Neighborhood Selection and Eigenvalues for Embedding Data Complex in Low Dimension

Liou, Jiun-Wei; Liou, Cheng-Yuan

doi:10.1007/978-3-642-28487-8_43

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Several methods dealing with this issue have been recently proposed (Saul, 2003;Zhang, 2012;Shao, 2012;Farahmand, 2007;Liou, 2012;Kouropteva, 2002). The number of nearest neighbors k and mapping dimensionality d for NPE are determined based on the normalized training data.…”

Section: Parameter Settingmentioning

confidence: 98%

Neighborhood preserving regression embedding based data regression and its applications on soft sensor modeling

Miao

2015

Chemometrics and Intelligent Laboratory Systems

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Section: Parameter Settingmentioning

confidence: 98%

Neighborhood preserving regression embedding based data regression and its applications on soft sensor modeling

Miao

2015

Chemometrics and Intelligent Laboratory Systems

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“…. , x i k ] ∈ R m×k is the k nearest neighbors of x i , the value of k can be determined by the [31]. λ > 0 is a regularization parameter that balances reconstruction error and sparsity,…”

Section: Multiway Sparse Weighted Neighborhood Preserving Embedding (...mentioning

confidence: 99%

Batch process monitoring based on sequential phase division multiway sparse weighted neighborhood preserving embedding

Zhang,

Zhao,

Cao

et al. 2023

Meas. Sci. Technol.

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Batch processes are often characterized by multiphase and different batch durations, which vary from phase to phase presenting multiple local neighborhood features. In this paper, a sequential phase division-multiway sparse weighted neighborhood preserving embedding method is proposed for monitoring batch processes more sensitively. First, batches with uneven durations are synchronized, and the phases are automatically determined in chronological order. Secondly, the nearest neighbors are computed at each phase and the optimal sparse representation (SR) is obtained based on the nearest neighbors. This improves the robustness of the algorithm to noise and outliers, and solves the problem of computational difficulties associated with global SR based. Thirdly, the distance values of the neighbor elements are considered to fully extract the neighbor structure when the optimal SR is calculated. Finally, after dimension reduction, T 2 and squared prediction error statistics are established in feature space and residual space respectively for fault detection. The effectiveness of the method is verified by a multiphase numerical simulation example and the penicillin fermentation process.

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“…If we do not know the values in advance, it is critical to specify the optimal [40,[50][51][52][53][54][55]. The first step of NSC-NPE is to identify the neighborhood for each data point.…”

Section: Parameter Settingmentioning

confidence: 99%

Nonlocal structure constrained neighborhood preserving embedding model and its application for fault detection

Miao

Song

et al. 2015

Chemometrics and Intelligent Laboratory Systems

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Neighborhood Selection and Eigenvalues for Embedding Data Complex in Low Dimension

Cited by 3 publications

References 9 publications

Neighborhood preserving regression embedding based data regression and its applications on soft sensor modeling

Neighborhood preserving regression embedding based data regression and its applications on soft sensor modeling

Batch process monitoring based on sequential phase division multiway sparse weighted neighborhood preserving embedding

Nonlocal structure constrained neighborhood preserving embedding model and its application for fault detection

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