Adaptive least squares

So far, we have considered the QSAR modeling of continuous biological data, that is, where the toxicity value is a number such as an LD50. However, some data are not continuous but are binary (e.g., toxic/ nontoxic) a common example is carcinogenicity, for which test results are almost invariably reported in this way. Clearly, one cannot perform, say, MLR on such classification data (although a method called fuzzy adaptive least squares [70] can be used). A number of methods are available for the modeling of classification data. 

Hirono, S., Nakagome, I., Hirano, H. Matsuhita, Y., Yoshi, F., Moriguchi, I., Non-congeneric structure-pharmacokinetic property correlation studies using fuzzy adaptive least squared oral bioavailability, Biol. Pharm. Bull. 1994, 37, 306—309. 

Prediction of bioavailability from molecular structure is quite difficult, since bioavailability depends on absorption and first-pass clearance [141]. By applying fuzzy adaptive least squares , Yoshida and Topliss generated a QSAR model using logD at pH 7.4 and 6.5 as input for physicochemical properties and the presence/absence of certain functional groups as structural input. They achieved a classification of drugs into one of four bioavailability categories with an overall accuracy of 60% [142]. 

Canonical Correlation Analysis Principal Component Regressionb Classification and Regression Trees (CART) Linear Learning Machine Neural Networks Adaptive Least Squares Genetic Programming Logistic Regression... 

Moriguchi, I., Hirono, S., Liu, Q. and Nakagome, I. (1992a). Fuzzy Adaptive Least Squares and Its Application to Structure-Activity Studies. Quant.Struct.-Act.Relat., 11,325-331. 

Qian, L., Hirono, S., Matsushita, Y. and Moriguchi, I. (1992). QSARs Based on Fuzzy Adaptive Least Squares Analysis for the Aquatic Toxicity of Organic Chemicals. Environ.Toxicol. Chem., 11, 953-959. 

One of the earliest in silico models of human bioavailability was reported by Hirono and coworkers [26]. This study employed a set of 188 compounds that were classified as low (<50%), medium (50-89%), or well (>90%) absorbed and used a classification routine, fuzzy adaptive least squares, to generate discriminant functions. The molecules were described by their physicochemical properties and substructural descriptors, which meant that functional groups or substructures that enhanced bioavailability (e.g., saturated carbon atoms in side chains) or reduced it (e.g., aliphatic hydroxyl groups) could be identified. The performance varied between the three classes with the lowest success for the well-absorbed compounds, perhaps the most important group of the three. 

Moriguchi, I. Fuzzy adaptive least-squares and its use in QSAR. In Computer Aided Innovation of Neiv Materials II. Proceedings of the International Conference on Exhibited and Computed Applied Materials, Molecular Science, and Engineering (M. Doyama, J. Kihara, M. Tanaka, and R. Yamamoto, Eds.), 2nd ed., pp. 1121-1126. North-Holland, Amsterdam, 1993. 

The adaptive least squares (ALS) method [396, 585 — 588] is a modification of discriminant analysis which separates several activity classes e.g. data ordered by a rating score) by a single discriminant function. The method has been compared with ordinary regression analysis, linear discriminant analysis, and other multivariate statistical approaches in most cases the ALS approach was found to be superior to categorize any numbers of classes of ordered data. ORMUCS (ordered multicate-gorial classification using simplex technique) [589] is an ALS-related approach which... 

Gruen, A., 1984 Adaptive least squares correlation - concept and first results. Intermediate Report, prepared for Helava Assoc., Inc., March 1984. 

Gruen, A., 1985a Adaptive least squares correlation - a powerful image matching technique. South African Journal of Photogrammetry, Remote Sensing and Cartography, 14 (3), pp. 175-187. 

I. Moriguchi, K. Komatsu, and Y. Matushita, J. Med. Chem., 23,20 (1980). Adaptive Least Squares Method Applied to Structure-Activity Correlation of Hypotensive N-Alkyl-N"-cyano-... 

Adaptive Least Squares method (5), is shown in equation 1. Equation 1 shows that herbicidal activity is maximized when the hydrophobic parameter of a substituent n has an optimum value of 1.75,... 

Liu et al. described the functional-link net architecture (FUNCLINK) (158). They claimed that, compared with methods such as adaptive least squares and back-propagation neural nets, FUNCLINK exhibited good recognition and high predictivity. However, Manallack and Livingstone found two disadvantages to the FUNCLINK technique (159). First, the natural ability of neural networks to develop nonlinear relationships is removed with FUNCLINK as these must be specified. Second, the large number of enhanced parameters produced by FUNCLINK increases the possibility of chance effects. They concluded that FUNCLINK adds little to the field of QSAR data analysis. 

Sekiya, T. Hata, S. Yamada, S. P3nimidine Derivatives. VII. Structure-Activity Relationship of Hypoglycaemic 4-Amino-2-(l-piperazinyl)pyrimidines Investigated by the Adaptive Least-Squares Method . Chem. Pharm. Bull. 1983, 31, 2432-2437. 

The fuzzy adaptive least-squares method (FALS) was developed to correlate structure with activity ratings of chemicals. liie QSAR is described by a FALS discriminant function according to... 

Moriguchi, L, Hirono, S. (1995). Fuzzy adaptive least squares and its use in quantitative structure-activity relationships In Fujita, T. (Ed.) QSAR and Drug Design - New Developments and Applications, Elsevier Science, B. V. 

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