arXiv subjects

Tetsuya Sakurai

Publications and source records attributed to Tetsuya Sakurai.

At least 37 records · Page 2Linked to original sources

arXiv2022

A Particle-Based Algorithm for Distributional Optimization on \textit{Constrained Domains} via Variational Transport and Mirror Descent

We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and algorithmic design. Inspired by the mirror descent algorithm for constrained optimization, we propose an iterative particle-based algorithm, named Mirrored Variational Transport (mirrorVT), extended from the Variational Transport framework [7] for dealing with the constrained domain. In particular, for each iteration, mirrorVT maps particles to an unconstrained dual domain induced by a mirror map and then approximately perform Wasserstein gradient descent on the manifold of distributions defined over the dual space by pushing particles. At the end of iteration, particles are mapped back to the original constrained domain. Through simulated experiments, we demonstrate the effectiveness of mirrorVT for minimizing the functionals over probability distributions on the simplex- and Euclidean ball-constrained domains. We also analyze its theoretical properties and characterize its convergence to the global minimum of the objective functional.

math.OC↗

arXiv2022

Divide-and-conquer based Large-Scale Spectral Clustering

Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long time. In this paper, we propose a divide-and-conquer based large-scale spectral clustering method to strike a good balance between efficiency and effectiveness. In the proposed method, a divide-and-conquer based landmark selection algorithm and a novel approximate similarity matrix approach are designed to construct a sparse similarity matrix within low computational complexities. Then clustering results can be computed quickly through a bipartite graph partition process. The proposed method achieves a lower computational complexity than most existing large-scale spectral clustering methods. Experimental results on ten large-scale datasets have demonstrated the efficiency and effectiveness of the proposed method. The MATLAB code of the proposed method and experimental datasets are available at https://github.com/Li-Hongmin/MyPaperWithCode.

cs.LG↗

arXiv2021

Contour Integral-based Quantum Algorithm for Estimating Matrix Eigenvalue Density

The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given interval. Our quantum algorithm is based on a method that approximates the eigenvalue counts by applying the numerical contour integral and the stochastic trace estimator applied to a matrix involving resolvent matrices. As components of our algorithm, the HHL solver is applied to an augmented linear system of the resolvent matrices, and the quantum Fourier transform (QFT) is adopted to represent the operation of the numerical contour integral. To reduce the size of the augmented system, we exploit a certain symmetry of the numerical integration. We also introduce a permutation formed by CNOT gates to make the augmented system solution consistent with the QFT input. The eigenvalue count in a given interval is derived as the probability of observing a bit pattern in a fraction of the qubits of the output state.

quant-ph↗

arXiv2021

A Parallel Computing Method for the Higher Order Tensor Renormalization Group

In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a $d$-dimensional $( d \geq 2 )$ simple lattice model. Sequential computation of the HOTRG requires $O ( χ^{4 d - 1} )$ computational cost, where $χ$ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires $O ( χ^{2d} )$ memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to $χ^2$ processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of $d \geq 3$, computational cost in each process is reduced to $O ( χ^{4 d - 3} )$ and memory space requirement in each process is kept to be $O ( χ^{2d - 1} )$.

hep-lat↗

arXiv2021

Complex moment-based method with nonlinear transformation for computing large and sparse interior singular triplets

This paper considers computing interior singular triplets corresponding to the singular values in some interval. Based on the concept of the complex moment-based parallel eigensolvers, in this paper, we propose a novel complex moment-based method with a nonlinear transformation. We also analyse the error bounds of the proposed method and provide some practical techniques. Numerical experiments indicate that the proposed complex moment-based method with the nonlinear transformation computes accurate singular triplets for both exterior and interior problems within small computation time compared with existing methods.

math.NA↗

arXiv2021

Unsupervised learning-based structural analysis: Search for a characteristic low-dimensional space by local structures in atomistic simulations

Owing to the advances in computational techniques and the increase in computational power, atomistic simulations of materials can simulate large systems with higher accuracy. Complex phenomena can be observed in such state-of-the-art atomistic simulations. However, it has become increasingly difficult to understand what is actually happening and mechanisms, for example, in molecular dynamics (MD) simulations. We propose an unsupervised machine learning method to analyze the local structure around a target atom. The proposed method, which uses the two-step locality preserving projections (TS-LPP), can find a low-dimensional space wherein the distributions of datapoints for each atom or groups of atoms can be properly captured. We demonstrate that the method is effective for analyzing the MD simulations of crystalline, liquid, and amorphous states and the melt-quench process from the perspective of local structures. The proposed method is demonstrated on a silicon single-component system, a silicon-germanium binary system, and a copper single-component system.

