Linear and non-linear canonical correlation analysis:an exploratory tool for the analysis of group-structured data

Luijtens, K.; Symons, F.; Vuylsteke-Wauters, M

doi:10.1080/757583648

Cited by 8 publications

(6 citation statements)

References 9 publications

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“…In this paper, we have used advanced, multivariate, data-analytical techniques (8,24,32,33) to describe, represent, and analyze immunological lymphocyte profiles in two-dimensional correlation biplots. This approach offers the considerable advantage of concisely representing the complex lymphocyte profile of each subject investigated.…”

Section: Discussionmentioning

confidence: 99%

“…The biplot is a procedure introduced by Gabriel (8) that graphically describes both relationships among multidimensional observations (''objects'') and relationships among numerical variables (''descriptors'') of any data table consisting of n rows or objects and p columns or descriptors (n 3 p data matrix). This procedure was further elaborated by Symons (24,32,33), who obtained easily interpretable biplot versions. Given an n 3 p data matrix, Y, with p standardized columns or descriptors y i (mean 5 0, and sum of squares 5 1) describing n objects, and an n 3 2 matrix, Z, with two uncorrelated standardized columns or descriptors, z 1 and z 2 (corresponding to the first two normalized principal components of Y) describing the same n objects, he proposed to obtain a 2 3 p matrix Z T Y 5 U, with columns u i having as elements the correlations between the corresponding descriptors, y i , and each of the two descriptors, z 1 and z 2 .…”

Section: Multivariate Data-analytical Techniquesmentioning

confidence: 99%

“…the first two standardized principal components (''factors'') of Y as the columns of Z in our applications, this sum was maximally approximated. This allowed for reconstructions showing the highest possible global fit (24,32,33). The global fitness of the two-dimensional reconstruction is evaluated by the sum of the first two eigenvalues of Y T Y with respect to the total sum (p).…”

Section: Multivariate Data-analytical Techniquesmentioning

confidence: 99%

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Multivariate reconstruction of lymphocyte profiles in a two-dimensional graphical model as a tool for the investigation of lymphocyte subset distribution in health and disease

Hove¹,

Symons

Vandenberghe³

et al. 1997

Cytometry

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Advanced multivariate data‐analytical techniques are proposed to concisely represent and evaluate complex lymphocyte profiles (i.e., compound lymphocyte subset distributions) of individual subjects in easily interpretable, two‐dimensional, graphical correlation biplots. The lymphocyte profile of each subject is represented by its location in the model, and the score of a subject for a particular lymphocyte subset is inferred from the perpendicular projection on a rotated axis that coincides with this lymphocyte subset. Simultaneously, the model yields information about the correlation between the lymphocyte subsets. Furthermore, individuals with aberrant lymphocyte profiles can be easily identified. In case studies of 80 healthy donors and of 40 patients with multiple myeloma, 10 patients with monoclonal gammopathy of undetermined significance, and 50 age‐ and sex‐matched healthy donors, reconstruction of the two‐dimensional lymphocyte profiles from 27 flow‐cytometric characterized lymphocyte subsets succeeded in representing 43% and 51% of the total information (variability) contained within the 80 × 27 (= 2,160) and 100 × 27 (= 2,700) flow cytometry measurements, respectively. It is concluded from the present studies that the correlation biplot represents a unique and powerful tool to concisely describe, represent, and analyze complex lymphocyte profiles of individual subjects and the heterogeneity in lymphocyte profiles among these subjects. Cytometry 28:220–227, 1997. © 1997 Wiley‐Liss, Inc.

