Confidence in prediction: an approach for dynamic weighted ensemble.

Combining classifiers in an ensemble is beneficial in achieving better prediction than using a single classifier. Furthermore, each classifier can be associated with a weight in the aggregation to boost the performance of the ensemble system. In this work, we propose a novel dynamic weighted ensemble method. Based on the observation that each classifier provides a different level of confidence in its prediction, we propose to encode the level of confidence of a classifier by associating with each classifier a credibility threshold, computed from the entire training set by minimizing the entropy loss function with the mini-batch gradient descent method. On each test sample, we measure the confidence of each classifier’s output and then compare it to the credibility threshold to determine whether a classifier should be attended in the aggregation. If the condition is satisfied, the confidence level and credibility threshold are used to compute the weight of contribution of the classifier in the aggregation. By this way, we are not only considering the presence but also the contribution of each classifier based on the confidence in its prediction on each test sample. The experiments conducted on a number of datasets show that the proposed method is better than some benchmark algorithms including a non-weighted ensemble method, two dynamic ensemble selection methods, and two Boosting methods

The binomial sequence spaces of nonabsolute type

Abstract In this paper, we introduce the binomial sequence spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ of nonabsolute type which include the spaces c 0 $c_{0}$ and c, respectively. Also, we prove that the spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ are linearly isomorphic to the spaces c 0 $c_{0}$ and c, in turn, and we investigate some inclusion relations. Moreover, we obtain the Schauder bases of those spaces and determine their α-, β-, and γ-duals. Finally, we characterize some matrix classes related to those spaces

Root canal morphology of primary maxillary second molars:a micro-computed tomography analysis

Aim Successful endodontic treatment of primary teeth requires comprehensive knowledge and understanding of root canal morphology. The purpose of this study was to investigate the root canal configurations of primary maxillary second molars using micro-computed tomography. Methods Extracted human primary maxillary second molars (n = 57) were scanned using micro-computed tomography and reconstructed to produce three-dimensional models. Each root canal system was analysed qualitatively according to Vertucci's classification. Results 22.8% (n = 13) of the sample presented with the fusion of the disto-buccal and palatal roots; of these, Type V was the most prevalent classification. For teeth with three separate roots (n = 44), the most common root canal type was Type 1 for the palatal canal (100%) and disto-buccal canal (77.3%) and Type V for the mesio-buccal canal (36.4%). Overall, 7% (n = 4) of mesio-buccal canals were 'unclassifiable'. Conclusion The root canal systems of primary maxillary second molars were not only complex but had a range of configurations that may contribute to unfavourable clinical outcomes after endodontic treatment

Automated Ham Quality Classification Using Ensemble Unsupervised Mapping Models

This multidisciplinary study focuses on the application and comparison of several topology preserving mapping models upgraded with some classifier ensemble and boosting techniques in order to improve those visualization capabilities. The aim is to test their suitability for classification purposes in the field of food industry and more in particular in the case of dry cured ham. The data is obtained from an electronic device able to emulate a sensory olfative taste of ham samples. Then the data is classified using the previously mentioned techniques in order to detect which batches have an anomalous smelt (acidity, rancidity and different type of taints) in an automated way

Binarized Support Vector Machines

The widely used support vector machine (SVM) method has shown to yield very good results in supervised classification problems. Other methods such as classification trees have become more popular among practitioners than SVM thanks to their interpretability, which is an important issue in data mining. In this work, we propose an SVM-based method that automatically detects the most important predictor variables and the role they play in the classifier. In particular, the proposed method is able to detect those values and intervals that are critical for the classification. The method involves the optimization of a linear programming problem in the spirit of the Lasso method with a large number of decision variables. The numerical experience reported shows that a rather direct use of the standard column generation strategy leads to a classification method that, in terms of classification ability, is competitive against the standard linear SVM and classification trees. Moreover, the proposed method is robust; i.e., it is stable in the presence of outliers and invariant to change of scale or measurement units of the predictor variables. When the complexity of the classifier is an important issue, a wrapper feature selection method is applied, yielding simpler but still competitive classifiers

Linear Programming Boosting via Column Generation

We examine linear program (LP) approaches to boosting and demonstrate their efficient solution using LPBoost, a column generation based simplex method. We formulate the problem as if all possible weak hypotheses had already been generated. The labels produced by the weak hypotheses become the new feature space of the problem. The boosting task becomes to construct a learning function in the label space that minimizes misclassification error and maximizes the soft margin. We prove that for classification, minimizing the 1-norm soft margin error function directly optimizes a generalization error bound. The equivalent linear program can be efficiently solved using column generation techniques developed for large-scale optimization problems. The resulting LPBoost algorithm can be used to solve any LP boosting formulation by iteratively optimizing the dual misclassification costs in a restricted LP and dynamically generating weak hypotheses to make new LP columns. We provide algorithms for soft margin classification, con dence-rated, and regression boosting problems. Unlike gradient boosting algorithms, which may converge in the limit only, LPBoost converges in a finite number of iterations to a global solution satisfying mathematically well-defined optimality conditions. The optimal solutions of LPBoost are very sparse in contrast with gradient based methods. Computationally, LPBoost is competitive in quality and computational cost to AdaBoost