Implementing PLS for distance-based regression: computational issues

Val, Eva Boj del; Grané, Aurea; Fortiana, Josep; Bielsa, M. Mercè Claramunt

doi:10.1007/s00180-007-0035-2

Cited by 7 publications

(2 citation statements)

References 10 publications

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“…) outof-core algorithms analogous to those presented in [26] for DB-PLS regression provide a workable path of solution. Larger sizes require special subsampling.…”

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confidence: 99%

Local Linear Functional Regression Based on Weighted Distance-based Regression

Val¹,

Delicado²,

Fortiana³

2008

Contributions to Statistics

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We consider the problem of nonparametrically predicting a scalar response variable y from a functional predictor χ. We have n observations (χ i , y i ) and we assign a weightis a semi-metric, K is a kernel function and h is the bandwidth. Then we fit a Weighted (Linear) Distance-Based Regression, where the weights are as above and the distances are given by a possibly different semi-metric. This approach can be extended to nonparametric predictions from other kind of explanatory variables (e.g., data of mixed type) in a natural way.

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“…) outof-core algorithms analogous to those presented in [26] for DB-PLS regression provide a workable path of solution. Larger sizes require special subsampling.…”

mentioning

confidence: 99%

Local Linear Functional Regression Based on Weighted Distance-based Regression

Val¹,

Delicado²,

Fortiana³

2008

Contributions to Statistics

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“…Se desarrollaron varios métodos para estos procesos de cuantificación, dentro de los cuales se encuentran los denominados Non Metric PLS (NM-PLS) tales como: Dual Scaling (Enfoque Clásico, HOMALS, …), Kruskal and Shepard, Prinqual, Princals entre otros (Gifi 1990, Linting et al 2007) y los más recientes denominados NM-NIPALS, NM-PLS1, NM-PLS2 y NM-PLSPM de Russolillo 2009. En general estos métodos se caracterizan por cuantificar las variables cualitativas tomando sólo la primera componente principal en la transformación. Cuadras 1989, Boj et al 2007, presentarón métodos de clasificación y regresión basados en distancia, con datos mixtos.…”

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Análisis conjunto de múltiples tablas de datos mixtos mediante PLS

González Rojas

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The fundamental content of this thesis corresponds to the development of the GNM-NIPALIS, GNM-PLS2 and GNM-RGCCA methods, used to quantify qualitative variables parting from the first k components given by the appropriate methods in the analysis of J matrices of mixed data. These methods denominated GNM-PLS (General Non Metric Partial Least Squares) are an extension of the NM-PLS methods that only take the first principal component in the quantification function. The transformation of the qualitative variables is done through optimization processes, usually maximizing functions of covariance or correlation, taking advantage of the flexibility of the PLS algorithms and keeping the properties of group belonging and order if it exists; The metric variables are keep their original state as well, excepting standardization. GNM-NIPALS has been created for the purpose of treating one (J = 1) mixed data matrix through the quantification via ACP type reconstruction of the qualitative variables parting from a k components aggregated function. GNM-PLS2 relates two (J = 2) mixed data sets Y~X through PLS regression, quantifying the qualitative variables of a space with the first H PLS components aggregated function of the other space, obtained through cross validation under PLS2 regression. When the endogenous matrix Y contains only one answer variable the method is denominated GNM-PLS1. Finally, in order to analyze more than two blocks (J = 2) of mixed data Y~X1+...+XJ through their latent variables (LV) the GNM-RGCCA was created, based on the RGCCA (Regularized Generalized Canonical Correlation Analysis) method, that modifies the PLS-PM algorithm implementing the new mode A and specifies the covariance or correlation maximization functions related to the process. The quantification of the qualitative variables on each Xj block is done through the inner Zj = Σj ej Yj function, which has J dimension due to the aggregation of the outer Yj estimations. Zj, as well as Yj estimate the ξj component associated to the j-th block. El contenido fundamental de esta tesis corresponde al desarrollo de los métodos GNM-NIPALS, GNM-PLS2 y GNM-RGCCA para la cuantificación de las variables cualitativas a partir de las primeras k componentes proporcionadas por los métodos apropiados en el análisis de J matrices de datos mixtos. Estos métodos denominados GNM-PLS (General Non Metric Partial Least Squares) son una extensión de los métodos NM-PLS que toman sólo la primera componente principal en la función de cuantificación. La trasformación de las variables cualitativas se lleva a cabo mediante procesos de optimización maximizando generalmente funciones de covarianza o correlación, aprovechando la flexibilidad de los algoritmos PLS y conservando las propiedades de pertenencia grupal y orden si existe; así mismo se conservan las variables métricas en su estado original excepto por estandarización. GNM-NIPALS ha sido creado para el tratamiento de una (J=1) matriz de datos mixtos mediante la cuantificación vía reconstitución tipo ACP de las variables cualitativas a partir de una función agregada de k componentes. GNM-PLS2 relaciona dos (J=2) conjuntos de datos mixtos Y~X mediante regresión PLS, cuantificando las variables cualitativas de un espacio con la función agregada de las primeras H componentes PLS del otro espacio, obtenidas por validación cruzada bajo regresión PLS2. Cuando la matriz endógena Y contiene sólo una variable de respuesta el método se denomina GNM-PLS1. Finalmente para el análisis de más de dos bloques (J>2) de datos mixtos Y~X1+...+XJ a través de sus variables latentes (LV) se implementa el método NM-RGCCA basado en el método RGCCA (Regularized Generalized Canonical Correlation Analysis) que modifica el algoritmo PLS-PM implementando el nuevo modo A y especifica las funciones de maximización de covarianzas o correlaciones asociadas al proceso. La cuantificación de las variables cualitativas en cada bloque Xj se realiza mediante la función inner Zj de dimensión J debido a la agregación de las estimaciones outer Yj. Tanto Zj como Yj estiman la componente ξj asociad al j-ésimo bloque.

