Iterative Regression Method Research Articles

ITERATIVE DESIGN OF NEURAL NETWORK CLASSIFIERS THROUGH REGRESSION

A method which modifies the objective function used far designing neural network classifiers is presented. The classical mean-square error criteria is relaxed by introducing two types of local error bias which are treated like free parameters. Open and closed form solutions are given for finding these bias parameters. The new objective function is seamlessly integrated into existing training algorithms such as back propagation (BP), output weight optimization (OWO), and hidden weight optimization (HWO). The resulting algorithms are successfully applied in training neural net classifiers having a linear final layer. Classifiers are trained and tested on several data sets from pattern recognition applications. Improvement over classical iterative regression methods is clearly demonstrated.

Search for Solar Periodicities in Tree-ring Widths from Conc�rdia (S.C., Brazil)

Tree ring studies are usually used to determine or verify climatic factors prevailing at a given place or region that may cause tree-ring width variations. Few studies are dedicated to the solar phenomena which may underlie these tree-ring width variations. Furthermore, it is known that some terrestrial phenomena are influenced by short- and long-time scale solar variability. An optical and computational method was set up and applied to tree samples (Araucaria angustifolia from Santa Catarina State in Southern Brazil) in order to obtain a growth ring width mean chronology. Spectral analysis is used for the search of periodicities, by maximum entropy and iterative regression methods. The results evidenced several embedded signals at periods which may be related to solar activity variations. Cross-correlation analysis between sunspot number and tree-ring data was performed and a lag of zero year was obtained. From our work, it seems that the tropical conifer species Araucaria angustifolia may be a good choice for studies on Sun-Earth relationships and their regional effects.

A simple method for a determination

The a term is a primary parameter that is used to indicate the deviation of the epithermal neutron distribution in the k0-standardization method of neutron activation analysis, k0-NAA. The calculation of a using a mathematical procedure is a challenge for some researchers. The calculation of a by the "bare-triple monitor" method is possible using the dedicated commercial software KAYZERO®/SOLCOI®. However, when this software is not available in the laboratory it is possible to carry out the calculation of a applying a simple iterative linear regression using any spreadsheets. This approach is described in this paper. The experimental data used in the example were obtained by the irradiation of a set of suitable monitors in the NAA #1 irradiation channel of the HANARO research reactor (KAERI, Korea). The results obtained by this iterative linear regression method agree well with the results calculated by the validated mathematical method.

Diaphragm Cell Measurement of Mutual Diffusion Coefficients for Potassium Hydroxide in Water from 1 °C to 25 °C

Integral diffusion coefficients were measured for potassium hydroxide over a concentration range of 0.1 M to 11 M at 1, 10, and 25 °C using the simplified diaphragm cell procedure of Mills, Woolf, and Watts. Differential diffusion coefficients were calculated using the iterative regression method of Stokes over the same concentration and temperature range. An empirical correlation relating the differential diffusion coefficients as a function of temperature and concentration was made with a standard error of 8 × 10-7 cm2·s-1 and an average deviation of 5 × 10-7 cm2·s-1.

Left ventricular performance assessed by echocardiographic automated border detection and arterial pressure.

Automated echocardiographic measures of left ventricular (LV) cavity area are closely correlated with changes in volume and can be coupled with LV pressure (PLV) to construct pressure-area loops in real time. The objective was to rapidly estimate LV contractility from end-systolic relationships of cavity area (as a surrogate for LV volume) and central arterial pressure (Pa) (as a surrogate for PLV) in a canine model using automated algorithms. In eight anesthetized mongrel dogs, we simultaneously measured PLV, LV area, and Pa (fluid-filled catheter). End-systolic pressure-area relationships in terms of pressure-area elastance (E'es)] from pressure-area loops during inferior vena caval occlusions were determined during basal conditions (control), dobutamine infusion (5-10 micrograms.mg-1.min-1), and after bolus propranolol (2 mg/kg) with both PLV and Pa by semiautomated and automated iterative regression methods. E'es increased during dobutamine infusion and decreased after propranolol infusion in all animals and with all iterative methods. Estimates of Ees from Pa were closely correlated with E'es from PLV by both the semiautomated and automated methods (r = 0.93; P < 0.01). The relationship between E'es obtained from Pn for the two methods was also closely correlated. Although the automated methods displayed larger differences from the semiautomated iterative technique by Bland-Altman analysis, the change in E'es with all techniques during dobutamine infusion and after propranolol infusion was of similar magnitude and direction among the three techniques. Greater variability with the dobutamine runs was partially due to abnormally conducted ventricular beats that minimized the number of consecutive beats that could be used for these analyses. We conclude that on-line Pa recordings from fluid-filled catheters can be used with echocardiographic automated border detection to rapidly calculate E'es as a means to estimate LV contractility.