cond-mat.mtrl-sci↗

arXiv2021

LSEC: Large-scale spectral ensemble clustering

Ensemble clustering is a fundamental problem in the machine learning field, combining multiple base clusterings into a better clustering result. However, most of the existing methods are unsuitable for large-scale ensemble clustering tasks due to the efficiency bottleneck. In this paper, we propose a large-scale spectral ensemble clustering (LSEC) method to strike a good balance between efficiency and effectiveness. In LSEC, a large-scale spectral clustering based efficient ensemble generation framework is designed to generate various base clusterings within a low computational complexity. Then all based clustering are combined through a bipartite graph partition based consensus function into a better consensus clustering result. The LSEC method achieves a lower computational complexity than most existing ensemble clustering methods. Experiments conducted on ten large-scale datasets show the efficiency and effectiveness of the LSEC method. The MATLAB code of the proposed method and experimental datasets are available at https://github.com/Li- Hongmin/MyPaperWithCode.

cs.LG↗

arXiv2021

Accuracy and Privacy Evaluations of Collaborative Data Analysis

Distributed data analysis without revealing the individual data has recently attracted significant attention in several applications. A collaborative data analysis through sharing dimensionality reduced representations of data has been proposed as a non-model sharing-type federated learning. This paper analyzes the accuracy and privacy evaluations of this novel framework. In the accuracy analysis, we provided sufficient conditions for the equivalence of the collaborative data analysis and the centralized analysis with dimensionality reduction. In the privacy analysis, we proved that collaborative users' private datasets are protected with a double privacy layer against insider and external attacking scenarios.

cs.LG↗

arXiv2020

Federated Learning System without Model Sharing through Integration of Dimensional Reduced Data Representations

Dimensionality Reduction is a commonly used element in a machine learning pipeline that helps to extract important features from high-dimensional data. In this work, we explore an alternative federated learning system that enables integration of dimensionality reduced representations of distributed data prior to a supervised learning task, thus avoiding model sharing among the parties. We compare the performance of this approach on image classification tasks to three alternative frameworks: centralized machine learning, individual machine learning, and Federated Averaging, and analyze potential use cases for a federated learning system without model sharing. Our results show that our approach can achieve similar accuracy as Federated Averaging and performs better than Federated Averaging in a small-user setting.

cs.LG↗

arXiv2020

Interpretable collaborative data analysis on distributed data

This paper proposes an interpretable non-model sharing collaborative data analysis method as one of the federated learning systems, which is an emerging technology to analyze distributed data. Analyzing distributed data is essential in many applications such as medical, financial, and manufacturing data analyses due to privacy, and confidentiality concerns. In addition, interpretability of the obtained model has an important role for practical applications of the federated learning systems. By centralizing intermediate representations, which are individually constructed in each party, the proposed method obtains an interpretable model, achieving a collaborative analysis without revealing the individual data and learning model distributed over local parties. Numerical experiments indicate that the proposed method achieves better recognition performance for artificial and real-world problems than individual analysis.

cs.LG↗

arXiv2020

Flexible subspace iteration with moments for an effective contour integration-based eigensolver

Contour integration schemes are a valuable tool for the solution of difficult interior eigenvalue problems. However, the solution of many large linear systems with multiple right hand sides may prove a prohibitive computational expense. The number of right hand sides, and thus, computational cost may be reduced if the projected subspace is created using multiple moments. In this work, we explore heuristics for the choice and application of moments with respect to various other important parameters in a contour integration scheme. We provide evidence for the expected performance, accuracy, and robustness of various schemes, showing that good heuristic choices can provide a scheme featuring good properties in all three of these measures.

math.NA↗

arXiv2019

A Parallel Computing Method for the Coupled-Cluster Singles and Doubles

In this paper, we present a parallel computing method for the coupled-cluster singles and doubles (CCSD) in periodic systems. The CCSD in periodic systems solves simultaneous equations for single-excitation and double-excitation amplitudes. In the simultaneous equations for double-excitation amplitudes, each equations are characterized by four spin orbitals and three independent momentums of electrons. One of key ideas of our method is to use process numbers in parallel computing to identify two indices which represent momentum of an electron. When momentum of an electron takes $N_{\bm{k}}$ values, $N_{\bm{k}}^2$ processes are prepared in our method. Such parallel distribution processing and way of distribution of known quantities in the simultaneous equations reduces orders of computational cost and required memory scales by $N_{\bm{k}}^2$ compared with a sequential method. In implementation of out method, communication between processes in parallel computing appears in the outmost loop in a nested loop but does not appear inner nested loop.

