LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT)
Most of the existing local linear embedding algorithms assume that the original data set is located in Euclidean space, but in reality almost all the original space is non-Euclidean space. Aiming at the problem that Euclidean space cannot effectively describe the nonlinear structure of the data and...
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| Format: | Article |
| Language: | zho |
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Editorial Office of Journal of Mechanical Strength
2022-01-01
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| Series: | Jixie qiangdu |
| Subjects: | |
| Online Access: | http://www.jxqd.net.cn/thesisDetails#10.16579/j.issn.1001.9669.2022.06.06 |
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| _version_ | 1841534409770008576 |
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| author | LIU QingQiang HE HongKai ZHENG ChangMin SUN YanRu LIU ZiXuan |
| author_facet | LIU QingQiang HE HongKai ZHENG ChangMin SUN YanRu LIU ZiXuan |
| author_sort | LIU QingQiang |
| collection | DOAJ |
| description | Most of the existing local linear embedding algorithms assume that the original data set is located in Euclidean space, but in reality almost all the original space is non-Euclidean space. Aiming at the problem that Euclidean space cannot effectively describe the nonlinear structure of the data and affects the performance of the feature extraction of the local linear embedding（LLE） algorithm, a local linear embedding algorithm based on the parameter matrix measurement on a symmetric positive definite（SPD-PMM-LLE） manifold is proposed. First, in order to find a suitable measurement method on the symmetric positive definite manifold to improve the performance of the algorithm, an efficient Riemann space metric learning method is introduced. The parameter matrix obtained by learning transforms the original manifold to a new and distinguishable manifold. Then use the locally linear embedding algorithm to mine the salient features. Finally, the efficiency of this method is verified by experimental results on multiple bearing data sets. |
| format | Article |
| id | doaj-art-62976ab839684fffb5b804003a020450 |
| institution | Kabale University |
| issn | 1001-9669 |
| language | zho |
| publishDate | 2022-01-01 |
| publisher | Editorial Office of Journal of Mechanical Strength |
| record_format | Article |
| series | Jixie qiangdu |
| spelling | doaj-art-62976ab839684fffb5b804003a0204502025-01-15T02:39:41ZzhoEditorial Office of Journal of Mechanical StrengthJixie qiangdu1001-96692022-01-011307131436350211LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT)LIU QingQiangHE HongKaiZHENG ChangMinSUN YanRuLIU ZiXuanMost of the existing local linear embedding algorithms assume that the original data set is located in Euclidean space, but in reality almost all the original space is non-Euclidean space. Aiming at the problem that Euclidean space cannot effectively describe the nonlinear structure of the data and affects the performance of the feature extraction of the local linear embedding（LLE） algorithm, a local linear embedding algorithm based on the parameter matrix measurement on a symmetric positive definite（SPD-PMM-LLE） manifold is proposed. First, in order to find a suitable measurement method on the symmetric positive definite manifold to improve the performance of the algorithm, an efficient Riemann space metric learning method is introduced. The parameter matrix obtained by learning transforms the original manifold to a new and distinguishable manifold. Then use the locally linear embedding algorithm to mine the salient features. Finally, the efficiency of this method is verified by experimental results on multiple bearing data sets.http://www.jxqd.net.cn/thesisDetails#10.16579/j.issn.1001.9669.2022.06.06Feature extractionSymmetric positive definite manifoldLocal linear embeddingRiemann space metric learningEuclidean space |
| spellingShingle | LIU QingQiang HE HongKai ZHENG ChangMin SUN YanRu LIU ZiXuan LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT) Jixie qiangdu Feature extraction Symmetric positive definite manifold Local linear embedding Riemann space metric learning Euclidean space |
| title | LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT) |
| title_full | LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT) |
| title_fullStr | LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT) |
| title_full_unstemmed | LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT) |
| title_short | LOCAL LINEAR EMBEDDING ALGORITHM FOR PARAMETER MATRIX MEASUREMENT IN SYMMETRIC POSITIVE DEFINITE MANIFOLD (MT) |
| title_sort | local linear embedding algorithm for parameter matrix measurement in symmetric positive definite manifold mt |
| topic | Feature extraction Symmetric positive definite manifold Local linear embedding Riemann space metric learning Euclidean space |
| url | http://www.jxqd.net.cn/thesisDetails#10.16579/j.issn.1001.9669.2022.06.06 |
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