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2 changes: 1 addition & 1 deletion content/code/causal_inference/_index.md
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link: "./causal_inference"
description: ""
type: "code"
layout: "structure_codes"
layout: "list2"
---
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description: ""
weight: 2
type: "code"
layout: "structure_codes"
layout: "list2"
---
2 changes: 1 addition & 1 deletion content/code/feature_extraction/_index.md
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description: ""
weight: 3
type: "code"
layout: "structure_codes"
layout: "list2"
---
2 changes: 0 additions & 2 deletions content/code/feature_extraction/ddr/_index.md
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Dimensionality Reduction via Regression (DRR) is a manifold learning technique aimed at removing residual statistical dependence between PCA components due to dataset curvature. DRR predicts PCA coefficients from neighboring coefficients using multivariate regression, generalizing PPA. It advances dimensionality reduction methods by using curves instead of straight lines.
references:
- "Dimensionality reduction via regression in hyperspectral imagery. Laparra, V., Malo, J., and Camps-Valls, G. IEEE Journal on Selected Topics in Signal Processing, 9(6):1026-1036, 2015."
type: "code"
layout: "single"
---
79 changes: 40 additions & 39 deletions content/code/feature_extraction/ddr/content.md
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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)."
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"
---
type: "code"
layout: "single_four"
images:
- link: "drr_image1.webp"
description: "The behavior of DRR and other dimensionality reduction algorithms."
- link: "drr_image2.webp"
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"
---

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).
2 changes: 0 additions & 2 deletions content/code/feature_extraction/hocca/_index.md
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HOCCA is a linear manifold learning technique that applies to datasets from the same source. It finds independent components in each dataset that are related across datasets, thus combining the goals of ICA and CCA.
references:
- "Spatio-Chromatic Adaptation via Higher-Order Canonical Correlation Analysis of Natural Images. Gutmann, M.U., Laparra, V., Hyvärinen, A., Malo, J. PLoS ONE, 9(2):e86481, 2014."
type: "code"
layout: "single"
---
53 changes: 27 additions & 26 deletions content/code/feature_extraction/hocca/content.md
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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."

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"
type: "code"
layout: "single_four"
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"
---
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.
2 changes: 0 additions & 2 deletions content/code/feature_extraction/ppa/_index.md
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Principal Polynomial Analysis (PPA) is a manifold learning technique that generalizes PCA by using principal polynomials to capture nonlinear data patterns. It improves PCA’s energy compaction ability, reducing dimensionality reduction errors. PPA defines a manifold-dependent metric that generalizes Mahalanobis distance for curved manifolds.
references:
- "Principal polynomial analysis. Laparra, V., Jiménez, S., Tuia, D., Camps-Valls, G., Malo, J. International Journal of Neural Systems, 24(7), 2014."
type: "code"
layout: "single"
---
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