Relevant bibliographies by topics / Active subspace

Academic literature on the topic 'Active subspace'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Active subspace"

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Holodnak, John T., Ilse C. F. Ipsen, and Ralph C. Smith. "A Probabilistic Subspace Bound with Application to Active Subspaces." SIAM Journal on Matrix Analysis and Applications 39, no. 3 (January 2018): 1208–20. http://dx.doi.org/10.1137/17m1141503.

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Xie, Ziqi, and Lihong Wang. "Active Block Diagonal Subspace Clustering." IEEE Access 9 (2021): 83976–92. http://dx.doi.org/10.1109/access.2021.3087575.

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Yu, Yu Min. "The Characteristics of Affine Bivariate Pseudoframes of Subspace Associated with a Bivariate Filter Functions." Key Engineering Materials 439-440 (June 2010): 926–31. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.926.

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Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.
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Li, Changsheng, Kaihang Mao, Lingyan Liang, Dongchun Ren, Wei Zhang, Ye Yuan, and Guoren Wang. "Unsupervised Active Learning via Subspace Learning." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (May 18, 2021): 8332–39. http://dx.doi.org/10.1609/aaai.v35i9.17013.

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Unsupervised active learning has been an active research topic in machine learning community, with the purpose of choosing representative samples to be labelled in an unsupervised manner. Previous works usually take the minimization of data reconstruction loss as the criterion to select representative samples which can better approximate original inputs. However, data are often drawn from low-dimensional subspaces embedded in an arbitrary high-dimensional space in many scenarios, thus it might severely bring in noise if attempting to precisely reconstruct all entries of one observation, leading to a suboptimal solution. In view of this, this paper proposes a novel unsupervised Active Learning model via Subspace Learning, called ALSL. In contrast to previous approaches, ALSL aims to discovery the low-rank structures of data, and then perform sample selection based on learnt low-rank representations. To this end, we devise two different strategies and propose two corresponding formulations to perform unsupervised active learning with and under low-rank sample representations respectively. Since the proposed formulations involve several non-smooth regularization terms, we develop a simple but effective optimization procedure to solve them. Extensive experiments are performed on five publicly available datasets, and experimental results demonstrate the proposed first formulation achieves comparable performance with the state-of-the-arts, while the second formulation significantly outperforms them, achieving a 13\% improvement over the second best baseline at most.
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Xu, Yong Fan. "Study of Matrix Multipliers for Normalized Frame Multi-Wavelets and Applications in Engineering Material Technology." Advanced Materials Research 753-755 (August 2013): 2321–24. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.2321.

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Frame theory has been the focus of active research for twenty years, both in theory and applications. Matrix Fourier multipliers send every orthonoamal wavelet to an orthonoamal wavelet. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.
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Erdal, Daniel, and Olaf A. Cirpka. "Global sensitivity analysis and adaptive stochastic sampling of a subsurface-flow model using active subspaces." Hydrology and Earth System Sciences 23, no. 9 (September 18, 2019): 3787–805. http://dx.doi.org/10.5194/hess-23-3787-2019.

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Abstract. Integrated hydrological modeling of domains with complex subsurface features requires many highly uncertain parameters. Performing a global uncertainty analysis using an ensemble of model runs can help bring clarity as to which of these parameters really influence system behavior and for which high parameter uncertainty does not result in similarly high uncertainty of model predictions. However, already creating a sufficiently large ensemble of model simulation for the global sensitivity analysis can be challenging, as many combinations of model parameters can lead to unrealistic model behavior. In this work we use the method of active subspaces to perform a global sensitivity analysis. While building up the ensemble, we use the already-existing ensemble members to construct low-order meta-models based on the first two active-subspace dimensions. The meta-models are used to pre-determine whether a random parameter combination in the stochastic sampling is likely to result in unrealistic behavior so that such a parameter combination is excluded without running the computationally expensive full model. An important reason for choosing the active-subspace method is that both the activity score of the global sensitivity analysis and the meta-models can easily be understood and visualized. We test the approach on a subsurface-flow model including uncertain hydraulic parameters, uncertain boundary conditions and uncertain geological structure. We show that sufficiently detailed active subspaces exist for most observations of interest. The pre-selection by the meta-model significantly reduces the number of full-model runs that must be rejected due to unrealistic behavior. An essential but difficult part in active-subspace sampling using complex models is approximating the gradient of the simulated observation with respect to all parameters. We show that this can effectively and meaningfully be done with second-order polynomials.
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Liu, Yanbei, Kaihua Liu, Changqing Zhang, Xiao Wang, Shaona Wang, and Zhitao Xiao. "Entropy-based active sparse subspace clustering." Multimedia Tools and Applications 77, no. 17 (April 20, 2018): 22281–97. http://dx.doi.org/10.1007/s11042-018-5945-1.