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Section: Discussionmentioning

confidence: 99%

Section: Multivariate Data-analytical Techniquesmentioning

confidence: 99%

Section: Multivariate Data-analytical Techniquesmentioning

confidence: 99%

See 1 more Smart Citation

Multivariate reconstruction of lymphocyte profiles in a two-dimensional graphical model as a tool for the investigation of lymphocyte subset distribution in health and disease

Hove¹,

Symons

Vandenberghe³

et al. 1997

Cytometry

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“…A linear canonical correlation analysis (CCA) was used to construct a Gabriel biplot with the data of the phosphatase activity in the perlite, which we considered as multivariate group-structured data (Luijtens, Symons & Vuylsteke-Wauters 1994). The first set of variables (P treatments) in the CCA contained the numerical data of enzyme activity, the second set of variables, the indicator matrix, was constructed from the variable 'fungus treatment'.…”

Section: Data Analysis and Statisticsmentioning

confidence: 99%

The use of inositol hexaphosphate as a phosphorus source by mycorrhizal and non‐mycorrhizal Scots Pine (Pinus sylvestris)

Colpaert¹,

Laere²,

Tichelen

et al. 1997

Functional Ecology

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Summary 1.The external mycelia of the ectomycorrhizal fungi Thelephora terrestris and Suillus luteus, associated with Pinus sylvestris roots, exhibited a substantial extracellular acid phosphatase activity. The activity was positively correlated with the ergosterol concentration in the growth substratum and decreased with an increasing P nutrition. 2. The pioneer species T. terrestris grew best at a high P i nutrition level whereas S. luteus, a 'late-stage' mycobiont, produced more active biomass at a low P i nutrition level. 3. The phytase activity of the external mycelia could not be detected; at the root surface a phytase activity was observed. Mycorrhizas had significantly higher activities than uninfected roots. 4. The addition of a relatively high concentration of a soluble phytate to the growth substratum resulted in an increased relative growth rate (RGR) in both mycorrhizal and non-mycorrhizal plants. The influence of the mycorrhizal fungi on the use of the phytate-P was small, despite the phytase activity of the mycorrhizal feeder roots. 5. The addition of phytate fixed on a HPLC resin did not result in an increase of the RGR and P uptake neither in the non-mycorrhizal nor in the mycorrhizal Pines. The experiment did not support the hypothesis that phytate, which has a low solubility in soils, is a useful P source for ectomycorrhizal plants.

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“…There exist multiple ways of incorporating nonlinear relations, ranging from the more traditional (Luijtens et al 1994) to more recent approaches based on neural networks (Cannon and Hsieh 2008;Hsieh 2000). Modeling nonlinear relationships is generally more complex than that of linear relationships, because care must be taken to avoid overfitting.…”

Section: O N T H L Y W E a T H E R R E V I E W Volume 00mentioning

confidence: 99%

Model Tuning with Canonical Correlation Analysis

Marzban

Sandgathe

Doyle

2014

Monthly Weather Review

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Knowledge of the relationship between model parameters and forecast quantities is useful because it can aid in setting the values of the former for the purpose of having a desired effect on the latter. Here it is proposed that a well-established multivariate statistical method known as canonical correlation analysis can be formulated to gauge the strength of that relationship. The method is applied to several model parameters in the Coupled Ocean-Atmosphere Mesoscale Prediction System (COAMPS) for the purpose of ''controlling'' three forecast quantities: 1) convective precipitation, 2) stable precipitation, and 3) snow. It is shown that the model parameters employed here can be set to affect the sum, and the difference between convective and stable precipitation, while keeping snow mostly constant; a different combination of model parameters is shown to mostly affect the difference between stable precipitation and snow, with minimal effect on convective precipitation. In short, the proposed method cannot only capture the complex relationship between model parameters and forecast quantities, it can also be utilized to optimally control certain combinations of the latter.

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Linear and non-linear canonical correlation analysis:an exploratory tool for the analysis of group-structured data

Cited by 8 publications

References 9 publications

Multivariate reconstruction of lymphocyte profiles in a two-dimensional graphical model as a tool for the investigation of lymphocyte subset distribution in health and disease

Multivariate reconstruction of lymphocyte profiles in a two-dimensional graphical model as a tool for the investigation of lymphocyte subset distribution in health and disease

The use of inositol hexaphosphate as a phosphorus source by mycorrhizal and non‐mycorrhizal Scots Pine (Pinus sylvestris)

Model Tuning with Canonical Correlation Analysis

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