Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, "Cross validatory choice and assessment of statistical predictions", J. R. Stast. Soc., Ser. B, 36, pp. 117-147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.

Givens rotation based fast backward elimination algorithm for RBF neural network pruning

A fast backward elimination algorithm is introduced based on a QR decomposition and Givens transformations to prune radial-basis-function networks. Nodes are sequentially removed using an increment of error variance criterion. The procedure is terminated by using a prediction risk criterion so as to obtain a model structure with good generalisation properties. The algorithm can be used to postprocess radial basis centres selected using a k-means routine and, in this mode, it provides a hybrid supervised centre selection approach.

Gas-Phase Nucleophilic and Elimination Reactions in Simple Alkyl Nitrates

There has been increasing interest in the gas-phase reactivity of alkyl nitrates because of their well-known applications as explosives and because of then role in atmospheric and in marine processes This manuscript describes an experimental study by FT-ICR techniques of the gas-phase reactions of OH(-) and F(-) with methyl and ethyl Innate For methyl nitrate, the main reaction channel is found to be an elimination process promoted by abstraction of an a proton from the methyl group. Nucleophilic displacement of nitrate anion through an S(N)2 process at the carbon center Is also found to he an important reaction channel with methyl nitrate In ethyl nitrate, Ruination of NO(3)(-) is greatly enhanced and this is attributed to the ease of an E2-type elimination process promoted by proton abstraction at the beta position of the ethyl group. Theoretical calculations at the MP2/6-311+G(3df,2p)//MP2/6-31+G(d) level of theory ale consistent with the relative importance of the reaction channels and suggest that these reactions proceed through a double well potential The calculations also predict that nucleophilic attack by OH(-) at the nitrogen center (Sn2@N) is energetically the rueful ad pathway but experiments with (18)OH(-) showed no evidence for this channel. Single-point calculations reveal a strong preference for approach to the emboli center and may explain the lack of reactivity at the nitrogen center. Calculations were also carried out or NH(2)(-) and SH(-) to establish the reactivity pattern to provide a better understanding of environmentally relevant nitrate esters.

Isolating conifer DNA: a superior polysaccharide elimination method

Genomic DNA was isolated from frozen needles of maturePinus radiata clones using a modified extraction technique incorporating cetyltrimethylammonium bromide (CTAB) for cell lysis. A high sodium chloride concentration (2 M) was used at 2 stages of the extraction procedure to eradicate polysaccharides, yielding pure genomic DNA suitable for restriction enzyme digestion and PCR amplification. Extractions were scaled down to suit 1.5-mL Eppendorf tubes, allowing easier handling and enhanced sterility.

The charge effect of cationic surfactants on the elimination of fibre beads in the electrospinning of polystyrene

Polystyrene nanofibres were electrospun with the inclusion of cationic surfactants, dodecyltrimethylammonium bromide (DTAB) or tetrabutylammonium chloride (TBAC), in the polymer solution. A small amount of cationic surfactant effectively stopped the formation of beaded fibres during the electrospinning. The cationic surfactants were also found to improve the solution conductivity, but had no effect on the viscosity. Only DTAB had an effect on the surface tension of the polymer solution, the surface tension decreasing slightly with an increase in the concentration of DTAB.

The formation of beaded fibres was attributed to an insufficient stretch of the filaments during the whipping of the jet, due to a low charge density. Adding the cationic surfactants improved the net charge density that enhanced the whipping instability. The jet was stretched under stronger charge repulsion and at a higher speed, resulting in an exhaustion of the bead structure. In addition, a polymer/surfactant interaction was found in the polystyrene–DTAB solution system, while this interaction was not found in the polystyrene–TBAC system. The polymer/surfactant interaction led to the formation of thinner fibres than those formed in the absence of the interaction.

The effects of a non-ionic surfactant, Triton X-405, on the electrospun fibres were also studied. The addition of Triton X-405 did not eliminate the fibre beads, but reduced the bead numbers and changed the morphology. Triton X-405 slightly improved the solution conductivity, and had a minor effect on the surface tension, but no effect on the viscosity.

Use of pineapple juice for elimination of egg stickiness of common carp (Cyprinus carpio L.)

Four treatments including three different concentrations of pineapple solution (I %, 3%, 5%) and the traditional method (salt/urea/tannin solutions) were used to eliminate egg stickiness of common carp. With the traditional method, fertilization and hatching rates were 74.5% ± 1.2 and 70.2% ± 1.1, respectively. The highest fertilization rate (89.3% ± 0.7) and hatching rate (86.6% ± 1.4) were found with treatment of 1% pineapple juice solution and was significantly different from those obtained with other treatments (P<0.05). Using pineapple juice for desticking common carp eggs also reduced the time of egg handling from almost one hour required with the traditional method, to about three minutes, as well as increasing fertilization and hatching rate under hatchery conditions.

Single transferable vote with Borda elimination: proportional representation, moderation, quasi-chaos and stability

Modifying single transferable vote (STV) by removing candidates according to their Borda scores creates a new vote counting system (STV-B) that is not quasi-chaotic, results in proportional representation, and promotes the election of moderate candidates. Dummett, M.A.E. [1997. Principles of Electoral Reform. Oxford University, New York] noted quasi-chaos in STV and proposed the “Quota/Borda system” (QBS) as a solution. STV-B and QBS retain proportional representation from STV, permit some influence on candidate selection to occur between voting blocks thereby promoting moderate results, and are much more stable than STV when subjected to small changes in voter preferences. Under STV-B, and not QBS, a minority that shares some preferences may elect a candidate even if the minority is not a solid coalition.