Sequential minimal optimization

Diverse Three TAACF datasets from PubChem 179 Naive Bayes, random forest, sequential minimal optimization, J48 decision tree. Used to create three models with different datasets. Naive Bayes had external test set accuracy 73-82.7, random forest 60.7-82.7%, SMO 55.9-83.3, and J48 61.3-80% Periwal et al. (36, 37)... 

The sequential minimal optimization (SMO) algorithm is derived from the idea of the decomposition method to its extreme and the optimization for a minimal subset of just two points at each iteration. It was first devised by Platt [110], and applied to text categorization problems. SMO is a simple algorithm that can quickly solve the SVM QP problem without any extra matrix storage and without using numerical QP optimization steps at all. SMO decomposes the overall QP problem into QP sub-problems, using Osuna s theorem to ensure convergence. 

Platt, J. (1998). Fast training of support vector machines using sequential minimal optimization, edited by Scholkopf, B., Burges, C. and Smola, A., Advances in kernel methods support vector learning. MIT Press. 

Burges, and A. J. Smola, Eds., MIT Press, Cambridge, Massachusetts, 1999, pp. 185-208. Fast Training of Support Vector Machines Using Sequential Minimal Optimization. 

The basic concept of the Nesbet-Shavitt method is based on iterative sequential optimization of the eigenvector elements. If the quantity p(C)=CTHC/CTC is known for some C° and p°=p(C°) is below all the diagonal elements of H, then sequential minimization of p(C) with respect to each element Ci [i.e. solving... 

Another simple optimization technique is to select n fixed search directions (usually the coordinate axes) for an objective function of n variables. Then fix) is minimized in each search direction sequentially using a one-dimensional search. This method is effective for a quadratic function of the form... 

Another useful program (E04HAA) provides constrained optimization with bounds for each parameter using a sequential penalty function technique, which effectively operates around unconstrained minimization cycles. 

In general, an objective function in the optimization problem can be chosen, depending on the nature of the problem. Here, two practical optimization problems related to batch operation maximization of product concentration in a fixed batch time and minimization of batch operation time given amount of desired product, are considered to determine an optimal reactor temperature profile. The first problem formulation is applied to a situation where we need to increase the amount of desired product while batch operation time is fixed. This is due to the limitation of complete production line in a sequential processing. However, in some circumstances, we need to reduce the duration of batch run to allow the operation of more runs per day. This requirement leads to the minimum time optimization problem. These problems can be described in details as follows. 

The hits identified by screening a small percentage of the database can be followed up using 2D methods and/or 3D pharmacophore-based further exploration of the database to retrieve more actives in a sequential screening fashion. The goal is to minimize the number of compounds screened and maximize the number of actives retrieved at the end of the screening rounds such that the relevant chemical space is explored with an optimal use of resources. 

This criterion may be used during a sequential optimization process (see chapter 5), leading to an acceptable result and to completion of the optimization process once the threshold value has been reached. Alternatively, it may be used to establish ranges of conditions in the parameter space for which the result will be acceptable. This latter approach has been followed by Glajch et al. [415], by Haddad et al. [424] and by Weyland et al. [425] and was referred to as resolution mapping by the former. Within the permitted area(s) secondary criteria are then required to select the optimum conditions. For example, the conditions at which the k value of the last peak (k is minimal while the minimum value for Rsexceeds 1 may be chosen as the optimum. Such a composite criterion can be described as... 

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