Prediction of seeding date in southern Alberta

Predicting seeding date is an important component of modeling the impact of climate change on agricultural production. The objective of this study was to develop and evaluate models for predicting seeding dates based on weather variables. Data from 60 yr of a long-term experiment conducted on a silty clay loam (Dark Brown Chernozem) at Lethbridge, Alberta, were used for modeling seeding dates. Four approaches were used: an empirical model, a stepwise regression analysis, an iterative regression analysis, and a neural network (NN). An accuracy analysis was utilized to compare the results produced by the four methods. The best method was the NN model. It required 17 inputs, derived from date, air temperature and precipitation. The empirical model — which required that maximum temperature be at least 13 °C, that precipitation be less than 1 mm, and that the surface 15 cm of soil moisture be no greater than 90% of field capacity for four consecutive days — was the next best model. Stepwise regression identified air temperature and precipitation as the two most important weather variables. The predictive capability of this method was not satisfactory. Iterative regression analysis, also using maximum air temperature and precipitation, did not produce a satisfactory model. The stepwise and iterative regression methods predicted average seeding dates accurately but did not account for the variability in seeding dates. Key words: Neural network, climate change, model comparisons

A Reexamination of Public-Versus Private-School Achievement: The Case for Missing Data

The purpose of this research was to evaluate the effects of four data-replacement techniques on the High School and Beyond data set. A review of several previous studies indicated that estimating missing values by employing regression-based techniques is superior to other methods, particularly the variable-mean method. Because previous studies examined the effects of Missing Data Techniques (MDTs) on generated data sets where values were deleted at random, the current study was designed to evaluate the impact of the missing data techniques on a real data set for which the missing data pattern was unknown. Three studies that had analyzed the High School and Beyond data set were replicated. Missing data were first replaced using the variable mean, simple regression, and iterative regression methods, and then the analyses were repeated. Results from the analyses of the treated data sets were compared with the results of the original analyses. The findings indicated that the use of data-replacement techniques did affect the conclusions of the three studies examined; the findings indicated a convergence of the conclusions toward a moderate positive effect favoring private schooling.

Simultaneous optimization of variables influencing selectivity and elution strength in micellar liquid chromatography : Effect of organic modifier and micelle concentration

Previously, the simultaneous enhancement of separation with elution strength was reported in micellar liquid chromatography (MLC) using the hybrid eluents of water—organic solvent—micelles The practical implication of this phenomenon is that better separations can be achieved in shorter analysis times by using the hybrid eluents. Since both micelle concentration and volume fraction of organic modifier influence selectivity and solvent strength, only an investigation of the effects of a simultaneous variation of these parameters will disclose the full separation capability of the method, i.e. the commonly used sequential solvent optimization approach of adjusting the solvent strength first and then improving selectivity in reversed-phase liquid chromatography is inefficient for the case of MLC with the hybrid eluents. This is illustrated in this paper with two examples: the optimization of the selectivity in the separation of a mixture of phenols and the optimization of a resolution-based criterion determined for the separation of a number of amino acids and small peptides.The large number of variables involved in the separation process in MLC necessitates a structured approach in the development of practical applications of this technique. A regular change in retention behavior is observed with the variation of the surfactant concentration and the concentration of organic modifier, which enables a successful prediction of retention times. Consequently interpretive optimization strategies such as the iterative regression method are applicable.