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Distinct microbial communities alter litter decomposition rates in a fertilized coastal plain wetland

Koceja¹,

Bledsoe²,

Goodwillie³

et al. 2021

Ecosphere

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Human activities have led to increased deposition of nitrogen (N) and phosphorus (P) into soils. Nutrient enrichment of soils is known to increase plant biomass and rates of microbial litter decomposition. However, interacting effects of hydrologic position and associated changes to soil moisture can constrain microbial activity and lead to unexpected nutrient feedbacks on microbial community structurefunction relationships. Examining feedbacks of nutrient enrichment on decomposition rates is essential for predicting microbial contributions to carbon (C) cycling as atmospheric deposition of nutrients persists. This study explored how long-term nutrient addition and contrasting litter chemical composition influenced soil bacterial community structure and function. We hypothesized that long-term nutrient enrichment of low fertility soils alters bacterial community structure and leads to higher rates of litter decomposition especially for low C:N litter, but low-nutrient and dry conditions limit microbial decomposition of high C:N ratio litter. We leveraged a long-term fertilization experiment to test how nutrient enrichment and hydrologic manipulation (due to ditches) affected decomposition and soil bacterial community structure in a nutrient-poor coastal plain wetland. We conducted a litter bag experiment and characterized litter-associated and bulk soil microbiomes using 16S rRNA bacterial sequencing and quantified litter mass losses and soil physicochemical properties. Results revealed that distinct bacterial communities were involved in decomposing higher C:N ratio litter more quickly in fertilized compared to unfertilized soils especially under drier soil conditions, while decomposition rates of lower C:N ratio litter were similar between fertilized and unfertilized plots. Bacterial community structure in part explained litter decomposition rates, and long-term fertilization and drier hydrologic status affected bacterial diversity and increased decomposition rates. However, community composition associated with high C:N litter was similar in wetter plots with available nitrate detected, regardless of fertilization treatment. This study provides insight into long-term fertilization effects on soil bacterial diversity and composition, decomposition, and the increased potential for soil C loss as nutrient enrichment and hydrology interact to affect historically lownutrient ecosystems.

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Implementing PLS for distance-based regression: computational issues

Cited by 7 publications

References 10 publications

Local Linear Functional Regression Based on Weighted Distance-based Regression

Local Linear Functional Regression Based on Weighted Distance-based Regression

Análisis conjunto de múltiples tablas de datos mixtos mediante PLS

Distinct microbial communities alter litter decomposition rates in a fertilized coastal plain wetland

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