'). The smooth term brings an exponentially weighted average of the metric projections of the current estimate onto linear varieties, of which the number grows as new measurements arrive. The presented recursive formula realizes an efficient computation of the average (the exponentially weighted adaptive parallel projection), which contributes the fast and stable convergence. The nonsmooth term, on the other hand, brings the weighted soft-thresholding, contributing the enhancement of the filter sparsity. The weights are adaptively controlled according to the filter coefficients so that the softthresholding gives significant impacts solely to inactive coefficients (coefficients close to zero). The numerical example demonstrates the efficacy of the proposed algorithm.
| Original language | English |
|---|---|
| Title of host publication | APSIPA ASC 2010 - Asia-Pacific Signal and Information Processing Association Annual Summit and Conference |
| Pages | 367-370 |
| Number of pages | 4 |
| Publication status | Published - 2010 |
| Externally published | Yes |
| Event | 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2010 - Biopolis, Singapore Duration: 2010 Dec 14 → 2010 Dec 17 |
Other
| Other | 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2010 |
|---|---|
| Country | Singapore |
| City | Biopolis |
| Period | 10/12/14 → 10/12/17 |
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ASJC Scopus subject areas
- Computer Networks and Communications
- Information Systems
Cite this
Sparse system identification by exponentially weighted adaptive parallel projection and generalized soft-thresholding. / Yamagishi, Masao; Yukawa, Masahiro; Yamada, Isao.
APSIPA ASC 2010 - Asia-Pacific Signal and Information Processing Association Annual Summit and Conference. 2010. p. 367-370.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Sparse system identification by exponentially weighted adaptive parallel projection and generalized soft-thresholding
AU - Yamagishi, Masao
AU - Yukawa, Masahiro
AU - Yamada, Isao
PY - 2010
Y1 - 2010
N2 - In this paper, we propose a novel online scheme named the adaptive proximal forward-backward splitting method to suppress the sum of'smooth' and'nonsmooth' convex functions, both of which are assumed time-varying. We derive a powerful algorithm for sparse system identification by defining each function as a certain average squared distance ('smooth') and a weighted ℓ1-norm ('nonsmooth'). The smooth term brings an exponentially weighted average of the metric projections of the current estimate onto linear varieties, of which the number grows as new measurements arrive. The presented recursive formula realizes an efficient computation of the average (the exponentially weighted adaptive parallel projection), which contributes the fast and stable convergence. The nonsmooth term, on the other hand, brings the weighted soft-thresholding, contributing the enhancement of the filter sparsity. The weights are adaptively controlled according to the filter coefficients so that the softthresholding gives significant impacts solely to inactive coefficients (coefficients close to zero). The numerical example demonstrates the efficacy of the proposed algorithm.
AB - In this paper, we propose a novel online scheme named the adaptive proximal forward-backward splitting method to suppress the sum of'smooth' and'nonsmooth' convex functions, both of which are assumed time-varying. We derive a powerful algorithm for sparse system identification by defining each function as a certain average squared distance ('smooth') and a weighted ℓ1-norm ('nonsmooth'). The smooth term brings an exponentially weighted average of the metric projections of the current estimate onto linear varieties, of which the number grows as new measurements arrive. The presented recursive formula realizes an efficient computation of the average (the exponentially weighted adaptive parallel projection), which contributes the fast and stable convergence. The nonsmooth term, on the other hand, brings the weighted soft-thresholding, contributing the enhancement of the filter sparsity. The weights are adaptively controlled according to the filter coefficients so that the softthresholding gives significant impacts solely to inactive coefficients (coefficients close to zero). The numerical example demonstrates the efficacy of the proposed algorithm.
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M3 - Conference contribution
AN - SCOPUS:79958127505
SP - 367
EP - 370
BT - APSIPA ASC 2010 - Asia-Pacific Signal and Information Processing Association Annual Summit and Conference
ER -