Deflation based nonlinear canonical correlation analysis

Sharma, Sanjay Kumar; Krüger, Uwe; Irwin, G.W.

doi:10.1016/j.chemolab.2005.12.008

Cited by 6 publications

(2 citation statements)

References 12 publications

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“…Canonical correlation analysis (CCA) is a well-established method that calculates the linear correlation between each one of the scores (TX and TY) and two independent PCA models X and Y (Amigo et al, 2012;Naes and Martens, 1984;Sharma et al, 2006) as indicated in equations (1) and (2):…”

Section: Data Treatmentmentioning

confidence: 99%

Relationship between levels of polycyclic aromatic hydrocarbons in pine needles and socio-geographic parameters

Fernández-Varela

Ratola

Alves

et al. 2015

Journal of Environmental Management

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The ability of pine needles to capture polycyclic aromatic hydrocarbons (PAHs) from the surrounding air is well known. In this work the current knowledge of this affinity will be enhanced, investigating the plausible links between the concentrations of PAHs found in pine needles collected in different sites in Portugal, and several socio-geographic variables with environmental relevance. Canonical correlation analysis (CCA) has proven to be a suitable and innovative technique to look for relationships within environmental datasets. In the current work, CCA will simultaneously include chemical information (concentration of PAHs found in pine needles) and socio-geographic information associated to the sampling areas. In order to be more robust in these conclusions, Pinus pinea and Pinus pinaster species were considered separately, allowing an accurate direct comparison between them. The information concerning the different seasons and land occupation was also taken into account. Our results demonstrate how CCA can be a useful tool in environmental impact assessment, and highlight the importance of pine needles as trustful biomonitors of the influence of socio-geographic parameters on the levels of PAHs in a given area.

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Section: Data Treatmentmentioning

confidence: 99%

Relationship between levels of polycyclic aromatic hydrocarbons in pine needles and socio-geographic parameters

Fernández-Varela

Ratola

Alves

et al. 2015

Journal of Environmental Management

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“…Then a question may naturally arise: Why are only X 1 ‐LVs used for deflation in both spaces? Actually, each pair of LVs ( t i − u i ) represents a single‐input, single‐output (SISO) model between two variable sets as pointed out by Sharma et al26 It means that some variations in one X 2 ‐LV ( u i ) cannot be predicted by the corresponding X 1 ‐LV ( t i ). If u i is removed from X 2 , it cannot be attained from the future X 2 ‐LVs either and thus shows no chance to be explained by other X 1 ‐LVs, leading to inferior prediction of X 2 .…”

Section: Methodsmentioning

confidence: 99%

A bidirectional between‐set statistical analysis method and its applications

Zhao

Gao

2011

AIChE Journal

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In this work, a bidirectional statistical modeling and analysis approach is developed to relate two data tables (X 1 and X 2 ) under the supervision of each other. Different from quality prediction where the interest was to interpret one set of variables by another set, the current task lies in modeling simultaneously both data spaces in bidirectional fashion (X 1 $ X 2 ) responding to different between-set relationships. It is performed in two steps. The first step aims at a bidirectional latent variable (Bi-LV) extraction and preparation, by which the between-set covarying relationship is preliminarily set up. In the second step, where a joint postprocessing is performed on the Bi-LV modeling result (here termed Bi-JPLV algorithm), different types of systematic variations are decomposed in each space. Correlated and unique variations are discriminated and evaluated in specific model parameters separately revealing between-set similarity and dissimilarity, respectively. The proposed method gives a good interpretation of the underlying information within each data space from a bidirectional viewpoint, revealing practical application potential. The feasibility and performance of the proposed method are illustrated with both numerical and real industrial cases.

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