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Non-negative low-rank and group-sparse matrix factorization 21

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Non-negative low-rank and group-sparse matrix factorization

21st International Conference on MultiMedia Modeling, MMM 2015

作者： Wu, Shuyi Zhang, Xiang Guan, Naiyang Tao, Dacheng Huang, Xuhui Luo, Zhigang Science and Technology on Parallel Distributed Processing Laboratory College of Computer National University of Defense Technology Changsha Hunan410073 China Department of Computer Science and Technology College of Computer National University of Defense Technology Changsha Hunan410073 China Centre for Quantum Computation & Intelligent Systems and the Faculty of Engineering and Information Technology University of Technology Sydney 235 Jones Street UltimoNSW2007 Australia

ISBN: (纸本)9783319144412

Non-negative matrix factorization (NMF) has been a popular data analysis tool and has been widely applied in computer vision. However, conventional NMF methods cannot adaptively learn grouping structure froma *** paper proposes a non-negative low-rank and group-sparse matrix factorization (NLRGS) method to overcome this deficiency. Particularly, NLRGS captures the relationships among examples by constraining rank of the coefficients meanwhile identifies the grouping structure via group sparsity regularization. By both constraints, NLRGS boosts NMF in both classification and clustering. However, NLRGS is difficult to be optimized because it needs to deal with the low-rank constraint. To relax such hard constraint, we approximate the low-rank constraint with the nuclear norm and then develop an optimization algorithm for NLRGS in the frame of augmented Lagrangian method(ALM). Experimental results of both face recognition and clustering on four popular face datasets demonstrate the effectiveness of NLRGS in quantities. © Springer International Publishing Switzerland 2015.

关键词： Non-negative matrix factorization

Strong form mesh-free hp-adaptive solution of linear elasticity problem

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arXiv 2022年

作者： Jančič, Mitja Kosec, Gregor Parallel and Distributed Systems Laboratory Institute Jožef Stefan Jamova Cesta 39 Ljubljana1000 Slovenia Jožef Stefan International Postgraduate School Jamova Cesta 39 Ljubljana1000 Slovenia

We present an algorithm for hp-adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve–estimate–mark–refine paradigm. The solve phase relies on the Radial Basis Function-generated Finite Differences (RBF-FD) using point clouds generated by advancing front node positioning algorithm that supports variable node density. In the estimate phase, we introduce an Implicit-Explicit (IMEX) error indicator, which assumes that the error relates to the difference between the implicitly obtained solution (from the solve phase) and a local explicit re-evaluation of the PDE at hand using a higher order approximation. Based on the IMEX error indicator, the modified Texas Three Step marking strategy is used to mark the computational nodes for h-, p- or hp-(de-)refinement. Finally, in the refine phase, nodes are repositioned and the order of the method is locally redefined using the variable order of the augmenting monomials according to the instructions from the mark phase. The performance of the introduced hp-adaptive method is first investigated on a two-dimensional Peak problem and further applied to two- and three-dimensional contact problems. We show that the proposed IMEX error indicator adequately captures the global behaviour of the error in all cases considered and that the proposed hp-adaptive solution procedure significantly outperforms the non-adaptive approach. The proposed hp-adaptive method stands for another important step towards a fully autonomous numerical method capable of solving complex problems in realistic geometries without the need for user intervention. Copyright © 2022, The Authors. All rights reserved.

关键词： Errors

Hyperviscosity stabilisation of the RBF-FD solution to natural convection

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arXiv 2024年

作者： Vaupotič, Žiga Rot, Miha Kosec, Gregor Parallel and Distributed Systems Laboratory Jožef Stefan Institute Jamova Cesta 39 Ljubljana1000 Slovenia Jožef Stefan International Postgraduate School Jamova Cesta 39 Ljubljana1000 Slovenia

The numerical stability of fluid flow is an important topic in computational fluid dynamics as fluid flow simulations usually become numerically unstable in the turbulent regime. Many mesh-based methods have already established numerical dissipation procedures that dampen the effects of the unstable advection term. When it comes to meshless methods, the prominent stabilisation scheme is hyperviscosity. It introduces numerical dissipation in the form of a higher-order Laplacian operator. Many papers have already discussed the general effects of hyperviscosity and its parameters. However, hyperviscosity in flow problems has not yet been analyzed in depth. In this paper, we discuss the effects of hyperviscosity on natural convection flow problems as we approach the turbulent regime. © 2024, CC BY.

