8 results
Search Results
2. Column-Wise Element Selection for Computationally Efficient Nonnegative Coupled Matrix Tensor Factorization.
- Author
-
Balasubramaniam, Thirunavukarasu, Nayak, Richi, Yuen, Chau, and Tian, Yu-Chu
- Subjects
- *
NONNEGATIVE matrices , *MATRIX decomposition , *ALGORITHMS , *LINEAR programming , *RECOMMENDER systems - Abstract
Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent patterns, prediction, and recommendation. However, due to the added complexity with coupling between tensor and matrix data, existing N-CMTF algorithms exhibit poor computation efficiency. In this paper, a computationally efficient N-CMTF factorization algorithm is presented based on the column-wise element selection, preventing frequent gradient updates. Theoretical and empirical analyses show that the proposed N-CMTF factorization algorithm is not only more accurate but also more computationally efficient than existing algorithms in approximating the tensor as well as in identifying the underlying nature of factors. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. ADMM Check Node Penalized Decoders for LDPC Codes.
- Author
-
Wei, Haoyuan and Banihashemi, Amir H.
- Subjects
- *
MONTE Carlo method , *ALGORITHMS , *LINEAR programming , *SIGNAL-to-noise ratio , *ERROR rates , *LOW density parity check codes , *DECODING algorithms - Abstract
Alternating direction method of multipliers (ADMM) is an efficient implementation of linear programming (LP) decoding for low-density parity-check (LDPC) codes. By adding penalty terms to the objective function of the LP decoding model, ADMM variable node (VN) penalized decoding can suppress the non-integral solutions and improve the frame error rate (FER) performance in the low signal-to-noise ratio (SNR) region. In this paper, we propose a novel ADMM check node (CN) penalized decoding algorithm. Codeword solutions which satisfy all parity-check equations will have smaller penalty values than non-codeword solutions, including the non-integral solutions. We discuss the required properties of CN-penalty functions, propose a few functions that satisfy those properties, and study their performance/complexity trade-offs. We also investigate the convergence properties of the proposed algorithm and prove that its performance is independent of the transmitted codeword. Using Monte Carlo simulations and instanton analysis, we then demonstrate that the proposed CN-penalized decoder outperforms ADMM VN penalized decoders in both waterfall and error floor regions. This comes at the expense of some increase in the decoding complexity. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
4. Distributed Resource Allocation Over Directed Graphs via Continuous-Time Algorithms.
- Author
-
Zhu, Yanan, Ren, Wei, Yu, Wenwu, and Wen, Guanghui
- Subjects
- *
RESOURCE allocation , *CONVEX sets , *ALGORITHMS , *SWARM intelligence , *CONVEX functions , *LINEAR programming , *DIRECTED graphs - Abstract
This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
5. The Estimation Performance of Nonlinear Least Squares for Phase Retrieval.
- Author
-
Huang, Meng and Xu, Zhiqiang
- Subjects
- *
NONLINEAR estimation , *ALACHLOR , *ALGORITHMS , *RANDOM matrices , *RANDOM variables - Abstract
Suppose that ${ { y}}= \lvert \text {A} { x}_{0}\rvert +\eta $ where ${ x}_{0}\in {\mathbb R} ^{{d}}$ is the target signal and $\eta \in {\mathbb R}^{{m}}$ is a noise vector. The aim of phase retrieval is to estimate ${x}_{0}$ from ${ { y}}$. A popular model for estimating ${ x}_{0}$ is the nonlinear least squares ${\widehat { {x}}}:={\mathrm{ argmin}}_{ x} \| \lvert \text {A} { x}\rvert - { { y}}\|_{2}$. One has already developed many efficient algorithms for solving the model, such as the seminal error reduction algorithm. In this paper, we present the estimation performance of the model with proving that $\| {\widehat { {x}}}- { x}_{0}\|\lesssim {\|\eta \|_{2}}/{\sqrt {{m}}}$ under the assumption of A being a Gaussian random matrix. We also prove the reconstruction error ${\|\eta \|_{2}}/{\sqrt {{m}}}$ is sharp. For the case where ${ x}_{0}$ is sparse, we study the estimation performance of both the nonlinear Lasso of phase retrieval and its unconstrained version. Our results are non-asymptotic, and we do not assume any distribution on the noise $\eta $. To the best of our knowledge, our results represent the first theoretical guarantee for the nonlinear least squares and for the nonlinear Lasso of phase retrieval. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
6. $\alpha$-Fair Power Allocation in Spectrum-Sharing Networks.
