Linear-Time Preprocessing in Optimal Numerical Range Partitioning

Only a subset of the boundary points—the segment borders—have to be taken into account in searching for the optimal multisplit of a numerical value range with respect to the most commonly used attribute evaluation functions of classification learning algorithms. Segments and their borders can be found efficiently in a linear-time preprocessing step.In this paper we expand the applicability of segment borders by showing that inspecting them alone suffices in optimizing any convex evaluation function. For strictly convex evaluation functions inspecting all segment borders is also necessary. These results are derived directly from Jensen's inequality.We also study the evaluation function Training Set Error which is not strictly convex. With that function the data can be preprocessed into an even smaller number of cut point candidates, called alternations, when striving for optimal partition. Examining all alternations also seems necessary, since—analogously to strictly convex functions—the placement of neighboring cut points affects the optimality of an alternation. We test empirically the reduction of the number of cut point candidates that can be obtained for Training Set Error on real-world data.     

General and Efficient Multisplitting of Numerical Attributes

Often in supervised learning numerical attributes require special treatment and do not fit the learning scheme as well as one could hope. Nevertheless, they are common in practical tasks and, therefore, need to be taken into account. We characterize the well-behavedness of an evaluation function, a property that guarantees the optimal multi-partition of an arbitrary numerical domain to be defined on boundary points. Well-behavedness reduces the number of candidate cut points that need to be examined in multisplitting numerical attributes. Many commonly used attribute evaluation functions possess this property; we demonstrate that the cumulative functions Information Gain and Training Set Error as well as the non-cumulative functions Gain Ratio and Normalized Distance Measure are all well-behaved. We also devise a method of finding optimal multisplits efficiently by examining the minimum number of boundary point combinations that is required to produce partitions which are optimal with respect to a cumulative and well-behaved evaluation function. Our empirical experiments validate the utility of optimal multisplitting: it produces constantly better partitions than alternative approaches do and it only requires comparable time. In top-down induction of decision trees the choice of evaluation function has a more decisive effect on the result than the choice of partitioning strategy; optimizing the value of most common attribute evaluation functions does not raise the accuracy of the produced decision trees. In our tests the construction time using optimal multisplitting was, on the average, twice that required by greedy multisplitting, which in its part required on the average twice the time of binary splitting.     

Modelling of Pressure Distribution inside the SEN in a Stopper‐rod controlled System

Shrouding tubes and submerged entry nozzles (SEN) are mainly used on steel transfer between process units of continuous casters. Molten steel flow in the SEN or shrouding tube causes a pressure drop which creates possibilities for air aspiration through refractory material. The objective of this research was to model the pressure distribution in the SEN of a continuous caster using a full scale water model. Effects of casting speed, SEN immersion depth and liquid level of tundish on the pressures at the SEN wall and centre were defined. The experiments proved that SEN immersion depth had the most remarkable effect on the pressure inside the SEN. However experiments did not show a significant effect of casting speed and tundish liquid level on the pressure inside the SEN. This research presents a simplified model for pressure distribution in SEN. The presented model agrees well with measurements at the SEN wall.     

Decomposing the value of cigarettes using experimental auctions.

Using a new brand of cigarettes with less nicotine content than conventional cigarettes, we conducted experimental auctions at two grocery stores to estimate smokers' value of nicotine. Our approach is novel because the brand of cigarettes auctioned was new to the market and the cigarette's nicotine content is reduced using genetic modification, with no effect on the taste of the cigarettes. We found smokers would be willing to pay US$1.25-$1.45 for a pack of cigarettes with no nicotine and $1.59-$1.66 for a pack of cigarettes with low levels of nicotine.     

Electrical Conductivity of the Screening Residuals of Coke Production in context of Ferrochromium Production in a Submerged Arc Furnace

Coke is used as a reducing agent in the production of ferrochromium in a submerged arc furnace (SAF). Its good electrical conductivity compared to other input materials makes it a dominant current conductivity substance in the burden. The resistance of the coke has to be high enough to ensure the proper functionality of the furnace. Used cokes for submerged arc furnace production are relatively small in size compared to e.g blast furnace (BF) cokes. A common practice is to use screening residual coke, which is too small for the BF, in SAF. The goal of this study was to show differences in the electrical properties of screening residual cokes compared to coke formed in different parts of the coke battery, in dependence of particle size. The resistances of different cokes were measured and XRD measurements were performed to define the crystallographic structure of the selected cokes. The results indicate that small coke particles have higher overall resistance, which is due to their internal properties. This small weakly carbonized coke is formed in the middle of the coking battery and is subject to changes in varying coking practices. Continuous quality control of screening residual coke is needed to use it in the SAF.     

Efficient Multisplitting Revisited: Optima-Preserving Elimination of Partition Candidates

We consider multisplitting of numerical value ranges, a task that is encountered as a discretization step preceding induction and also embedded into learning algorithms. We are interested in finding the partition that optimizes the value of a given attribute evaluation function. For most commonly used evaluation functions this task takes quadratic time in the number of potential cut points in the numerical range. Hence, it is a potential bottleneck in data mining algorithms.We present two techniques that speed up the optimal multisplitting task. The first one aims at discarding cut point candidates in a quick linear-time preprocessing scan before embarking on the actual search. We generalize the definition of boundary points by Fayyad and Irani to allow us to merge adjacent example blocks that have the same relative class distribution. We prove for several commonly used evaluation functions that this processing removes only suboptimal cut points. Hence, the algorithm does not lose optimality.Our second technique tackles the quadratic-time dynamic programming algorithm, which is the best schema for optimizing many well-known evaluation functions. We present a technique that dynamically—i.e., during the search—prunes partitions of prefixes of the sorted data from the search space of the algorithm. The method works for all convex and cumulative evaluation functions.Together the use of these two techniques speeds up the multisplitting process considerably. Compared to the baseline dynamic programming algorithm the speed-up is around 50 percent on the average and up to 90 percent in some cases. We conclude that optimal multisplitting is fully feasible on all benchmark data sets we have encountered.     

Weibull Skewness and Kurtosis as a Function of the Shape Parameter

Numerical results are presented for points in the (β₁, β₂) plane for the Weibull shape parameter values 0.2 to 25.0.