Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space

By Roman Rosipal, L. Trejo. Journal of machine learning research, 2002

1,023 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a3305c4ae89142b97dd42324eb18bba2e0c298a3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Covariance discriminative learning: A natural and efficient approach to image set classification (2012, methodology): “In the kernel formulation of PLS (KPLS) [19], we use the same notation as in KLDA for consistency and simplicity.”
The Geometry Of Kernel Canonical Correlation Analysis (2003, methodology): “…it can easily be derived that if y is a centered [m × 1] vector and a linear kernel for y is used then the KCCA solution gives the estimator of the least square regression estimator of C X onto y which is equivalent to the kernel principal component regression estimator (Rosipal and Trejo 2001).”
Online chemical modeling environment (OCHEM): web platform for data storage, model development and publishing of chemical information (2011, methodology): “Currently OCHEM supports linear and Kernel Ridge Regression (KRR) [21], ASsociative Neural Networks (ASNN) [22], Kernel Partial Least Squares (KPLS) [23], a correction-based LogP-LIBRARY model [24], Support Vector Machines (SVM) [25], Fast Stagewise Multivariate Linear Regression (FSMLR) and k…”
Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds (2011, methodology): “In order to model the nonlinear relationship between sets of data, a kernelized variant of PLS was first proposed by Rosipal and Trejo [42] and later followed by others [43–46].”
Use of kernel deep convex networks and end-to-end learning for spoken language understanding (2012, unknown): “…discriminant, empirical kernel map, regularized least square classifier, extreme learning machine, and kernel partial least squares regression (e.g. Rosipal As a summary, the K-DCN described in this section has a set of highly desirable properties from the machine learning and pattern recognition…”
On Learning Vector − Valued Functions (2003, methodology): “Recent work by Trejo and Rosipal [23] and Bennett and Embrechts [6] has reconsidered PLS in the context of scalar RKHS.”
Deep Learning-Based Feature Representation and Its Application for Soft Sensor Modeling With Variable-Wise Weighted SAE (2018, methodology): “Also, nonlinear techniques such as kernel PCA [14], kernel PLS [15], and ANN [12] have been developed to describe more complex 1551-3203 © 2018 IEEE.”
Overview and Recent Advances in Partial Least Squares (2005, methodology): “The nonlinear kernel PLS methodology was proposed for the modeling of relations between sets of observed variables, regression and classification problems [34, 35].”
Digging Deep into the Layers of CNNs: In Search of How CNNs Achieve View Invariance (2015, methodology): “4) KPLS-regression measures: Kernel Partial Least Squares (KPLS) (Rosipal & Trejo, 2002) is a supervised regression method.”
Regression Error Characteristic Curves (2003, methodology): “The models were constructed using classic recession SVM trained with different values of e (Vapnik, 1995), linear partial least squares (PLS) (Wold, 1966), kernel partial least squares (KPLS) (Rosipal & Trejo, 2001)1.”
3D skeleton-based human action classification: A survey (2016, methodology): “Partial least squares (PLS) [119] is used to weight the importance of the joints and kernel-PLS SVM [120] is adopted for classi ﬁ cation purposes.”
Support Vector Machines with Applications (2006, methodology): “To name a few, there are extensions to PCA [70], Fisher discriminant analysis [6, 44], cluster analysis [8, 46], partial least squares [66], time series analysis [50], multivariate density estimation [49, 68, 54], classification with asymmetric proximities [52], combination with neural network model”
Kernel Sliced Inverse Regression with Applications to Classification (2008, methodology): “…and Anouar 2000; Roth and Steinhage 2000), kernel canonical correlation analysis (KCCA) (Lai and Fyfe 2000), and kernel partial least squares (KPLS) (Rosipal and Trejo 2001) have been presented in the machine learning and data mining literature (Bach and Jordan 2002; Sch¨olkopf and Smola 2002).”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, unknown): “…in a matrix form, this yields tr = Φ(1) rwr where rwr = w (N) r b ¨ ¨ ¨ b w (1) r and ur = Ψ(1)rvr where rvr = v (N) r b ¨ ¨ ¨ b v (1) r , which can be solved by a kernelized version of the eigenvalue problem, i.e., Φ(1)Φ T (1)Ψ(1)Ψ T (1)tr = λtr and ur = Ψ(1)Ψ T (1)tr [Rosipal and Trejo, 2002].”