Improvement of classification accuracy for stochastic discrimination - Multi-class classification

In this paper, an improved stochastic discrimination (SD) is introduced to reduce the error rate of the standard SD in the context of multi-class classification problem. The learning procedure of the improved SD consists of two stages. In the first stage, a standard SD, but with shorter learning period is carried out to identify an important space where all the misclassified samples are located. In the second stage, the standard SD is modified by (i) restricting sampling in the important space; and (ii) introducing a new discriminant function for samples in the important space. It is shown by mathematical derivation that the new discriminant function has the same mean, but smaller variance than that of standard SD for samples in the important space. It is also analyzed that the smaller the variance of the discriminant function, the lower the error rate of the classifier. Consequently, the proposed improved SD improves standard SD by its capability of achieving higher classification accuracy. Illustrative examples axe provided to demonstrate the effectiveness of the proposed improved SD.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

On improvement of classification accuracy for stochastic discrimination

Stochastic discrimination (SD) depends on a discriminant function for classification. In this paper, an improved SD is introduced to reduce the error rate of the standard SD in the context of a two-class classification problem. The learning procedure of the improved SD consists of two stages. Initially a standard SD, but with shorter learning period is carried out to identify an important space where all the misclassified samples are located. Then the standard SD is modified by 1) restricting sampling in the important space, and 2) introducing a new discriminant function for samples in the important space. It is shown by mathematical derivation that the new discriminant function has the same mean, but with a smaller variance than that of the standard SD for samples in the important space. It is also analyzed that the smaller the variance of the discriminant function, the lower the error rate of the classifier. Consequently, the proposed improved SD improves standard SD by its capability of achieving higher classification accuracy. Illustrative examples are provided to demonstrate the effectiveness of the proposed improved SD.

The multiple team formation problem using sociometry

The Team Formation problem (TFP) has become a well-known problem in the OR literature over the last few years. In this problem, the allocation of multiple individuals that match a required set of skills as a group must be chosen to maximise one or several social positive attributes. Speci�cally, the aim of the current research is two-fold. First, two new dimensions of the TFP are added by considering multiple projects and fractions of people's dedication. This new problem is named the Multiple Team Formation Problem (MTFP). Second, an optimization model consisting in a quadratic objective function, linear constraints and integer variables is proposed for the problem. The optimization model is solved by three algorithms: a Constraint Programming approach provided by a commercial solver, a Local Search heuristic and a Variable Neighbourhood Search metaheuristic. These three algorithms constitute the first attempt to solve the MTFP, being a variable neighbourhood local search metaheuristic the most effi�cient in almost all cases. Applications of this problem commonly appear in real-life situations, particularly with the current and ongoing development of social network analysis. Therefore, this work opens multiple paths for future research.

Probability density function estimation using orthogonal forward regression

Using the classical Parzen window estimate as the target function, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density estimates. The proposed algorithm incrementally minimises a leave-one-out test error score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights are finally updated using the multiplicative nonnegative quadratic programming algorithm, which has the ability to reduce the model size further. Except for the kernel width, the proposed algorithm has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Two examples are used to demonstrate the ability of this regression-based approach to effectively construct a sparse kernel density estimate with comparable accuracy to that of the full-sample optimised Parzen window density estimate.

Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

The effect of adding stinging nettle (Urtica dioica) haylage to a total mixed ration on performance and rumen function of lactating dairy cows

In vitro studies found that inclusion of dried stinging nettle (Urtica dioica) at 100 mg/g dry matter (DM) increased the pH of a rumen fluid inoculated fermentation buffer by 30% and the effect was persistent for 7 days. Our objective was to evaluate the effects of adding stinging nettle haylage to a total mixed ration on feed intake, eating and rumination activity, rumen pH, milk yield, and milk composition of lactating dairy cows. Six lactating Holstein-Friesian cows were used in a replicated 3 × 3 Latin Square design experiment with 3 treatments and 3 week periods. Treatments were a control (C) high-starch (311 g/kg DM) total mixed ration diet and two treatment diets containing 50 (N5) and 100 (N10) g nettle haylage (DM/kg) as a replacement for ryegrass silage (Lolium perenne). There was an increase (linear, P < 0.010) in the proportion of large particles and a reduction in medium (linear, P = 0.045) and fine particles (linear, P = 0.026) in the diet offered with increasing nettle inclusion. A numerical decrease (linear, P = 0.106) in DM intake (DMI) was observed as nettle inclusion in the diet increased. Milk yield averaged 20.3 kg/day and was not affected by diet. There was a decrease (quadratic, P = 0.01) in the time animals spent ruminating as nettle inclusion in the diet increased, in spite of an increase in the number of boli produced daily for the N5 diet (quadratic, P = 0.031). Animals fed the N10 diet spent less time with a rumen pH below 5.5 (P < 0.05) than cows fed the N5 diet. Averaged over an 8.5 h sampling period, there were no changes in the concentration or proportions of acetate or propionate in the rumen, but feeding nettle haylage reduced the concentrations of n-butyrate (quadratic, P < 0.001), i-butyrate (linear, P < 0.009) and n-caproate (linear, P < 0.003). Milk and fat and protein corrected milk yield were not affected when nettles replaced ryegrass silage in the diet of lactating dairy cows, despite a numerical reduction in feed intake. Rumination activity was reduced by the addition of nettle haylage to the diet, which may reflect differences in fibre structure between the nettle haylage and ryegrass silage fed. Changes observed in rumen pH suggest potential benefits of feeding nettle haylage for reducing rumen acidosis. However, the extent to which these effects were due to the fermentability and structure of the nettle haylage compared to the ryegrass silage fed, or a bioactive component of the nettles, is not certain