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Seshadri, P., S. Yuchi, G. T. Parks, and S. Shahpar. "Supporting multi-point fan design with dimension reduction." Aeronautical Journal 124, no. 1279 (July 27, 2020): 1371–98. http://dx.doi.org/10.1017/aer.2020.50.

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AbstractMotivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades—under the same parametrisation—largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection—a non-linear least-squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.
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Liu, Guangcan, and Shuicheng Yan. "Active Subspace: Toward Scalable Low-Rank Learning." Neural Computation 24, no. 12 (December 2012): 3371–94. http://dx.doi.org/10.1162/neco_a_00369.

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We address the scalability issues in low-rank matrix learning problems. Usually these problems resort to solving nuclear norm regularized optimization problems (NNROPs), which often suffer from high computational complexities if based on existing solvers, especially in large-scale settings. Based on the fact that the optimal solution matrix to an NNROP is often low rank, we revisit the classic mechanism of low-rank matrix factorization, based on which we present an active subspace algorithm for efficiently solving NNROPs by transforming large-scale NNROPs into small-scale problems. The transformation is achieved by factorizing the large solution matrix into the product of a small orthonormal matrix (active subspace) and another small matrix. Although such a transformation generally leads to nonconvex problems, we show that a suboptimal solution can be found by the augmented Lagrange alternating direction method. For the robust PCA (RPCA) (Candès, Li, Ma, & Wright, 2009 ) problem, a typical example of NNROPs, theoretical results verify the suboptimality of the solution produced by our algorithm. For the general NNROPs, we empirically show that our algorithm significantly reduces the computational complexity without loss of optimality.
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N., Navaneeth, and Souvik Chakraborty. "Surrogate assisted active subspace and active subspace assisted surrogate—A new paradigm for high dimensional structural reliability analysis." Computer Methods in Applied Mechanics and Engineering 389 (February 2022): 114374. http://dx.doi.org/10.1016/j.cma.2021.114374.

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Dissertations / Theses on the topic "Active subspace"

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Zhu, Weizhong Allen Robert B. "Text clustering and active learning using a LSI subspace signature model and query expansion /." Philadelphia, Pa. : Drexel University, 2009. http://hdl.handle.net/1860/3077.

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Nijsse, Gerard. "A subspace based approach to the design, implementation and validation of algorithms for active vibration isolation control." Enschede : University of Twente [Host], 2006. http://doc.utwente.nl/51108.

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Onder, Murat. "Face Detection And Active Robot Vision." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/2/12605290/index.pdf.

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The main task in this thesis is to design a robot vision system with face detection and tracking capability. Hence there are two main works in the thesis: Firstly, the detection of the face on an image that is taken from the camera on the robot must be achieved. Hence this is a serious real time image processing task and time constraints are very important because of this reason. A processing rate of 1 frame/second is tried to be achieved and hence a fast face detection algorithm had to be used. The Eigenface method and the Subspace LDA (Linear Discriminant Analysis) method are implemented, tested and compared for face detection and Eigenface method proposed by Turk and Pentland is decided to be used. The images are first passed through a number of preprocessing algorithms to obtain better performance, like skin detection, histogram equalization etc. After this filtering process the face candidate regions are put through the face detection algorithm to understand whether there is a face or not in the image. Some modifications are applied to the eigenface algorithm to detect the faces better and faster. Secondly, the robot must move towards the face in the image. This task includes robot motion. The robot to be used for this purpose is a Pioneer 2-DX8 Plus, which is a product of ActivMedia Robotics Inc. and only the interfaces to move the robot have been implemented in the thesis software. The robot is to detect the faces at different distances and arrange its position according to the distance of the human to the robot. Hence a scaling mechanism must be used either in the training images, or in the input image taken from the camera. Because of timing constraint and low camera resolution, a limited number of scaling is applied in the face detection process. With this reason faces of people who are very far or very close to the robot will not be detected. A background independent face detection system is tried to be designed. However the resultant algorithm is slightly dependent to the background. There is no any other constraints in the system.
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Aguiar, Izabel Pirimai. "Dynamic Active Subspaces| A Data-driven Approach to Computing Time-dependent Active Subspaces in Dynamical Systems." Thesis, University of Colorado at Boulder, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10826096.

