Learning Manifolds from Dynamic Process Data

Scientific data, generated by computational models or from experiments, are typically results of nonlinear interactions among several latent processes. Such datasets are typically high-dimensional and exhibit strong temporal correlations. Better understanding of the underlying processes requires mapping such data to a low-dimensional manifold where the dynamics of the latent processes are evident. While nonlinear spectral dimensionality reduction methods, e.g., Isomap, and their scalable variants, are conceptually fit candidates for obtaining such a mapping, the presence of the strong temporal correlation in the data can significantly impact these methods. In this paper, we first show why such methods fail when dealing with dynamic process data. A novel method, Entropy-Isomap, is proposed to handle this shortcoming. We demonstrate the effectiveness of the proposed method in the context of understanding the fabrication process of organic materials. The resulting low-dimensional representation correctly characterizes the process control variables and allows for informative visualization of the material morphology evolution.

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Building Recognition on Subregion’s Multiscale Gist Feature Extraction and Corresponding Columns Information Based Dimensionality Reduction

Journal of Applied Mathematics ◽

10.1155/2014/898705 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Bin Li ◽

Wei Pang ◽

Yuhao Liu ◽

Xiangchun Yu ◽

Anan Du ◽

...

Keyword(s):

Dimensionality Reduction ◽

Dimensional Subspace ◽

Dimensional Manifold ◽

Feature Maps ◽

High Dimensions ◽

Recognition Method ◽

Second Stage ◽

Building Recognition ◽

Reduction Methods ◽

Low Dimensional

In this paper, we proposed a new building recognition method named subregion’s multiscale gist feature (SM-gist) extraction and corresponding columns information based dimensionality reduction (CCI-DR). Our proposed building recognition method is presented as a two-stage model: in the first stage, a building image is divided into 4 × 5 subregions, and gist vectors are extracted from these regions individually. Then, we combine these gist vectors into a matrix with relatively high dimensions. In the second stage, we proposed CCI-DR to project the high dimensional manifold matrix to low dimensional subspace. Compared with the previous building recognition method the advantages of our proposed method are that (1) gist features extracted by SM-gist have the ability to adapt to nonuniform illumination and that (2) CCI-DR can address the limitation of traditional dimensionality reduction methods, which convert gist matrices into vectors and thus mix the corresponding gist vectors from different feature maps. Our building recognition method is evaluated on the Sheffield buildings database, and experiments show that our method can achieve satisfactory performance.

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Scientific data interpolation with low dimensional manifold model

Journal of Computational Physics ◽

10.1016/j.jcp.2017.09.048 ◽

2018 ◽

Vol 352 ◽

pp. 213-245 ◽

Cited By ~ 5

Author(s):

Wei Zhu ◽

Bao Wang ◽

Richard Barnard ◽

Cory D. Hauck ◽

Frank Jenko ◽

...

Keyword(s):

Scientific Data ◽

Dimensional Manifold ◽

Data Interpolation ◽

Low Dimensional ◽

Low Dimensional Manifold

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Spectral quasi equilibrium manifold and intrinsic low dimensional manifold: A multi-step reaction mechanism

International Communications in Heat and Mass Transfer ◽

10.1016/j.icheatmasstransfer.2020.105098 ◽

2021 ◽

Vol 121 ◽

pp. 105098

Author(s):

Faisal Sultan ◽

Muhammad Shahzad ◽

Mehboob Ali

Keyword(s):

Reaction Mechanism ◽

Quasi Equilibrium ◽

Dimensional Manifold ◽

Equilibrium Manifold ◽

Low Dimensional ◽

Low Dimensional Manifold

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Experimental and low-dimensional numerical study on the application of conventional NOx reduction methods in pulse detonation combustion

Combustion and Flame ◽

10.1016/j.combustflame.2021.111593 ◽

2021 ◽

Vol 233 ◽

pp. 111593

Author(s):

Niclas Garan ◽

Neda Djordjevic

Keyword(s):

Numerical Study ◽

Nox Reduction ◽

Pulse Detonation ◽

Detonation Combustion ◽

Reduction Methods ◽

Low Dimensional

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Supervised dimensionality reduction for big data

Nature Communications ◽

10.1038/s41467-021-23102-2 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Joshua T. Vogelstein ◽

Eric W. Bridgeford ◽

Minh Tang ◽

Da Zheng ◽

Christopher Douville ◽

...

Keyword(s):

Dimensionality Reduction ◽

Data Science ◽

Real Data ◽

Low Rank ◽

Conditional Moment ◽

Desktop Computer ◽

Reduction Techniques ◽

Reduction Methods ◽

The Individual ◽

Low Dimensional

AbstractTo solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because sample sizes are typically orders of magnitude smaller than the dimensionality of these data, valid inferences require finding a low-dimensional representation that preserves the discriminating information (e.g., whether the individual suffers from a particular disease). There is a lack of interpretable supervised dimensionality reduction methods that scale to millions of dimensions with strong statistical theoretical guarantees. We introduce an approach to extending principal components analysis by incorporating class-conditional moment estimates into the low-dimensional projection. The simplest version, Linear Optimal Low-rank projection, incorporates the class-conditional means. We prove, and substantiate with both synthetic and real data benchmarks, that Linear Optimal Low-Rank Projection and its generalizations lead to improved data representations for subsequent classification, while maintaining computational efficiency and scalability. Using multiple brain imaging datasets consisting of more than 150 million features, and several genomics datasets with more than 500,000 features, Linear Optimal Low-Rank Projection outperforms other scalable linear dimensionality reduction techniques in terms of accuracy, while only requiring a few minutes on a standard desktop computer.