An Expert System Approach to Eluent Optimisation in Reverse-Phase Liquid Chromatography with Multichannel Detection

Abstract The optimisation of eluent composition in reversed-phase liquid chromatography is a complex process, which often requires the expenditure of a significant amount of effort on the part of the chromatographer. To assist in this task an expert system has been developed which used a gradient elution experiment to determine the appropriate initial solvent strength, followed by response-surface modelling using an iterative regression method to determine the mobile phase composition for optimum resolution. Spectral information from a multichannel diode array detector is used to provide retention information for this model. Peak homogeneity is assessed by a number of independent modules, the output from which is interpreted by the expert system and used to validate the response surface model constructed by the optimisation procedure.

Practical optimization of the separation of a limited subset of components by using isoeluotropic ternary eluent mixtures in reversed-phase high-performance liquid chromatography

A fully integrated procedure is presented for the separation optimization of all or a limited subset of components by means of isoeluotropic ternary solvent mixtures along with the iterative regression method in reversed-phase high-performance liquid chromatography. The optimization search area is defined for both full and limited optimization by utilizing a statistical approach in combination with an extended gradient isocratic scanning procedure. Starting eluent compositions are selected with respect to the complexity of the sample mixture, and the merits of the procedure are evaluated by performing the full and limited (3-out-of-9) optimization of a nine-component aromatic solute mixture. Three resolution-based optimization criteria are used and selected sequentially to achieve satisfactory resolution for the peaks of interest in the shortest possible analysis time. In order to guide the analyst through the selection of the criteria and to assist in the evaluation of the optimum found, an “expert” algorithm has been integrated in the optimization program. The use of the algorithm in the optimization of the analysis time is also demonstrated (while resolution is maintained at the required level) by applying a suitable criterion and allowing column length variation.

Estimation of the uteroplacental perfusion by use of 113mIn-transferrin and an iterative regression method.

For the clinical evaluation of the uteroplacental blood flow the radioactivity curve over the placenta is recorded by means of a gamma scintillation camera and is calculated by iterative regression method. The flow curves were attributable with good clinical relevance to 3 perfusion types: perfusion type I indicates unimpaired uteroplacental flow. Type II is a transitional type to the pathological type III. Over two-thirds of the type III cases gave births to babies with signs of moderate to severe malnutrition and in 1 case an intrauterine death occurred.

A Continuation Method for Nonlinear Regression

Many iterative regression methods only perform well near a solution. One may construct a modified problem with a free parameter $(k)$, which has a known solution for a particular k. By suitably deforming this problem through k-space one may, always remaining close to an intermediate solution, eventually solve the original problem. The continuation method was used to perform three nonlinear least squares regressions where the conventional Newton methods failed to converge. In particular, the third problem was associated with experimental kinetic data and differential equations which needed to be integrated numerically. No satisfactory answers were obtainable from the Gauss–Newton method, while the continuation (parameter variation) method showed its robustness by converging for a large range of initial values.

Urban population density function of two polar variables

Sanders E. (1974) Urban population density function of two polar variables, Reg. Studies 9, 63–68. For urban population densities a two polar variable function has been tested for the residential population in the Paris metropolitan area, using an iterative non-linear regression method on cumulative population values. The function is continuous for central distance and discontinuous for angle of azimuth. After an introduction on dynamic analysis of the negative exponential density model, the two variable function and results for Paris are given. Results include shape, time evolution and forecasts for a total population of 12 millions, of singular rings having at a given instant, density at maximum value in time, and maximum time rates of density increase and decline.

Simplified Herd-Level Age-Correction Factors

Summary An iterative regression method of calculating within-herd age-correction factors has been outlined in earlier work (4). A simplification of this system utilizing known multiplicative correction factors is now presented. The method is applicable to any situation where data are to be corrected on a herd, flock, or group basis.