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Computational models are aiding in the advancement of science – from biological, to engineering, to social systems. To trust the predictions of computational models, however, we must understand how the errors in the models’ inputs (i.e., through measurement error) affect the output of the systems: we must quantify the uncertainty that results from these input errors. Uncertainty quantification (UQ) becomes computationally complex when there are many parameters in the model. In such cases it is useful to reduce the dimension of the problem by identifying unimportant parameters and disregarding them for UQ studies. This makes an otherwise intractable UQ problem tractable. Active subspaces extend this idea by identifying important linear combinations of parameters, enabling more powerful and effective dimension reduction. Although active subspaces give model insight and computational tractability for scalar-valued functions, it is not enough. This analysis does not extend to time-dependent systems. In this thesis we discuss time-dependent, dynamic active subspaces. We develop a methodology by which to compute and approximate dynamic active subspaces, and introduce the analytical form of dynamic active subspaces for two cases. To highlight these methods we find dynamic active subspaces for a linear harmonic oscillator and a nonlinear enzyme kinetics system.

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Lund, Kathryn. "A new block Krylov subspace framework with applications to functions of matrices acting on multiple vectors." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/493337.

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Mathematics
Ph.D.
We propose a new framework for understanding block Krylov subspace methods, which hinges on a matrix-valued inner product. We can recast the ``classical" block Krylov methods, such as O'Leary's block conjugate gradients, global methods, and loop-interchange methods, within this framework. Leveraging the generality of the framework, we develop an efficient restart procedure and error bounds for the shifted block full orthogonalization method (Sh-BFOM(m)). Regarding BFOM as the prototypical block Krylov subspace method, we propose another formalism, which we call modified BFOM, and show that block GMRES and the new block Radau-Lanczos method can be regarded as modified BFOM. In analogy to Sh-BFOM(m), we develop an efficient restart procedure for shifted BGMRES with restarts (Sh-BGMRES(m)), as well as error bounds. Using this framework and shifted block Krylov methods with restarts as a foundation, we formulate block Krylov subspace methods with restarts for matrix functions acting on multiple vectors f(A)B. We obtain convergence bounds for \bfomfom (BFOM for Functions Of Matrices) and block harmonic methods (i.e., BGMRES-like methods) for matrix functions. With various numerical examples, we illustrate our theoretical results on Sh-BFOM and Sh-BGMRES. We also analyze the matrix polynomials associated to the residuals of these methods. Through a variety of real-life applications, we demonstrate the robustness and versatility of B(FOM)^2 and block harmonic methods for matrix functions. A particularly interesting example is the tensor t-function, our proposed definition for the function of a tensor in the tensor t-product formalism. Despite the lack of convergence theory, we also show that the block Radau-Lanczos modification can reduce the number of cycles required to converge for both linear systems and matrix functions.
Temple University--Theses
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Teixeira, Parente Mario Manuel [Verfasser], Barbara [Akademischer Betreuer] Wohlmuth, Barbara [Gutachter] Wohlmuth, and Krzysztof [Gutachter] Podgórski. "Active Subspaces in Bayesian Inverse Problems / Mario Manuel Teixeira Parente ; Gutachter: Barbara Wohlmuth, Krzysztof Podgórski ; Betreuer: Barbara Wohlmuth." München : Universitätsbibliothek der TU München, 2020. http://d-nb.info/1220319333/34.

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Lund, Kathryn [Verfasser]. "A new block Krylov subspace framework with applications to functions of matrices acting on multiple vectors / Kathryn Lund." Wuppertal : Universitätsbibliothek Wuppertal, 2018. http://d-nb.info/1164098926/34.

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Xue, Cheng. "Improve the Active Subspace Method by Partitioning the Parameter Space." Master's thesis, 2018. http://hdl.handle.net/1885/173619.