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Automatic configuration of spectral dimensionality reduction methods

Pattern Recognition Letters ◽

10.1016/j.patrec.2010.05.025 ◽

2010 ◽

Vol 31 (12) ◽

pp. 1720-1727 ◽

Cited By ~ 6

Author(s):

Michał Lewandowski ◽

Dimitrios Makris ◽

Jean-Christophe Nebel

Keyword(s):

Dimensionality Reduction ◽

Reduction Methods ◽

Spectral Dimensionality

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An Improved and Low-dimensional Fingerprint-based Localization Method in Collocated Massive MIMO-OFDM Systems

10.21203/rs.3.rs-187259/v1 ◽

2021 ◽

Author(s):

Seyedeh Samira Moosavi ◽

Paul Fortier

Keyword(s):

Computational Complexity ◽

Gaussian Process ◽

Massive Mimo ◽

High Reliability ◽

Gaussian Process Regression ◽

Location Estimation ◽

Ofdm Systems ◽

Process Data ◽

Localization Method ◽

Low Dimensional

Abstract Localization has drawn significant attention in 5G due to the fast-growing demand for location-based service (LBS). Massive multiple-input multiple-output (M-MIMO) has been introduced in 5G as a powerful technology due to its evident potentials for communication performance enhancement and localization in complicated environments. Fingerprint-based (FP) localization are promising methods for rich scattering environments thanks to their high reliability and accuracy. The Gaussian process regression (GPR) method could be used as an FP-based localization method to facilitate localization and provide high accuracy. However, this method has high computational complexity, especially in large-scale environments. In this study, we propose an improved and low-dimensional FP-based localization method in collocated massive MIMO orthogonal frequency division multiplexing (OFDM) systems using principal component analysis (PCA), the affinity propagation clustering (APC) algorithm, and Gaussian process regression (GPR) to estimate the user's location. Fingerprints are first extracted based on instantaneous channel state information (CSI) by taking full advantage of the high-resolution angle and delay domains. First, PCA is used to pre-process data and reduce the feature dimension. Then, the training fingerprints are clustered using the APC algorithm to increase prediction accuracy and reduce computation complexity. Finally, each cluster's data distribution is accurately modelled using GPR to provide support for further localization. Simulation results reveal that the proposed method improves localization performance significantly by reducing the location estimation error. Additionally, it reduces the matching complexity and computational complexity.

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An Evaluation of Precipitation Forecasts from Operational Models and Reanalyses Including Precipitation Variations Associated with MJO Activity

Monthly Weather Review ◽

10.1175/2010mwr3436.1 ◽

2010 ◽

Vol 138 (12) ◽

pp. 4542-4560 ◽

Cited By ~ 23

Author(s):

John E. Janowiak ◽

Peter Bauer ◽

Wanqiu Wang ◽

Phillip A. Arkin ◽

Jon Gottschalck

Keyword(s):

Prediction Models ◽

Coupled Model ◽

Warm Season ◽

Temporal Correlation ◽

Operational Model ◽

Temporal Correlations ◽

Operational Models ◽

Environmental Prediction ◽

The Tropics ◽

Model Precipitation

Abstract In this paper, the results of an examination of precipitation forecasts for 1–30-day leads from global models run at the European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) during November 2007–February 2008 are presented. The performance of the model precipitation forecasts are examined in global and regional contexts, and results of a case study of precipitation variations that are associated with a moderate to strong Madden–Julian oscillation (MJO) event are presented. The precipitation forecasts from the ECMWF and NCEP operational prediction models have nearly identical temporal correlation with observed precipitation at forecast leads from 2 to 9 days over the Northern Hemisphere during the cool season, despite the higher resolution of the ECMWF operational model, while the ECMWF operational model forecasts are slightly better in the tropics and the Southern Hemisphere during the warm season. The ECMWF Re-Analysis Interim (ERA-Interim) precipitation forecasts perform only slightly worse than the NCEP operational model, while NCEP’s Climate Forecast System low-resolution coupled model forecasts perform the worst among the four models. In terms of bias, the ECMWF operational model performs the best among the four model forecasts that were examined, particularly with respect to the ITCZ regions in both the Atlantic and Pacific. Local temporal correlations that were computed on daily precipitation totals for day-2 forecasts against observations indicate that the operational models at ECMWF and NCEP perform the best during the 4-month study period, and that all of the models have low to insignificant correlations over land and over much of the tropics. They perform the best in subtropical and extratropical oceanic regions. Also presented are results that show that striking improvements have been made over the past two decades in the ability of the models to represent precipitation variations that are associated with MJO. The model precipitation forecasts exhibit the ability to characterize the evolution of precipitation variations during a moderate–strong period of MJO conditions for forecast leads as long as 10 days.

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