Nonlinear model structure detection using optimum experimental design and orthogonal least squares

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the subset selection cost function includes an A-optimality design criterion to minimize the variance of the parameter estimates that ensures the adequacy and parsimony of the final model. An illustrative example is included to demonstrate the effectiveness of the new approach.

Iterative Methods for Equality-Constrained Least Squares Problems

We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn–Tucker equations associated with the LSE problem. We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.

A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method

In this paper a modified algorithm is suggested for developing polynomial neural network (PNN) models. Optimal partial description (PD) modeling is introduced at each layer of the PNN expansion, a task accomplished using the orthogonal least squares (OLS) method. Based on the initial PD models determined by the polynomial order and the number of PD inputs, OLS selects the most significant regressor terms reducing the output error variance. The method produces PNN models exhibiting a high level of accuracy and superior generalization capabilities. Additionally, parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional PNN algorithm. Three benchmark examples are elaborated, including modeling of the gas furnace process as well as the iris and wine classification problems. Extensive simulation results and comparison with other methods in the literature, demonstrate the effectiveness of the suggested modeling approach.

Evaluation of milk compositional variables on coagulation properties using partial least squares

The aim of this study was to investigate the effects of numerous milk compositional factors on milk coagulation properties using Partial Least Squares (PLS). Milk from herds of Jersey and Holstein-Friesian cattle was collected across the year and blended (n=55), to maximize variation in composition and coagulation. The milk was analysed for casein, protein, fat, titratable acidity, lactose, Ca2+, urea content, micelles size, fat globule size, somatic cell count and pH. Milk coagulation properties were defined as coagulation time, curd firmness and curd firmness rate measured by a controlled strain rheometer. The models derived from PLS had higher predictive power than previous models demonstrating the value of measuring more milk components. In addition to the well-established relationships with casein and protein levels, CMS and fat globule size were found to have as strong impact on all of the three models. The study also found a positive impact of fat on milk coagulation properties and a strong relationship between lactose and curd firmness, and urea and curd firmness rate, all of which warrant further investigation due to current lack of knowledge of the underlying mechanism. These findings demonstrate the importance of using a wider range of milk compositional variable for the prediction of the milk coagulation properties, and hence as indicators of milk suitability for cheese making.

Zero attracting recursive least squares algorithms

The l1-norm sparsity constraint is a widely used technique for constructing sparse models. In this contribution, two zero-attracting recursive least squares algorithms, referred to as ZA-RLS-I and ZA-RLS-II, are derived by employing the l1-norm of parameter vector constraint to facilitate the model sparsity. In order to achieve a closed-form solution, the l1-norm of the parameter vector is approximated by an adaptively weighted l2-norm, in which the weighting factors are set as the inversion of the associated l1-norm of parameter estimates that are readily available in the adaptive learning environment. ZA-RLS-II is computationally more efficient than ZA-RLS-I by exploiting the known results from linear algebra as well as the sparsity of the system. The proposed algorithms are proven to converge, and adaptive sparse channel estimation is used to demonstrate the effectiveness of the proposed approach.

A constrained recursive least squares algorithm for adaptive combination of multiple models

In this paper, we develop a novel constrained recursive least squares algorithm for adaptively combining a set of given multiple models. With data available in an online fashion, the linear combination coefficients of submodels are adapted via the proposed algorithm.We propose to minimize the mean square error with a forgetting factor, and apply the sum to one constraint to the combination parameters. Moreover an l1-norm constraint to the combination parameters is also applied with the aim to achieve sparsity of multiple models so that only a subset of models may be selected into the final model. Then a weighted l2-norm is applied as an approximation to the l1-norm term. As such at each time step, a closed solution of the model combination parameters is available. The contribution of this paper is to derive the proposed constrained recursive least squares algorithm that is computational efficient by exploiting matrix theory. The effectiveness of the approach has been demonstrated using both simulated and real time series examples.

Chemotaxonomic relationships in Celastraceae inferred from principal component analysis (PCA) and partial least squares (PLS)

This paper describes a chemotaxonomic analysis of a database of triterpenoid compounds from the Celastraceae family using principal component analysis (PCA). The numbers of occurrences of thirty types of triterpene skeleton in different tribes of the family were used as variables. The study shows that PCA applied to chemical data can contribute to an intrafamilial classification of Celastraceae, once some questionable taxa affinity was observed, from chemotaxonomic inferences about genera and they are in agreement with the phylogeny previously proposed. The inclusion of Hippocrateaceae within Celastraceae is supported by the triterpene chemistry.

Monotone approximation of aggregation operators using least squares splines

The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.

Least squares splines with free knots: global optimization approach

Splines with free knots have been extensively studied in regard to calculating the optimal knot positions. The dependence of the accuracy of approximation on the knot distribution is highly nonlinear, and optimisation techniques face a difficult problem of multiple local minima. The domain of the problem is a simplex, which adds to the complexity. We have applied a recently developed cutting angle method of deterministic global optimisation, which allows one to solve a wide class of optimisation problems on a simplex. The results of the cutting angle method are subsequently improved by local discrete gradient method. The resulting algorithm is sufficiently fast and guarantees that the global minimum has been reached. The results of numerical experiments are presented.

Shape preserving approximation using least squares splines

Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.

Should partial least squares be used for analysing psychological constructs?

This paper critically examines an analytical tool - partial least squares regression, or P LS - that is increasingly being used in the academic business literature to validate measures of psychological constructs, and to test hypotheses based on these. The paper provides a contextual and historical review of the resurgence of P LS, and explores several of the claims made by its developers and supporters when it was first promoted in the 1980s, and, more recently, when it reappeared in the information systems literature. Many claims appear plausible but rest on non-mainstream uses of terms and concepts taken from the psychometric field. The paper also canvasses why P LS is a poor analytical tool for research that involves psychological constructs.

Partial least squares and principal components analysis of wine vintage by high performance liquid chromatography with chemiluminescence detection

HPLC with acidic potassium permanganate chemiluminescence detection was employed to analyse 17 Cabernet Sauvignon wines across a range of vintages (1971–2003). Partial least squares regression analysis and principal components analysis was used in order to investigate the relationship between wine composition and vintage. Tartaric acid, vanillic acid, catechin, sinapic acid, ethyl gallate, myricetin, procyanadin B and resveratrol were found to be important components in terms of differences between the vintages.