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| --- | ||
| title: "Dimensionality Reduction via Regression (DRR)" | ||
| abstract: "This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between the PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservation, and straightforward out-of-sample extension, makes DRR interpretable and easy to apply. Properties of DRR enable learning a broader class of data manifolds than recently proposed Non-linear Principal Components Analysis (NLPCA) and Principal Polynomial Analysis (PPA). The figure below illustrates the behavior of different algorithms in this family: from the rigid (linear) PCA to the flexible Sequential Principal Curves Analysis (SPCA). In the paper, we illustrate the performance of the representation in reducing the dimensionality of hyperspectral images. In particular, we tackle two common problems: processing very high dimensional spectral information such as in image sounding data, and dealing with spatial-spectral image patches of multispectral images. Both settings pose collinearity and ill-determination problems. Evaluation of the expressive power of the features is assessed in terms of truncation error, estimating atmospheric variables, and surface land cover classification error. Results show that DRR outperforms linear PCA and recently proposed invertible extensions based on neural networks (NLPCA) and univariate regressions (PPA)." | ||
| images: | ||
| - link: "drr_image1.webp" | ||
| # title: "Image 1" | ||
| description: "The behavior of DRR and other dimensionality reduction algorithms." | ||
| - link: "drr_image2.webp" | ||
| # title: "Image 2" | ||
| description: "Performance comparison of DRR with NLPCA, PPA, and SPCA." | ||
| references: | ||
| - title: "Dimensionality Reduction via Regression in Hyperspectral Imagery" | ||
| authors: "V. Laparra, J. Malo, G. Camps-Valls" | ||
| publication: "IEEE J. Selected Topics in Signal Processing, Sept. 2015" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/drr_jstsp2014_final.pdf" | ||
| - title: "Principal Polynomial Analysis (PPA)" | ||
| authors: "V. Laparra, S. Jiménez, D. Tuia, G. Camps-Valls, J. Malo" | ||
| publication: "Int. J. Neural Syst., Nov. 2014" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/IJNS_Laparra14_accepted_v5.pdf" | ||
| - title: "Visual Aftereffects and Sensory Nonlinearities from a single Statistical Framework (SPCA)" | ||
| authors: "V. Laparra, J. Malo" | ||
| publication: "Frontiers in Human Neuroscience, 2015" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/frontiers_laparra_malo_Accepted_15.pdf" | ||
| - title: "Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis" | ||
| authors: "V. Laparra, S. Jiménez, G. Camps-Valls, J. Malo" | ||
| publication: "Neural Computation 24(10): 2751-2788, Oct. 2012" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/Neco_accepted_2012.pdf" | ||
| - title: "V1 Nonlinearities emerge from local-to-global Nonlinear ICA" | ||
| authors: "J. Malo, J. Gutiérrez" | ||
| publication: "Network: Comput. in Neural Syst. 17(1): 85-102, 2006" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/V1_from_non_linear_ICA.pdf" | ||
| - title: "Non-Linear Principal Components Analysis" | ||
| authors: "Scholz, M. Fraunholz, and J. Selbig" | ||
| publication: "Springer, 2007, ch. 2, pp. 44–67" | ||
| link: "http://www.nlpca.org/" | ||
| links: | ||
| - title: "DRR Toolbox" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/DRR_toolbox_v1.zip" | ||
| - title: "DRR Paper" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/drr_jstsp2014_final.pdf" | ||
| imagenes: | ||
| - ruta: "drr_image1.webp" | ||
| # titulo: "Image 1" | ||
| descripcion: "The behavior of DRR and other dimensionality reduction algorithms." | ||
| - ruta: "drr_image2.webp" | ||
| # titulo: "Image 2" | ||
| descripcion: "Performance comparison of DRR with NLPCA, PPA, and SPCA." | ||
| referencias: | ||
| - nombre: "Dimensionality Reduction via Regression in Hyperspectral Imagery" | ||
| autores: "V. Laparra, J. Malo, G. Camps-Valls" | ||
| publicacion: "IEEE J. Selected Topics in Signal Processing, Sept. 2015" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/drr_jstsp2014_final.pdf" | ||
| - nombre: "Principal Polynomial Analysis (PPA)" | ||
| autores: "V. Laparra, S. Jiménez, D. Tuia, G. Camps-Valls, J. Malo" | ||
| publicacion: "Int. J. Neural Syst., Nov. 2014" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/IJNS_Laparra14_accepted_v5.pdf" | ||
| - nombre: "Visual Aftereffects and Sensory Nonlinearities from a single Statistical Framework (SPCA)" | ||
| autores: "V. Laparra, J. Malo" | ||
| publicacion: "Frontiers in Human Neuroscience, 2015" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/frontiers_laparra_malo_Accepted_15.pdf" | ||