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The active subspace method is a powerful tool that can be applied in many fields such as uncertainty quantification, inverse problems and optimisation. However, the standard active subspace method constructs an active subspace over the whole parameter space, which makes the method only applicable to functions that have ridge or near-ridge structures in other words, it only works for a function f such that f (x) g(WTx), where x is an mdimensional parameter space and W is m n, n < m. In this thesis, we propose two families of algorithms that use Voronoi diagrams to (randomly and adaptively) partition the input space and hence construct an active subspace for each region. Our proposed methods work on functions that have local ridges from region to region. Based on the four test functions that we employed in this thesis, we find that our proposed algorithms produce more accurate response surfaces than those generated by the standard active subspace method. To evaluate the accuracy, we test the response surfaces with a separate test set of points and calculate their mean squared error for each response surface. Our proposed algorithms achieve a lower MSE than the active subspace method.We also introduce a new algorithm that may work for more general functions.
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(8734437), Rohit Tripathy. "Surrogate Modeling for Uncertainty Quantification in systems Characterized by expensive and high-dimensional numerical simulators." Thesis, 2020.

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Physical phenomena in nature are typically represented by complex systems of ordinary differential equations (ODEs) or partial differential equations (PDEs), modeling a wide range of spatio-temporal scales and multi-physics. The field of computational science has achieved indisputable success in advancing our understanding of the natural world - made possible through a combination of increasingly sophisticated mathematical models, numerical techniques and hardware resources. Furthermore, there has been a recent revolution in the data-driven sciences - spurred on by advances in the deep learning/stochastic optimization communities and the democratization of machine learning (ML) software.

With the ubiquity of use of computational models for analysis and prediction of physical systems, there has arisen a need for rigorously characterizing the effects of unknown variables in a system. Unfortunately, Uncertainty quantification (UQ) tasks such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying physical models. In order to deal with the high cost of the forward model, one typically resorts to the surrogate idea - replacing the true response surface with an approximation that is both accurate as well cheap (computationally speaking). However, state-ofart numerical systems are often characterized by a very large number of stochastic parameters - of the order of hundreds or thousands. The high cost of individual evaluations of the forward model, coupled with the limited real world computational budget one is constrained to work with, means that one is faced with the task of constructing a surrogate model for a system with high input dimensionality and small dataset sizes. In other words, one faces the curse of dimensionality.

In this dissertation, we propose multiple ways of overcoming the curse of dimensionality when constructing surrogate models for high-dimensional numerical simulators. The core idea binding all of our proposed approach is simple - we try to discover special structure in the stochastic parameter which captures most of the variance of the output quantity of interest. Our strategies first identify such a low-rank structure, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the low dimensional structure is small enough, learning the map between this reduced input space to the output is a much easier task in
comparison to the original surrogate modeling task.
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Books on the topic "Active subspace"

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Constantine, Paul G. Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies. SIAM-Society for Industrial and Applied Mathematics, 2015.

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Book chapters on the topic "Active subspace"

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Joshi, Vineet, and Raj Bhatnagar. "eSelect: Effective Subspace Selection for Detection of Anomalies." In Active Media Technology, 251–62. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09912-5_21.

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Joshi, Vineet, and Raj Bhatnagar. "Outlier Analysis Using Lattice of Contiguous Subspaces." In Active Media Technology, 238–50. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09912-5_20.

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Jia, Chengcheng, and Yun Fu. "Subspace Learning for Action Recognition." In Human Activity Recognition and Prediction, 49–69. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-27004-3_3.

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Oreifej, Omar, and Mubarak Shah. "Action Recognition by Motion Trajectory Decomposition." In Robust Subspace Estimation Using Low-Rank Optimization, 55–67. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04184-1_5.

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Beleza, Suzana R. A., and Kazuhiro Fukui. "Slow Feature Subspace for Action Recognition." In Pattern Recognition. ICPR International Workshops and Challenges, 702–16. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68796-0_51.

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Paternain, Gabriel P. "The Geodesic Flow Acting on Lagrangian Subspaces." In Geodesic Flows, 31–50. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1600-1_3.

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Luong, Vinh D., Lipo Wang, and Gaoxi Xiao. "Action Recognition Using Hierarchical Independent Subspace Analysis with Trajectory." In Proceedings in Adaptation, Learning and Optimization, 549–59. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-13359-1_42.