cond-mat.str-el↗

arXiv2019

Multiclass spectral feature scaling method for dimensionality reduction

Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space. The proposed method exploits spectral clustering to derive scaling factors that are used to modify the features. Specifically, we reformulate the Laplacian eigenproblem of the spectral clustering as an eigenproblem of a linear matrix pencil whose eigenvector has the scaling factors. Numerical experiments show that the proposed method outperforms well-established supervised dimensionality reduction methods for toy problems with more samples than features and real-world problems with more features than samples.

cs.LG↗

arXiv2019

Data collaboration analysis for distributed datasets

In this paper, we propose a data collaboration analysis method for distributed datasets. The proposed method is a centralized machine learning while training datasets and models remain distributed over some institutions. Recently, data became large and distributed with decreasing costs of data collection. If we can centralize these distributed datasets and analyse them as one dataset, we expect to obtain novel insight and achieve a higher prediction performance compared with individual analyses on each distributed dataset. However, it is generally difficult to centralize the original datasets due to their huge data size or regarding a privacy-preserving problem. To avoid these difficulties, we propose a data collaboration analysis method for distributed datasets without sharing the original datasets. The proposed method centralizes only intermediate representation constructed individually instead of the original dataset.

cs.LG↗

arXiv2018

Classification of X-Ray Protein Crystallization Using Deep Convolutional Neural Networks with a Finder Module

Recently, deep convolutional neural networks have shown good results for image recognition. In this paper, we use convolutional neural networks with a finder module, which discovers the important region for recognition and extracts that region. We propose applying our method to the recognition of protein crystals for X-ray structural analysis. In this analysis, it is necessary to recognize states of protein crystallization from a large number of images. There are several methods that realize protein crystallization recognition by using convolutional neural networks. In each method, large-scale data sets are required to recognize with high accuracy. In our data set, the number of images is not good enough for training CNN. The amount of data for CNN is a serious issue in various fields. Our method realizes high accuracy recognition with few images by discovering the region where the crystallization drop exists. We compared our crystallization image recognition method with a high precision method using Inception-V3. We demonstrate that our method is effective for crystallization images using several experiments. Our method gained the AUC value that is about 5% higher than the compared method.

cs.CV↗

arXiv2018

Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.

physics.comp-ph↗

arXiv2018

Spectral feature scaling method for supervised dimensionality reduction

Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of the data. Thus, we consider aggressively modifying the scales of the features to obtain the desired classification. Using prior knowledge on the labels of partial samples to specify the Fiedler vector, we formulate an eigenvalue problem of a linear matrix pencil whose eigenvector has the feature scaling factors. The resulting factors can modify the features of entire samples to form clusters in the reduced space, according to the known labels. In this study, we propose new dimensionality reduction methods supervised using the feature scaling associated with the spectral clustering. Numerical experiments show that the proposed methods outperform well-established supervised methods for toy problems with more samples than features, and are more robust regarding clustering than existing methods. Also, the proposed methods outperform existing methods regarding classification for real-world problems with more features than samples of gene expression profiles of cancer diseases. Furthermore, the feature scaling tends to improve the clustering and classification accuracies of existing unsupervised methods, as the proportion of training data increases.

stat.ML↗

arXiv2018

Efficient and Scalable Calculation of Complex Band Structure using Sakurai-Sugiura Method

Complex band structures (CBSs) are useful to characterize the static and dynamical electronic properties of materials. Despite the intensive developments, the first-principles calculation of CBS for over several hundred atoms is still computationally demanding. We here propose an efficient and scalable computational method to calculate CBSs. The basic idea is to express the Kohn-Sham equation of the real-space grid scheme as a quadratic eigenvalue problem and compute only the solutions which are necessary to construct the CBS by Sakurai-Sugiura method. The serial performance of the proposed method shows a significant advantage in both runtime and memory usage compared to the conventional method. Furthermore, owing to the hierarchical parallelism in Sakurai-Sugiura method and the domain-decomposition technique for real-space grids, we can achieve an excellent scalability in the CBS calculation of a boron and nitrogen doped carbon nanotube consisting of more than 10,000 atoms using 2,048 nodes (139,264 cores) of Oakforest-PACS.

cond-mat.mtrl-sci↗