关键词： Stabilization

Spatially dependent node regularity in meshless approximation of partial differential equations

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arXiv 2024年

作者： Rot, Miha Jančič, Mitja Kosec, Gregor International Postgraduate School Jožef Stefan Jamova Cesta 39 Ljubljana1000 Slovenia Institute Jožef Stefan Parallel and Distributed Systems Laboratory Jamova cesta 39 Ljubljana1000 Slovenia

In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with scattered nodes, only regions with geometric details are covered with scattered nodes, while the rest of the domain is discretized with regular nodes. A simpler approximation can be used in regions covered by regular nodes, effectively reducing the required stencil size and computational cost compared to the approximation on scattered nodes where a set of polyharmonic splines is added to ensure convergent behaviour. This paper is an extended version of conference paper entitled "Spatially-varying meshless approximation method for enhanced computational efficiency" [1] presented at "International Conference on Computational Science (ICCS) 2023". The paper is extended with discussion on development and implementation of a hybrid regular-scattered node positioning algorithm (HyNP). The performance of the proposed HyNP algorithm is analysed in terms of separation distance and maximal empty sphere radius. Furthermore, it is demonstrated that HyNP nodes can be used for solving problems from fluid flow and linear elasticity, both in 2D and 3D, using meshless methods. The extension also provides additional analyses of computational efficiency and accuracy of the numerical solution obtained on the spatially-variable regularity of discretization nodes. In particular, different levels of refinement aggressiveness and scattered layer widths are considered to exploit the computational efficiency gains offered by such solution procedure. © 2024, CC BY.

关键词： Navier Stokes equations

A hybrid RBF-FD and WLS mesh-free strong-form approximation method

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arXiv 2022年

作者： Jančič, Mitja Kosec, Gregor "Jožef Stefan" Institute Parallel Distributed Systems Laboratory Jamova cesta 39 Ljubljana1000 Slovenia "Jožef Stefan" International Postgraduate School Jamova cesta 39 Ljubljana1000 Slovenia

Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local mesh-free strong-form method that combines the stability of Radial Basis Function-Generated Finite Differences (RBF-FD) with the computational effectiveness of Diffuse Approximation Method (DAM), forming a so-called hybrid method. To demonstrate the advantages of a hybrid method, we evaluate its computational complexity and accuracy of the obtained numerical solution by solving a two-dimensional Poisson problem with an exponentially strong source in the computational domain. Finally, we employ the hybrid method to solve a three-dimensional Boussinesq’s problem on an isotropic half-space and show that the implementation overhead can be justified. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite difference method

P-refined RBF-FD solution of a Poisson problem

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arXiv 2021年

作者： Jančič, Mitja Slak, Jure Kosec, Gregor Jožef Stefan International Postgraduate School Jamova cesta 39 Ljubljana1000 Slovenia Jožef Stefan Institute Parallel and Distributed Systems Laboratory Jamova cesta 39 Ljubljana1000 Slovenia

Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined. In this work, we employ RBF-FD approximation method with polyharmonic splines augmented with monomials and study the numerical properties of p-refined solutions, such as convergence orders and execution time. To fully exploit the refinement advantages, the numerical performance is studied on a Poisson problem with a strong source within the domain. Copyright © 2021, The Authors. All rights reserved.

关键词： Radial basis function networks

sNPU: Trusted Execution Environments on Integrated NPUs

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sNPU: Trusted Execution Environments on Integrated NPUs

Annual International Symposium on Computer Architecture, ISCA

作者： Erhu Feng Dahu Feng Dong Du Yubin Xia Haibo Chen Institute of Parallel and Distributed Systems SEIEE Shanghai Jiao Tong University Department of Precision Instrument Tsinghua University Engineering Research Center for Domain-specific Operating Systems Ministry of Education China Key Laboratory of System Software (Chinese Academy of Sciences)

ISBN: (数字)9798350326581

ISBN: (纸本)9798350326598

Trusted execution environment (TEE) promises strong security guarantee with hardware extensions for security-sensitive tasks. Due to its numerous benefits, TEE has gained widespread adoption, and extended from CPU-only TEEs to FPGA and GPU TEE systems. However, existing TEE systems exhibit inadequate and inefficient support for an emerging (and significant) processing unit, NPU. For instance, commercial TEE systems resort to coarse-grained and static protection approaches for NPUs, resulting in notable performance degradation (10%–20%), limited (or no) multitasking capabilities, and suboptimal resource utilization. In this paper, we present a secure NPU architecture, known as sNPU, which aims to mitigate vulnerabilities inherent to the design of NPU architectures. First, sNPU proposes NPU Guarder to enhance the NPU’s access control. Second, sNPU defines new attack surfaces leveraging in-NPU structures like scratchpad and NoC, and designs NPU Isolator to guarantee the isolation of scratchpad and NoC routing. Third, our system introduces a trusted software module called NPU Monitor to minimize the software TCB. Our prototype, evaluated on FPGA, demonstrates that sNPU significantly mitigates the runtime costs associated with security checking (from upto 20% to 0%) while incurring less than 1% resource costs.