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Xu, Lu, Xian Zhong, Wenxuan Liu, Shilei Zhao, Zhengwei Yang, and Luo Zhong. "Subspace Enhancement and Colorization Network for Infrared Video Action Recognition." In PRICAI 2021: Trends in Artificial Intelligence, 321–36. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89370-5_24.

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Tezzele, Marco, Francesco Ballarin, and Gianluigi Rozza. "Combined Parameter and Model Reduction of Cardiovascular Problems by Means of Active Subspaces and POD-Galerkin Methods." In SEMA SIMAI Springer Series, 185–207. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96649-6_8.

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Kairies, Hans-Heinrich. "Properties of an Operator Acting on the Space of Bounded Real Functions and Certain Subspaces." In Functional Equations — Results and Advances, 175–86. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-5288-5_13.

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Conference papers on the topic "Active subspace"

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Seshadri, Pranay, Shahrokh Shahpar, Paul Constantine, Geoffrey Parks, and Mike Adams. "Turbomachinery Active Subspace Performance Maps." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64528.

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Turbomachinery active subspace performance maps are 2D contour plots that illustrate the variation of key flow performance metrics with different blade designs. While such maps are easy to construct for design parameterizations with two variables, in this paper maps will be generated for a fan blade with twenty-five design variables. Turbomachinery active subspace performance maps combine active subspaces — a new set of ideas for dimension reduction — with fundamental turbomachinery aerodynamics and design spaces. In this paper, contours of (i) cruise efficiency, (ii) cruise pressure ratio, (iii) maximum climb flow capacity and (iv) sensitivity to manufacturing variations, are plotted as objectives for the fan. These maps are then used to infer pedigree design rules: how best to increase fan efficiency; how best to desensitize blade aerodynamics to the impact of manufacturing variations? In the present study, the former required both a reduction in pressure ratio and flow capacity — leading to a reduction of the strength of the leading edge bow wave — while the latter required strictly a reduction in flow capacity. While such pedigree rules can be obtained from first principles, in this paper these rules are derived from the active subspaces. This facilitates a more detailed quantification of the aerodynamic trade-offs. Thus, instead of simply stating that a particular design is more sensitive to manufacturing variations; or that it lies on a hypothetical ‘efficiency cliff’, this paper seeks to visualize, quantify and make precise such notions of turbomachinery design.
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Leon, Lider S., Ralph C. Smith, William S. Oates, and Paul Miles. "Identifiability and Active Subspace Analysis for a Polydomain Ferroelectric Phase Field Model." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3845.

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We consider subset selection and active subspace techniques for parameters in a continuum phase-field polydomain model for ferroelectric materials. This analysis is necessary to mathematically determine the parameter subset or subspace critically affecting the response, prior to model calibration using either experimental or synthetic data constructed using density functional theory (DFT) simulations. For the 180° domain wall model, we employ identifiability analysis using a Fisher information matrix methodology, and subspace selection to determine the active subspace. We demonstrate the implementation and interpretation of techniques that accommodate the model structure and discuss results in the context of identifiable parameter subsets and active subspaces quantifying the strongest influence on the model output. Our results indicate that the governing domain wall gradient energy exchange parameter is most identifiable.
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Xiaofei He and Deng Cai. "Active subspace learning." In 2009 IEEE 12th International Conference on Computer Vision (ICCV). IEEE, 2009. http://dx.doi.org/10.1109/iccv.2009.5459329.

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Lipor, John, and Laura Balzano. "Margin-based active subspace clustering." In 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2015. http://dx.doi.org/10.1109/camsap.2015.7383815.

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Peng, Hankui, and Nicos G. Pavlidis. "Subspace Clustering with Active Learning." In 2019 IEEE International Conference on Big Data (Big Data). IEEE, 2019. http://dx.doi.org/10.1109/bigdata47090.2019.9006361.

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Tripathy, Rohit, and Ilias Bilionis. "Deep Active Subspaces: A Scalable Method for High-Dimensional Uncertainty Propagation." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98099.

