Application of nonlinear dimensionality reduction methods in discrimination of the gradation of Longjing tea

2014 ◽  
Author(s):  
Ruicong Zhi ◽  
Lei Zhao ◽  
Bolin Shi
Keyword(s):  
Dimensionality Reduction ◽  
Nonlinear Dimensionality Reduction ◽  
Reduction Methods

scholarly journals Nonlinear dimensionality reduction methods for synthetic biology biobricks’ visualization

2017 ◽  
Vol 18 (1) ◽  
Author(s):  
Jiaoyun Yang ◽  
Haipeng Wang ◽  
Huitong Ding ◽  
Ning An ◽  
Gil Alterovitz
Keyword(s):  
Synthetic Biology ◽  
Dimensionality Reduction ◽  
Nonlinear Dimensionality Reduction ◽  
Reduction Methods

scholarly journals Ensembles of Random Projections for Nonlinear Dimensionality Reduction

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Amir Hossein Karimi ◽  
Mohammad Javad Shafiee ◽  
Ali Ghodsi ◽  
Alexander Wong
Keyword(s):  
Dimensionality Reduction ◽  
Experimental Analysis ◽  
Random Projections ◽  
Nonlinear Dimensionality Reduction ◽  
Generalization Performance ◽  
Highly Efficient ◽  
Efficiency Of Algorithms ◽  
Reduction Methods ◽  
Embedding Performance

Dimensionality reduction methods are widely used in informationprocessing systems to better understand the underlying structuresof datasets, and to improve the efficiency of algorithms for bigdata applications. Methods such as linear random projections haveproven to be simple and highly efficient in this regard, however,there is limited theoretical and experimental analysis for nonlinearrandom projections. In this study, we review the theoretical frameworkfor random projections and nonlinear rectified random projections,and introduce ensemble of nonlinear maximum random projections.We empirically evaluate the embedding performance on 3commonly used natural datasets and compare with linear randomprojections and traditional techniques such as PCA, highlightingthe superior generalization performance and stable embedding ofthe proposed method.

scholarly journals Multiple Kernel Dimensionality Reduction via Ratio-Trace and Marginal Fisher Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Hui Xu ◽  
Yongguo Yang ◽  
Xin Wang ◽  
Mingming Liu ◽  
Hongxia Xie ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Convex Combination ◽  
Multiple Kernel Learning ◽  
Nonlinear Dimensionality Reduction ◽  
Kernel Discriminant Analysis ◽  
Restrictive Assumption ◽  
Optimal Weights ◽  
Multiple Kernel ◽  
Benchmark Datasets ◽  
Reduction Methods

Traditional supervised multiple kernel learning (MKL) for dimensionality reduction is generally an extension of kernel discriminant analysis (KDA), which has some restrictive assumptions. In addition, they generally are based on graph embedding framework. A more general multiple kernel-based dimensionality reduction algorithm, called multiple kernel marginal Fisher analysis (MKL-MFA), is presented for supervised nonlinear dimensionality reduction combined with ratio-race optimization problem. MKL-MFA aims at relaxing the restrictive assumption that the data of each class is of a Gaussian distribution and finding an appropriate convex combination of several base kernels. To improve the efficiency of multiple kernel dimensionality reduction, the spectral regression frameworks are incorporated into the optimization model. Furthermore, the optimal weights of predefined base kernels can be obtained by solving a different convex optimization. Experimental results on benchmark datasets demonstrate that MKL-MFA outperforms the state-of-the-art supervised multiple kernel dimensionality reduction methods.

Efficient history matching with dimensionality reduction methods for reservoir simulations

SIMULATION ◽  
2017 ◽  
Vol 94 (8) ◽  
pp. 739-751 ◽  
Author(s):  
Dongmei Zhang ◽  
Ao Shen ◽  
Xinwei Jiang ◽  
Zhijiang Kang
Keyword(s):  
Dimensionality Reduction ◽  
Evolutionary Algorithm ◽  
History Matching ◽  
Model Performance ◽  
Nonlinear Dimensionality Reduction ◽  
Unknown Parameters ◽  
Improve Model ◽  
Reservoir History Matching ◽  
Reduction Methods ◽  
Gradient Based

Oil reservoir history matching is a well-known inverse problem for predicting production by optimizing enormous unknown parameters with numerical simulation. Typically it can be formulated in a Bayesian framework with geological priors. Instead of gradient-based optimization with the possibility of converging to a local minimum, evolutionary algorithms have been introduced to globally find optimal parameters. Due to the high-dimensional parameters, the optimization could become inefficient; therefore, many dimensionality reduction algorithms have been applied in history matching. However, these methods suffer from the linear assumption or the pre-image problem, which could affect the model optimization. In this paper, based on the evolutionary algorithm termed Multi-objective Evolutionary Algorithm Based on Decomposition, which is capable of simultaneously optimizing the parameters with respect to the data of several oil wells, we propose history matching with dimensionality reduction by explicitly utilizing the nonlinear dimensionality reduction model Auto-Encoder to reduce the number of unknown parameters, which can naturally handle the pre-image problem and then improve model performance in terms of precision and complexity. Experimental results based on PUNQ-S3 data verify the efficiency of the newly proposed methods.

scholarly journals Behavior of Linear and Nonlinear Dimensionality Reduction for Collective Variable Identi�cation of Small Molecule Solution-Phase Reactions

2021 ◽  
Author(s):  
Hung Le ◽  
Sushant Kumar ◽  
Nathan May ◽  
Ernesto Martinez-Baez ◽  
Ravishankar Sundararaman ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Chemical Reactions ◽  
Principal Component ◽  
Projection Methods ◽  
Nucleophilic Attack ◽  
Nonlinear Dimensionality Reduction ◽  
Collective Variables ◽  
Reduction Methods ◽  
Solvent Molecules ◽  
Dynamic Exchange

Identifying collective variables for chemical reactions is essential to reduce the 3$N$ dimensional energy landscape into lower dimensional basins and barriers of interest. However in condensed phase processes, the non-meaningful motions of bulk solvent often overpower the ability of dimensionality reduction methods to identify correlated motions that underpin collective variables. Yet solvent can play important indirect or direct roles in reactivity and much can be lost through treatments that remove or dampen solvent motion. This has been amply demonstrated within principal component analysis, although less is known about the behavior of nonlinear dimensionality reduction methods, e.g., UMAP, that have become more popular recently. The latter presents an interesting alternative to linear methods though often at the expense of interpretability. This work presents distance attenuated projection methods of atomic coordinates that facilitate the application of both PCA and UMAP to identify collective variables in solution, and further the specific identity of solvent molecules that participate in chemical reactions. The performance of both methods is examined in detail for two reactions where the explicit solvent plays very different roles within the collective variables. The first reaction consists of the dynamic exchange of a cation about a polyhydroxy anion that is facilitated by waters of solvation, while the second reaction consists of a nucleophilic attack of water upon ethylene to initiate cis/trans isomerization. When applied to raw data, both PCA and UMAP representations are dominated by bulk solvent motions. On the other hand, when applied to data preprocessed by our attenuated projection methods, both PCA and UMAP identify the appropriate collective variables in solution.

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