- Author
-
Guo, Chongtao, Zhang, Yan, Sheng, Min, Wang, Xijun, and Li, Yuzhou
- Subjects
- *
TELECOMMUNICATION spectrum , *SPECTRUM allocation , *CHANNEL spacing (Telecommunication) , *COGNITIVE radio , *ALGORITHMS - Abstract
To efficiently trade off system sum-rate and link fairness, this paper is dedicated to maximizing the sum of \alpha-fair utility in spectrum-sharing networks, where multiple interfering links share one channel. In the literature, three special cases, including \alpha=\mbox{0} (sum-rate maximization), \alpha=\mbox{1} (proportional fairness), and \alpha=\infty (max-min fairness), have been investigated; the complexity for cases \mbox{1} < \alpha < \infty and \mbox{0} < \alpha < \mbox{1} is still unknown. In this paper, we prove that the problem is convex when \mbox1 < \alpha < \infty and is NP-hard when \mbox0 < \alpha < \mbox1. To deal with the latter case, we transform the objective function and represent it by the difference of two concave functions (D.C.). Then, a power allocation algorithm is proposed with fast convergence to a local optimal point. Simulation results show that the proposed algorithm can obtain global optimality in two-link cases when \mbox0 < \alpha < \mbox1. In addition, we can get a flexible tradeoff between sum-rate and fairness in terms of Jain's index by adjusting $\alpha$. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
7. A Proximal Gradient Algorithm for Decentralized Composite Optimization.
- Author
-
Shi, Wei, Ling, Qing, Wu, Gang, and Yin, Wotao
- Subjects
- *
ALGORITHMS , *DIGITAL signal processing , *NONSMOOTH optimization , *QUADRATIC programming , *COMPRESSED sensing - Abstract
This paper proposes a decentralized algorithm for solving a consensus optimization problem defined in a static networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form. Examples of such problems include decentralized constrained quadratic programming and compressed sensing problems, as well as many regularization problems arising in inverse problems, signal processing, and machine learning, which have decentralized applications. This paper addresses the need for efficient decentralized algorithms that take advantages of proximal operations for the nonsmooth terms. We propose a proximal gradient exact first-order algorithm (PG-EXTRA) that utilizes the composite structure and has the best known convergence rate. It is a nontrivial extension to the recent algorithm EXTRA. At each iteration, each agent locally computes a gradient of the smooth part of its objective and a proximal map of the nonsmooth part, as well as exchanges information with its neighbors. The algorithm is “exact” in the sense that an exact consensus minimizer can be obtained with a fixed step size, whereas most previous methods must use diminishing step sizes. When the smooth part has Lipschitz gradients, PG-EXTRA has an ergodic convergence rate of O\left(1\over k\right) in terms of the first-order optimality residual. When the smooth part vanishes, PG-EXTRA reduces to P-EXTRA, an algorithm without the gradients (so no “G” in the name), which has a slightly improved convergence rate at o\left(1\over k\right) in a standard (non-ergodic) sense. Numerical experiments demonstrate effectiveness of PG-EXTRA and validate our convergence results [ABSTRACT FROM PUBLISHER]
- Published
- 2015
- Full Text
- View/download PDF
8. Sparse Learning with Stochastic Composite Optimization.
- Author
-
Zhang, Weizhong, Zhang, Lijun, Jin, Zhongming, Jin, Rong, Cai, Deng, Li, Xuelong, Liang, Ronghua, and He, Xiaofei
- Subjects
- *
EDUCATION , *MATHEMATICAL programming , *ALGORITHMS , *MATHEMATICAL optimization , *FIBERS - Abstract
In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate \mathcal O(1/\lambda T)
with $\delta$- Published
- 2017
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.