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- Multilinear_principal_component_analysis abstract "Multilinear principal component analysis (MPCA) is a mathematical procedure that uses multiple orthogonal transformations to convert a set of multidimensional objects into another set of multidimensional objects of lower dimensions. There is one orthogonal (linear) transformation for each dimension (mode); hence multilinear. This transformation aims to capture as high a variance as possible, accounting for as much of the variability in the data as possible, subject to the constraint of mode-wise orthogonality. MPCA is a multilinear extension of principal component analysis (PCA). The major difference is that PCA needs to reshape a multidimensional object into a vector, while MPCA operates directly on multidimensional objects through mode-wise processing. For example, for 100x100 images, PCA operates on vectors of 10000x1 while MPCA operates on vectors of 100x1 in two modes. For the same amount of dimension reduction, PCA needs to estimate 49*(10000/(100*2)-1) times more parameters than MPCA. Thus, MPCA is more efficient and better conditioned in practice.MPCA is a basic algorithm for dimension reduction via multilinear subspace learning. In wider scope, it belongs to tensor-based computation. Its origin can be traced back to the Tucker decomposition in 1960s and it is closely related to higher-order singular value decomposition, (HOSVD) and to the best rank-(R1, R2, ..., RN ) approximation of higher-order tensors.".
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- Multilinear_principal_component_analysis wikiPageRevisionID "652977913".
- Multilinear_principal_component_analysis wikiPageWikiLink Boosting_(machine_learning).
- Multilinear_principal_component_analysis wikiPageWikiLink Boosting_(meta-algorithm).
- Multilinear_principal_component_analysis wikiPageWikiLink Category:Dimension_reduction.
- Multilinear_principal_component_analysis wikiPageWikiLink Category:Machine_learning.
- Multilinear_principal_component_analysis wikiPageWikiLink Category:Multivariate_statistics.
- Multilinear_principal_component_analysis wikiPageWikiLink Dimension_reduction.
- Multilinear_principal_component_analysis wikiPageWikiLink Dimensionality_reduction.
- Multilinear_principal_component_analysis wikiPageWikiLink Feature_extraction.
- Multilinear_principal_component_analysis wikiPageWikiLink Feature_vector.
- Multilinear_principal_component_analysis wikiPageWikiLink Higher-order_singular_value_decomposition.
- Multilinear_principal_component_analysis wikiPageWikiLink Multilinear_subspace_learning.
- Multilinear_principal_component_analysis wikiPageWikiLink Principal_component_analysis.
- Multilinear_principal_component_analysis wikiPageWikiLink Tensor.
- Multilinear_principal_component_analysis wikiPageWikiLink Tucker_decomposition.
- Multilinear_principal_component_analysis wikiPageWikiLinkText "Multilinear PCA".
- Multilinear_principal_component_analysis wikiPageWikiLinkText "Multilinear Principal Component Analysis".
- Multilinear_principal_component_analysis wikiPageWikiLinkText "Multilinear principal component analysis".
- Multilinear_principal_component_analysis wikiPageWikiLinkText "multilinear PCA".
- Multilinear_principal_component_analysis wikiPageWikiLinkText "multilinear principal component analysis".
- Multilinear_principal_component_analysis hasPhotoCollection Multilinear_principal_component_analysis.
- Multilinear_principal_component_analysis wikiPageUsesTemplate Template:Context.
- Multilinear_principal_component_analysis wikiPageUsesTemplate Template:Reflist.
- Multilinear_principal_component_analysis subject Category:Dimension_reduction.
- Multilinear_principal_component_analysis subject Category:Machine_learning.
- Multilinear_principal_component_analysis subject Category:Multivariate_statistics.
- Multilinear_principal_component_analysis hypernym Procedure.
- Multilinear_principal_component_analysis type AnatomicalStructure.
- Multilinear_principal_component_analysis type Article.
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- Multilinear_principal_component_analysis comment "Multilinear principal component analysis (MPCA) is a mathematical procedure that uses multiple orthogonal transformations to convert a set of multidimensional objects into another set of multidimensional objects of lower dimensions. There is one orthogonal (linear) transformation for each dimension (mode); hence multilinear.".
- Multilinear_principal_component_analysis label "Multilinear principal component analysis".
- Multilinear_principal_component_analysis sameAs m.0gg4sf9.
- Multilinear_principal_component_analysis sameAs Q6934740.
- Multilinear_principal_component_analysis sameAs Q6934740.
- Multilinear_principal_component_analysis sameAs 多線性主成分分析.
- Multilinear_principal_component_analysis wasDerivedFrom Multilinear_principal_component_analysis?oldid=652977913.
- Multilinear_principal_component_analysis isPrimaryTopicOf Multilinear_principal_component_analysis.