Application of Linear and Nonlinear Dimensionality Reduction Methods

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.

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Augmented Design-Space Exploration by Nonlinear Dimensionality Reduction Methods

Machine Learning, Optimization, and Data Science - Lecture Notes in Computer Science ◽

10.1007/978-3-030-13709-0_13 ◽

2019 ◽

pp. 154-165

Author(s):

Danny D’Agostino ◽

Andrea Serani ◽

Emilio Fortunato Campana ◽

Matteo Diez

Keyword(s):

Dimensionality Reduction ◽

Design Space Exploration ◽

Design Space ◽

Space Exploration ◽

Nonlinear Dimensionality Reduction ◽

Reduction Methods ◽

Augmented Design

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

Mathematical Problems in Engineering ◽

10.1155/2019/6941475 ◽

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.

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