Gap-based estimation: Choosing the smoothing parameters for Probabilistic and general regression neural networks

Probabilistic neural networks (PNN) and general regression neural networks (GRNN) represent knowledge by simple but interpretable models that approximate the optimal classifier or predictor in the sense of expected value of the accuracy. These models require the specification of an important smoothing parameter, which is usually chosen by crossvalidation or clustering. In this letter, we demonstrate the problems with the cross-validation and clustering approaches to specify the smoothing parameter, discuss the relationship between this parameter and some of the data statistics, and attempt to develop a fast approach to determine the optimal value of this parameter. Finally, through experimentation, we show that our approach, referred to as a gap-based estimation approach, is superior in speed to the compared approaches, including support vector machine, and yields good and stable accuracy

Occurrences and distribution characteristics of organophosphate ester flame retardants and plasticizers in the sediments of the Bohai and Yellow Seas, China

Concentrations and distribution characteristics of organophosphate esters (OPEs) in surface sediment samples were analyzed and discussed for the first time in the open Bohai Sea (BS) and YellowSea (YS). Three halogenated OPEs [ tris-(2-chloroethyl) phosphate (TCEP), tris-(1-chloro-2-propyl) phosphate (TCPP), and tris-(1,3-dichloro2- propyl) phosphate (TDCPP)] and five non-halogenated OPEs [ tri-isobutyl phosphate (TiBP), tri-n-butyl phosphate (TnBP), tripentyl phosphate (TPeP), triphenyl phosphate (TPhP) and tris-(2-ethylhexyl) phosphate (TEHP)] were detected in this region. The concentrations of eight OPEs in total (Sigma 8OPEs) ranged from 83 to 4552 pg g(-1) dry weight (dw). The halogenated OPEs showed higher abundances than the non-halogenated ones did, with TCEP, TCPP, and TEHP the main compounds. Generally, concentrations of OPEs in the BS were higher than those in the YS. Riverine input (mainly the Changjiang DilutedWater (CDW)) and deposition effect in the mud areas might have influenced the spatial distributions of OPEs. Correlation between OPE concentrations and total organic carbon (TOC) indicated TOC was an effective indicator for the distribution of OPEs. Inventory analysis of OPEs implied that sea sediment might not be the major reservoir of these compounds. (C) 2017 Elsevier B.V. All rights reserved.</p

Microstructure and mechanical properties of Cu joints soldered with a Sn-based composite solder, reinforced by metal foam

In this study, Ni foam, Cu coated Ni foam and Cu-Ni alloy foams were used as strengthening phases for pure Sn solder. Cu-Cu joints were fabricated by soldering with these Sn-based composite solders at 260 °C for different times. The tensile strength of pure Sn solder was improved significantly by the addition of metal foams, and the Cu-Ni alloy/Sn composite solder exhibited the highest tensile strength of 50.32 MPa. The skeleton networks of the foams were gradually dissolved into the soldering seam with increasing soldering time, accompanied by the massive formation of (Cu,Ni)6Sn5 phase in the joint. The dissolution rates of Ni foam, Cu coated Ni foam and Cu-Ni alloy foams into the Sn matrix increased successively during soldering. An increased dissolution rate of the metal foam leads to an increase in the Ni content in the soldering seam, which was found to be beneficial in refining the (Cu,Ni)6Sn5 phase and inhibiting the formation of the Cu3Sn IMC layer on the Cu substrate surface. The average shear strength of the Cu joints was improved with increasing soldering time, and a shear strength of 61.2 MPa was obtained for Cu joints soldered with Cu-Ni alloy/Sn composite solder for 60 min

An Analysis Of Misclassification Rates For Decision Trees

The decision tree is a well-known methodology for classification and regression. In this dissertation, we focus on the minimization of the misclassification rate for decision tree classifiers. We derive the necessary equations that provide the optimal tree prediction, the estimated risk of the tree\u27s prediction, and the reliability of the tree\u27s risk estimation. We carry out an extensive analysis of the application of Lidstone\u27s law of succession for the estimation of the class probabilities. In contrast to existing research, we not only compute the expected values of the risks but also calculate the corresponding reliability of the risk (measured by standard deviations). We also provide an explicit expression of the k-norm estimation for the tree\u27s misclassification rate that combines both the expected value and the reliability. Furthermore, our proposed and proven theorem on k-norm estimation suggests an efficient pruning algorithm that has a clear theoretical interpretation, is easily implemented, and does not require a validation set. Our experiments show that our proposed pruning algorithm produces accurate trees quickly that compares very favorably with two other well-known pruning algorithms, CCP of CART and EBP of C4.5. Finally, our work provides a deeper understanding of decision trees

K-Norm Misclassification Rate Estimation For Decision Trees

The decision tree classifier is a well-known methodology for classification. It is widely accepted that a fully grown tree is usually over-fit to the training data and thus should be pruned back. In this paper, we analyze the overtraining issue theoretically using an the k-norm risk estimation approach with Lidstone\u27s Estimate. Our analysis allows the deeper understanding of decision tree classifiers, especially on how to estimate their misclassification rates using our equations. We propose a simple pruning algorithm based on our analysis and prove its superior properties, including its independence from validation and its efficiency

Properties Of The K-Norm Pruning Algorithm For Decision Tree Classifiers

Pruning is one of the key procedures in training decision tree classifiers. It removes trivial rules from the raw knowledge base built from training examples, in order to avoid over-using noisy, conflicting, or fuzzy inputs, so that the refined model can generalize better with unseen cases. In this paper, we present a number of properties of k-norm pruning, a recently proposed pruning algorithm, which has clear theoretical interpretation. In an earlier paper it was shown that k-norm pruning compares very favorably in terms of accuracy and size with Minimal Cost-Complexity Pruning and Error Based Pruning, two ofthe most cited decision tree pruning methods; it was also shown that k-norm pruning is llzore efficient, at times orders of magnitude more efficient than Minimal Cost-Complexity Pruning and Error Based Pruning. In this paper, we demonstrate the validity ofthe k-norm properties through a series of theorel11s, and explain their practical significance. © 2008 IEEE