• The Korean Journal of Applied Statistics
• /
• v.28 no.2
• /
• pp.281-288
• /
• 2015

In this paper, we study an approximate procedure to evaluate a penalized maximum likelihood estimator (MLE) for a mixed effects model. The procedure approximates the Hessian matrix of the penalized MLE with a structured sparse matrix or an arrowhead type matrix to speed its computation. In this paper, we numerically investigate the gain in computation time as well as approximation error from the considered approximation procedure.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.12 no.6
• /
• pp.2806-2825
• /
• 2018

Unsupervised learning has shown good performance on image, video and audio classification tasks, and much progress has been made so far. It studies how systems can learn to represent particular input patterns in a way that reflects the statistical structure of the overall collection of input patterns. Many promising deep learning systems are commonly trained by the greedy layerwise unsupervised learning manner. The performance of these deep learning architectures benefits from the unsupervised learning ability to disentangling the abstractions and picking out the useful features. However, the existing unsupervised learning algorithms are often difficult to train partly because of the requirement of extensive hyperparameters. The tuning of these hyperparameters is a laborious task that requires expert knowledge, rules of thumb or extensive search. In this paper, we propose a simple and effective unsupervised feature learning algorithm for image classification, which exploits an explicit optimizing way for population and lifetime sparsity. Firstly, a sparse target matrix is built by the competitive rules. Then, the sparse features are optimized by means of minimizing the Euclidean norm ($L_2$) error between the sparse target and the competitive layer outputs. Finally, a classifier is trained using the obtained sparse features. Experimental results show that the proposed method achieves good performance for image classification, and provides discriminative features that generalize well.

• Journal of Korea Multimedia Society
• /
• v.20 no.2
• /
• pp.363-370
• /
• 2017

Data assimilation is an initializing method for air quality forecasting such as PM10. It is very important to enhance the forecasting accuracy. Optimal interpolation is one of the data assimilation techniques. It is very effective and widely used in air quality forecasting fields. The technique, however, requires too much memory space and long execution time. It makes the PM10 air quality forecasting difficult in real time. We propose a fast optimal interpolation data assimilation method for PM10 air quality forecasting using a new kernel tridiagonal sparse matrix and CUDA massively parallel processing architecture. Experimental results show the proposed method is 5~56 times faster than conventional ones.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.6
• /
• pp.2748-2766
• /
• 2016

Compared with traditional patch-based sparse representation, recent studies have concluded that group-based sparse representation (GSR) can simultaneously enforce the intrinsic local sparsity and nonlocal self-similarity of images within a unified framework. This article investigates an accelerated split Bregman method (SBM) that is based on GSR which exploits image compressive sensing (CS). The computational efficiency of accelerated SBM for the measurement matrix of a partial Fourier matrix can be further improved by the introduction of a fast Fourier transform (FFT) to derive the enhanced algorithm. In addition, we provide convergence analysis for the proposed method. Experimental results demonstrate that accelerated SBM is potentially faster than some existing image CS reconstruction methods.

• The KIPS Transactions:PartA
• /
• v.8A no.3
• /
• pp.227-234
• /
• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditiner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to $1025{\times}1024$. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications, The results show that Multi-Color Block SOR is scalabl and gives the best performances.

• Journal of Communications and Networks
• /
• v.15 no.4
• /
• pp.370-382
• /
• 2013

Distributed massive MIMO systems, which have high bandwidth efficiency and can accommodate a tremendous amount of traffic using algorithms such as zero-forcing beam forming (ZFBF), may be deployed in large public venues with the antennas mounted under-floor. In this case the channel gain matrix H can be modeled as a multi-banded matrix, in which off-diagonal entries decay both exponentially due to heavy human penetration loss and polynomially due to free space propagation loss. To enable practical implementation of such systems, we present a multi-banded matrix inversion algorithm that substantially reduces the complexity of ZFBF by keeping the most significant entries in H and the precoding matrix W. We introduce a parameter p to control the sparsity of H and W and thus achieve the tradeoff between the computational complexity and the system throughput. The proposed algorithm includes dense and sparse precoding versions, providing quadratic and linear complexity, respectively, relative to the number of antennas. We present analysis and numerical evaluations to show that the signal-to-interference ratio (SIR) increases linearly with p in dense precoding. In sparse precoding, we demonstrate the necessity of using directional antennas by both analysis and simulations. When the directional antenna gain increases, the resulting SIR increment in sparse precoding increases linearly with p, while the SIR of dense precoding is much less sensitive to changes in p.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.5 no.1
• /
• pp.85-100
• /
• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditioner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024 x 1024, and for an ill-conditioned matrix from the shell problem from the Harwell-Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR converges.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1131-1141
• /
• 2010

We develop an algorithm for computing a sparse approximate inverse for a nonsymmetric positive definite matrix based upon the FFAPINV algorithm. The sparse approximate inverse is computed in the factored form and used to work with some Krylov subspace methods. The preconditioner is breakdown free and, when used in conjunction with Krylov-subspace-based iterative solvers such as the GMRES algorithm, results in reliable solvers. Some numerical experiments are given to show the efficiency of the preconditioner.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.17 no.7
• /
• pp.739-748
• /
• 1992

A CGM iterative systolic algorithm to solve large sparse linear systems of equations is presented. For implementation of the algorithm, a systolic array using the stripe structure is proposed. The matrix A is decomposed into a strictly lower triangular matrix, a diagonal matrix, and a strictly up-per triangular matrix, and the two formers and the tatter· are concurrently computed by different linear arrays. Hence, the execution time of this approach Is reduced to half of the execution time of the that a linear array is used. computation of the Irregularly distributed sparse matrix can be executed effectively by using the stripe structure.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
• /
• v.10 no.5
• /
• pp.409-416
• /
• 2017

In this paper, we consider a framework of compressed sensing over finite fields. One measurement sample is obtained by an inner product of a row of a sensing matrix and a sparse signal vector. A recovery algorithm proposed in this study for sparse signals based probabilistic decoding is used to find a solution of compressed sensing. Until now compressed sensing theory has dealt with real-valued or complex-valued systems, but for the processing of the original real or complex signals, the loss of the information occurs from the discretization. The motivation of this work can be found in efforts to solve inverse problems for discrete signals. The framework proposed in this paper uses a parity-check matrix of low-density parity-check (LDPC) codes developed in coding theory as a sensing matrix. We develop a stochastic algorithm to reconstruct sparse signals over finite field. Unlike LDPC decoding, which is published in existing coding theory, we design an iterative algorithm using probability distribution of sparse signals. Through the proposed recovery algorithm, we achieve better reconstruction performance as the size of finite fields increases. Since the sensing matrix of compressed sensing shows good performance even in the low density matrix such as the parity-check matrix, it is expected to be actively used in applications considering discrete signals.