关键词： Costs Runtime Prototypes Computer architecture Routing Software Resource management

On the potential of NoC virtualization for multicore chips

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Scalable Computing 2008年第3期9卷 165-177页

作者： Flich, J. Rodrigo, S. Duato, J. Sødring, T. Solheim, A.G. Skeie, T. Lysne, O. Parallel Architectures Group Technical University of Valencia Spain Networks and Distributed Systems Department Simula Research Laboratory University College Oslo Norway Department of Journalism Library and Information Science University College Oslo Norway Department of Informatics University of Oslo Norway

As the end of Moores-law is on the horizon, power becomes a limiting factor to continuous increases in performance gains for single-core processors. Processor engineers have shifted to the multicore paradigm and many-core processors are a reality. Within the context of these multicore chips, three key metrics point themselves out as being of major importance, performance, fault-tolerance (including yield), and power consumption. A solution that optimizes all three of these metrics is challenging. As the number of cores increases the importance of the interconnection network-on-chip (NoC) grows as well, and chip designers should aim to optimize these three key metrics in the NoC context as well. In this paper we identify and discuss the main properties that a NoC must exhibit in order to enable such optimizations. In particular, we propose the use of virtualization techniques at the NoC level. As a major finding, we identify the implementation of unicast and broadcast routing algorithms to become a key design parameter in order to achieve an effective virtualization of the chip. The intention behind this paper is for it to serve as a position paper on the topic of virtualization for NoC and the challenges that should be met at the routing layer in order to optimize performance, fault-tolerance and power consumption in multicore chips. © 2008 SCPE.

关键词： Network-on-chip

Quantization improvements for LU Decomposition to Solve Linear Equations *

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Quantization improvements for LU Decomposition to Solve Line...

IEEE International Conference on Big Data and Cloud Computing (BdCloud)

作者： Lin Chen Kang He Hao Jiang Roberto Barrio Jie Liu Tiejun Li Science and Technology on Parallel and Distributed Processing Laboratory Laboratory of Software Engineering for Complex Systems National University of Defense Technology Changsha China College of Computer Science and Technology National University of Defense Technology Changsha China University of Zaragoza Zaragoza Spain

Quantization is an effective method for compressing Deep Neural Networks. Now, it is considered to accelerate the traditional HPC applications. In this article, we present a quantization method (q8gemm) using integer 8-bits(INT8) for matrix multiplication, which is implemented by block techniques to overcome the overflow problem. We choose different scales for one matrix’s each row and those for the other matrix’s each column to keep the numbers in range. With the intel advanced matrix extension cblas_gemm_s8u8s32, our q8gemm can accelerate panel-matrix multiplication in LU factorization. Furthermore, we propose a new mixed-precision solver (q8gesv 1 ) for the linear equations. Using q8gemm in INT8, q8gesv modifies LU factorization in FP32 and then utilizes GMRES iterative refinement in FP64 to bring the solution back to 64 bits accuracy. Numerical tests show that on two Intel CPU platforms with avx2 and avx512, q8gemm achieves a speedup of 1.313-1.621 over cblas_sgemm of MKL. The execution time of cblas_gemm_s8u8s32 makes up 86.78%-90.85% of the q8gemm. By means of q8gemm, our q8gesv can achieve a speedup of 1.176-1.493 over the optimized Higham’s mixed-precision algorithm utilized in the HPL-AI benchmark and a speedup of 1.1-1.459 over the LAPACKE_dsgesv function from MKL LAPACK. Meanwhile, q8gesv runs up to 2.859X faster on Intel(R) Core(TM) i5-10600KF and to 2.224X faster on Intel(R) Xeon(R) Gold 6130 than the LAPACKE_dgesv function from MKL LAPACK.

关键词： Deep learning Gold Quantization (signal) Benchmark testing