| - nombre: "Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis" | ||
| autores: "V. Laparra, S. Jiménez, G. Camps-Valls, J. Malo" | ||
| publicacion: "Neural Computation 24(10): 2751-2788, Oct. 2012" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/Neco_accepted_2012.pdf" | ||
| - nombre: "V1 Nonlinearities emerge from local-to-global Nonlinear ICA" | ||
| autores: "J. Malo, J. Gutiérrez" | ||
| publicacion: "Network: Comput. in Neural Syst. 17(1): 85-102, 2006" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/V1_from_non_linear_ICA.pdf" | ||
| - nombre: "Non-Linear Principal Components Analysis" | ||
| autores: "Scholz, M. Fraunholz, and J. Selbig" | ||
| publicacion: "Springer, 2007, ch. 2, pp. 44–67" | ||
| url: "http://www.nlpca.org/" | ||
| enlaces: | ||
| - nombre: "DRR Toolbox" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/DRR_toolbox_v1.zip" | ||
| - nombre: "DRR Paper" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/drr_jstsp2014_final.pdf" | ||
| --- |
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| --- | ||
| title: "Spatio-Chromatic Adaptation via Higher-Order Canonical Correlation Analysis of Natural Images" | ||
| abstract: "Independent component and canonical correlation analysis are twogeneral-purpose statistical methods with wide applicability. Inneuroscience, independent component analysis of chromatic naturalimages explains the spatio-chromatic structure of primary corticalreceptive fields in terms of properties of the visual environment.Canonical correlation analysis explains similarly chromatic adaptationto different illuminations. But, as we show in this paper, neither ofthe two methods generalizes well to explain both spatio-chromaticprocessing and adaptation at the same time. We propose a statisticalmethod which combines the desirable properties of independent componentand canonical correlation analysis: It finds independent components ineach data set which, across the two data sets, are related to eachother via linear or higher-order correlations. The new method is aswidely applicable as canonical correlation analysis, and also to morethan two data sets. We call it higher-order canonical correlationanalysis. When applied to chromatic natural images, we found that itprovides a single (unified) statistical framework which accounts forboth spatio-chromatic processing and adaptation. Filters withspatio-chromatic tuning properties as in the primary visual cortexemerged and corresponding-colors psychophysics was reproducedreasonably well. We used the new method to make a theory-driventestable prediction on how the neural response to colored patternsshould change when the illumination changes. We predict shifts in theresponses which are comparable to the shifts reported for chromaticcontrast habituation." | ||
| references: | ||
| - title: "Spatio-Chromatic Adaptation via Higher-Order Canonical Correlation Analysis of Natural Images" | ||
| authors: "M. U. Gutmann, V. Laparra, A. Hyvärinen, J. Malo" | ||
| publication: "PLOS ONE, 9(2), e86481, 2014" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/Gutmann_PLOS_ONE_2014.pdf" | ||
| links: | ||
| - title: "HOCCA Toolbox" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/HOCCA_toolbox_v1.zip" | ||
| - title: "HOCCA Paper" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/Gutmann_PLOS_ONE_2014.pdf" | ||
| - title: Content | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/content.txt" | ||
| - title: Code (zip) | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/code.zip" | ||
| - title: ColorDataBase (zip) | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/ColorDataBase.zip" | ||
| - title: "ColorLab (zip)" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/colorlab.zip" | ||
| - title: "Matfiles for figures (zip)" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/matfiles.for_figures_in_paper.zip" | ||
| - title: "Matfiles for paper (zip)" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/matfiles.paper.zip" | ||
| - title: "Matfiles (zip)" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/matfiles.zip" | ||
| referencias: | ||
| - nombre: "Spatio-Chromatic Adaptation via Higher-Order Canonical Correlation Analysis of Natural Images" | ||
| autores: "M. U. Gutmann, V. Laparra, A. Hyvärinen, J. Malo" | ||
| publicacion: "PLOS ONE, 9(2), e86481, 2014" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/Gutmann_PLOS_ONE_2014.pdf" | ||
| enlaces: | ||
| - nombre: "HOCCA Toolbox" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/HOCCA_toolbox_v1.zip" | ||
| - nombre: "HOCCA Paper" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/Gutmann_PLOS_ONE_2014.pdf" | ||
| - nombre: Content | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/content.txt" | ||
