Abstract. This work provides a novel derivation based on optimization for the partial least squares (PLS) algorithm for linear regression and the kernel partial least squares (K-PLS) algorithm for nonlinear regression. This derivation makes the PLS algorithm, popularly and successfully used for chemometrics applications, more accessible to machine learning researchers. The work introduces Direct K-PLS, a novel way to kernelize PLS based on direct factorization of the kernel matrix. Computational results and discussion illustrate the relative merits of K-PLS and Direct K-PLS versus closely related kernel methods such as support vector machines and kernel ridge regression. ∗ This work was supported by NSF grant number IIS-9979860. Many thanks to Roman Rosipal, Nello Cristianini, and Johan Suykens for many helpful discussions on PLS and kernel methods, Sean Ekans from Concurrent Pharmaceutical for providing molecule descriptions for the Albumin data set, Curt Breneman and N. Sukumar for generating descriptors for the Albumin data, and Tony Van Gestel for an efficient Gaussian kernel

Large quantities of measured data are being routinely collected in a variety of industries and used for extracting linear models for tasks such as, process control, fault diagnosis and process monitoring. However, existing linear modeling methods do not fully utilize all the information contained in the measurements. This paper presents a new approach for linear process modeling that makes maximum use of available process data and process knowledge. This approach, called Bayesian Latent Variable Regression (BLVR), permits extraction and incorporation of knowledge about the statistical behavior of measurements in developing linear process models. Furthermore, unlike existing methods, BLVR is able to handle noise in inputs and outputs, collinear variables, and incorporate prior knowledge about the regression parameters and measured variables. The resulting model is usually more accurate than that obtained by existing methods including, OLS, PCR and PLS. In this paper, BLVR considers a univariate output, and assumes the underlying variables and noise to be Gaussian, but the approach may be easily used for multivariate outputs and other distributions. An empirical Bayes approach is developed to extract the prior information from historical data or from the maximum likelihood solution of available data. Illustrative examples of steady state, dynamic and inferential modeling demonstrate the superior accuracy of BLVR over existing methods even when the assumptions of Gaussian distributions are violated. The relationship between BLVR and existing methods and opportunities for future work based on the proposed framework are also discussed. 1.

* Information from on-line imaging sensors has great potential for the monitoring and control of quality in spatially distributed systems. The major difficulty lies in the efficient extraction of information from the images, information such as the frequencies of occurrence of specific and often subtle features, and their locations in the product or process space. This paper presents an overview of multivariate image analysis methods based on Principal Component Analysis and Partial Least Squares for decomposing the highly correlated data present in multi-spectral images. The frequencies of occurrence of certain features in the image, regardless of their spatial locations, can be easily monitored in the space of the principal components. The spatial locations of these features can then be obtained by transposing highlighted pixels from the PC score space into the original image space. In this manner it is possible to easily detect and locate even very subtle features from online imaging sensors for the purpose of statistical process control or feedback control of spatial processes. The concepts and potential of the approach are illustrated using a sequence of LANDSAT satellite multispectral images, depicting a pass over a certain region of the earth’s surface. Potential applications in industrial process monitoring using these methods will be discussed from a variety of areas such as pulp and paper sheet products, lumber and polymer films.

www.abeq.org.br/bjche Abstract- Neural networks currently play a major role in the modeling, control and optimization of polymerization processes and in polymer resin development. This paper is a brief tutorial on simple and practical procedures that can help in selecting and training neural networks and addresses complex cases where the application of neural networks has been successful in the field of polymerization. Keywords: Neural network; Polymerization; Simulation.

Combinatorial chemistry needs focused molecular diversity applied to the druglike chemical space (drugspace). A drugspace map can be obtained by systematically applying the same conventions when examining the chemical space, in a manner similar to the Mercator convention in geography: Rules are equivalent to dimensions (e.g., longitude and latitude), while structures are equivalent to objects (e.g., cities and countries). Selected rules include size, lipophilicity, polarizability, charge, flexibility, rigidity, and hydrogen bond capacity. For these, extreme values were set, e.g., maximum molecular weight 1500, calculated negative logarithm of the octanol/water partition between-10 and 20, and up to 30 nonterminal rotatable bonds. Only S, N, O, P, and halogens were considered as elements besides C and H. Selected objects include a set of “satellite” structures and a set of representative drugs (“core ” structures). Satellites, intentionally placed outside drugspace, have extreme values in one or several of the desired properties, while containing druglike chemical fragments. ChemGPS (chemical global positioning system) is a tool that combines these predefined rules and objects to provide a global drugspace map. The ChemGPS drugspace map coordinates are t-scores extracted via principal component analysis (PCA) from 72 descriptors that evaluate the above-mentioned rules on a total set of 423 satellite and core structures. Global ChemGPS scores describe well the latent structures extracted with PCA for a set of 8599 monocarboxylates, a set of 45 heteroaromatic compounds, and for 87 R-amino acids. ChemGPS positions novel structures in drugspace via PCA-score prediction, providing a unique mapping device for the druglike chemical space. ChemGPS scores are comparable across a large number of chemicals and do not change as new structures are predicted, making this tool a wellsuited reference system for comparing multiple libraries and for keeping track of previously explored regions of the chemical space.

Orthogonal projections to latent structures as a strategy for microarray data normalization

in grossly underdetermined systems: