Locally Linear Embedding for dimensionality reduction in QSAR

Current practice in Quantitative Structure Activity Relationship (QSAR) methods usually involves generating a great number of chemical descriptors and then cutting them back with variable selection techniques. Variable selection is an effective method to reduce the dimensionality but may discard some valuable information. This paper introduces Locally Linear Embedding (LLE), a local non-linear dimensionality reduction technique, that can statistically discover a low-dimensional representation of the chemical data. LLE is shown to create more stable representations than other non-linear dimensionality reduction algorithms, and to be capable of capturing non-linearity in chemical data.

[1]  Nello Cristianini,et al.  On the Concentration of Spectral Properties , 2001, NIPS.

[2]  Nicolas Le Roux,et al.  Learning Eigenfunctions Links Spectral Embedding and Kernel PCA , 2004, Neural Computation.

[3]  John Shawe-Taylor,et al.  The Stability of Kernel Principal Components Analysis and its Relation to the Process Eigenspectrum , 2002, NIPS.

[4]  D. Hoekman.  Exploring QSAR Fundamentals and Applications in Chemistry and Biology, Volume 1. Hydrophobic, Electronic and Steric Constants, Volume 2 J. Am. Chem. Soc. 1995, 117, 9782 , 1996 .

[5]  Lawrence K. Saul,et al.  Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifold , 2003, J. Mach. Learn. Res..

[6]  J. Friedman,et al.  A Statistical View of Some Chemometrics Regression Tools , 1993 .

[7]  Gilles Blanchard,et al.  Statistical properties of Kernel Prinicipal Component Analysis , 2019 .

[9]  S. J. Ireland,et al.  Syntheses, pharmacological evaluation and molecular modelling of substituted 6-alkoxyimidazo[1,2-b]pyridazines as new ligands for the benzodiazepine receptor , 1996 .

[10]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[11]  T. Halgren.  Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94 , 1996, J. Comput. Chem..

[12]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[13]  Frank R. Burden,et al.  Use of Automatic Relevance Determination in QSAR Studies Using Bayesian Neural Networks , 2000, J. Chem. Inf. Comput. Sci..

[14]  Gilles Blanchard,et al.  Statistical properties of kernel principal component analysis , 2007, Machine Learning.

[15]  Matthias W. Seeger,et al.  Using the Nyström Method to Speed Up Kernel Machines , 2000, NIPS.

[16]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[17]  F E Blaney,et al.  Comparison of azabicyclic esters and oxadiazoles as ligands for the muscarinic receptor. , 1991, Journal of medicinal chemistry.

[18]  Nicolas Le Roux,et al.  Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering , 2003, NIPS.

[19]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.