| - nombre: Code (zip) | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/code.zip" | ||
| - nombre: ColorDataBase (zip) | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/ColorDataBase.zip" | ||
| - nombre: "ColorLab (zip)" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/colorlab.zip" | ||
| - nombre: "Matfiles for figures (zip)" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/matfiles.for_figures_in_paper.zip" | ||
| - nombre: "Matfiles for paper (zip)" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/matfiles.paper.zip" | ||
| - nombre: "Matfiles (zip)" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/matfiles.zip" | ||
| --- |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,20 +1,20 @@ | ||
| --- | ||
| title: "Principal Polynomial Analysis (PPA)" | ||
| abstract: "This paper (and toolbox) presents a new framework for manifold learning based on the use of a sequence of principal polynomials that capture the eventually nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) is shown to generalize PCA by admitting curves instead of straight lines. As opposed to previous approaches following the same rationale, PPA reduces to performing canonical, univariate regressions which make it computationally feasible and easy to interpret analytically. We show that the PPA transform is a volume-preserving map, which guarantees the existence of the inverse since the determinant of the Jacobian is bounded. We propose a closed-form solution for the inverse map. Invertibility is an important advantage over other nonlinear dimensionality reduction methods because it permits to understand the identified features in the input domain where data have physical meaning. Moreover, invertibility allows to evaluate the dimensionality reduction performance in sensible units. Preserving the volume also allows to compute the reduction in multi-information achieved by the transform using only marginal operations. Additionally, PPA leads to a clear geometrical interpretation of the manifold: the computation of Frenet-Serret frames along the identified curves allow us to obtain generalized curvature and torsion of the manifold. Moreover, the analytical expression of the Jacobian simplifies the computation of the metric induced by the data. Performance in dimensionality reduction and redundancy reduction, as well as the theoretical properties of PPA, are experimentally tested in datasets from the UCI machine learning repository." | ||
| images: | ||
| - link: "ppa1.webp" | ||
| title: "First Principal Curve and generalized curvatures using PPA in 3D Helix" | ||
| description: "The application of the Principal Polynomial Analysis (PPA) to a 3D Helix, demonstrating the first principal curve and its generalized curvatures." | ||
| - link: "ppa2.webp" | ||
| title: "Discrimination ellipsoids according to the PPA generalized Mahalanobis metric" | ||
| description: "The discrimination ellipsoids according to the PPA's generalized Mahalanobis metric, which provides a geometrical interpretation of the dataset." | ||
| references: | ||
| - title: "Principal Polynomial Analysis" | ||
| authors: "V. Laparra, S. Jiménez, D. Tuia, G. Camps-Valls, J. Malo" | ||
| publication: "Int. J. Neural Syst., July 2014 (in press)" | ||
| links: | ||
| - title: "PPA Toolbox (general purpose code)" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/PPA.zip" | ||
| - title: "Specific code to reproduce the experiments in the paper" | ||
| link: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/experiments_ppa_paper.rar" | ||
| imagenes: | ||
| - ruta: "ppa1.webp" | ||
| titulo: "First Principal Curve and generalized curvatures using PPA in 3D Helix" | ||
| descripcion: "The application of the Principal Polynomial Analysis (PPA) to a 3D Helix, demonstrating the first principal curve and its generalized curvatures." | ||
| - ruta: "ppa2.webp" | ||
| titulo: "Discrimination ellipsoids according to the PPA generalized Mahalanobis metric" | ||
| descripcion: "The discrimination ellipsoids according to the PPA's generalized Mahalanobis metric, which provides a geometrical interpretation of the dataset." | ||
| referencias: | ||
| - nombre: "Principal Polynomial Analysis" | ||
| autores: "V. Laparra, S. Jiménez, D. Tuia, G. Camps-Valls, J. Malo" | ||
| publicacion: "Int. J. Neural Syst., July 2014 (in press)" | ||
| enlaces: | ||
| - nombre: "PPA Toolbox (general purpose code)" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/PPA.zip" | ||
| - nombre: "Specific code to reproduce the experiments in the paper" | ||
| url: "https://huggingface.co/datasets/isp-uv-es/Web_site_legacy/resolve/main/code/soft_feature/experiments_ppa_paper.rar" | ||
| --- |
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