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Abstract A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accurate surrogate modeling in such systems, is further compounded by data scarcity brought about by the large cost of forward model evaluations. Traditional response surface techniques, such as Gaussian process regression (or Kriging) and polynomial chaos are difficult to scale to high dimensions. To make surrogate modeling tractable in expensive high-dimensional systems, one must resort to dimensionality reduction of the stochastic parameter space. A recent dimensionality reduction technique that has shown great promise is the method of ‘active subspaces’. The classical formulation of active subspaces, unfortunately, requires gradient information from the forward model — often impossible to obtain. In this work, we present a simple, scalable method for recovering active subspaces in high-dimensional stochastic systems, without gradient-information that relies on a reparameterization of the orthogonal active subspace projection matrix, and couple this formulation with deep neural networks. We demonstrate our approach on challenging synthetic datasets and show favorable predictive comparison to classical active subspaces.
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Beck, Joseph A., Jeffrey M. Brown, Alex A. Kaszynski, and Emily B. Carper. "Active Subspace Development of Integrally Bladed Disk Dynamic Properties due to Manufacturing Variations." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76800.

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The impact of geometry variations on integrally bladed disk eigenvalues is investigated. A large population of industrial Bladed Disks (Blisks) are scanned via a structured light optical scanner to provide as-measured geometries in the form of point-cloud data. The point cloud data is transformed using Principal Component Analysis that results in a Pareto of Principal Components (PCs). The PCs are used as inputs to predict the variation in a Blisk’s eigenvalues due to geometry variations from nominal when all blades have the same deviations. A large subset of the PCs are retained to represent the geometry variation, which proves challenging in probabilistic analyses because of the curse of dimensionality. To overcome this, the dimensionality of the problem is reduced by computing an active subspace that describes critical directions in the PC input space. Active variables in this subspace are then fit with a surrogate model of a Blisk’s eigenvalues. This surrogate can be sampled efficiently with the large subset of PCs retained in the active subspace formulation to yield a predicted distribution in eigenvalues. The ability of building an active subspace mapping PC coefficients to eigenvalues is demonstrated. Results indicate that exploitation of the active subspace is capable of capturing eigenvalue variation.
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Biao Niu, Yifan Zhang, Jinqiao Wang, Jian Cheng, and Hanqing Lu. "Subspace learning based active learning for image retrieval." In 2013 IEEE International Conference on Multimedia and Expo Workshops (ICMEW). IEEE, 2013. http://dx.doi.org/10.1109/icmew.2013.6618268.

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Xie, Ziqi, and Lihong Wang. "Active Structure Learning for Block Diagonal Subspace Clustering." In 2020 13th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI). IEEE, 2020. http://dx.doi.org/10.1109/cisp-bmei51763.2020.9263491.

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10

Pongpairoj, Harin, Vineet Chaparala, and Farzad Pourboghrat. "Real-Time Subspace Identification and Optimal Control for Active Noise Cancellation." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-59894.

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Abstract:
In this paper, a combination of a novel recursive subspace identification and receding horizon optimal control is developed for real-time implementation, via a digital signal processor (DSP), using only input-output measurements. The proposed recursive strategy can be parameterized in terms of recursive approximation of subspace intersections and adaptive estimation of state sequences. The proposed integrated modeling-control strategy can be implemented, in real time, with minimum knowledge of the controlled system. Actual hardware experiments on feedback active noise control problem in a duct have been carried out in order to verify the performance of the proposed methodology.
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Reports on the topic "Active subspace"

1

Wang, Qiqi. Active Subspace Methods for Data-Intensive Inverse Problems. Office of Scientific and Technical Information (OSTI), April 2017. http://dx.doi.org/10.2172/1353429.

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2

Constantine, Paul. Active Subspace Methods for Data-Intensive Inverse Problems. Office of Scientific and Technical Information (OSTI), September 2019. http://dx.doi.org/10.2172/1566065.

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Bui-Thanh, Tan. Active Subspace Methods for Data-Intensive Inverse Problems (Final Report). Office of Scientific and Technical Information (OSTI), February 2019. http://dx.doi.org/10.2172/1494035.

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4

Williams, Brian J., Kayla Coleman, Ralph C. Smith, and Max D. Morris. Gradient-Free Construction of Active Subspaces for Dimension Reduction. Office of Scientific and Technical Information (OSTI), May 2019. http://dx.doi.org/10.2172/1523205.

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