Commonly used **classification** and regression tree methods like the CART algorithm are recursive partitioning methods that build the model in a forward stepwise search. Although this approach is known to be an efficient heuristic, the results of recursive tree methods are only locally **optimal**, as splits are chosen to maximize homogeneity at the next step only. An alternative way to search over the parameter space of trees is to use global optimization methods like evolutionary algorithms. This pa- per describes the evtree package, which implements an evolutionary algorithm for learning globally **optimal** **classification** and regression trees in R. Computationally intensive tasks are fully computed in C++ while the partykit (Hothorn and Zeileis 2011) package is leveraged for representing the resulting trees in R, providing unified infrastructure for summaries, visualizations, and predictions. evtree is compared to rpart (Therneau and Atkinson 1997), the open-source CART implementation, and conditional inference trees (ctree, Hothorn, Hornik, and Zeileis 2006). The usefulness of evtree is illustrated in a textbook customer **classification** task and a benchmark study of predictive accuracy in which evtree achieved at least similar and most of the time better results compared to the recursive algorithms rpart and ctree.

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We formulate the problem of constructing the **optimal** de- cision tree of a given depth as an binary linear program. We call our method BinOCT, a Binary encoding for constructing **Optimal** **Classification** Trees. Our novel formulation models the selection of decision threshold via a binary search pro- cedure encoded using a type of big-M constraints. This re- quires a very small number of binary decision variables and is therefore able to find good quality solutions within limited time. Noteworthy is that the number of decision variables is largely independent of the number of training data rows: it only depends logarithmically on the number of unique feature values. Furthermore, our formulation requires fewer constraints than existing approaches. Although this number still depends linearly on the number of data rows. We show using experiments that BinOCT outperforms existing MO based approaches on a variety of data sets in terms of accu- racy and computation time.

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vision applications (M. Dubuisson, A. Jain, 1994; Jacobs et al., 2000) — all of which are semimetrics. An additional line of work (M. Dubuisson, A. Jain, 1994; Jacobs et al., 2000, 1998; Weinshall et al., 1998) underscored the effectiveness of non-metric distances in various applications (mainly vision), and among these, semimetrics again play a prominent role (Basri et al., 1995; Cox et al., 1996; Gdalyahu and Weinshall, 1999; Huttenlocher et al., 1993; Jain and Zongker, 1997; J. Puzicha, J. Buhmann, Y. Rubner, C. Tomasi, 1999). Main results. We initiate the rigorous study of **classification** for semimetric spaces. We define the density dimension (dens = dens(X )) of a semimetric space X as the logarithm of the density constant µ = µ(X ), which intuitively is the smallest number such that any r-radius open ball in X contains at most µ points at mutual interpoint distance at least r/2; a formal definition is given in Equation (2). We then demonstrate that dens plays a central role in the statistical and algorithmic feasibility of learning in this setting by showing that it controls the packing numbers of X . Crucially for learning, this insight implies that there is

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Abstract— We propose a powerful symmetric kernel classifier for nonlinear detection in challenging rank-deficient multiple- antenna aided communication systems. By exploiting the in- herent odd symmetry of the **optimal** Bayesian detector, the proposed symmetric kernel classifier is capable of approaching the **optimal** **classification** performance using noisy training data. The classifier construction process is robust to the choice of the kernel width and is computationally efficient. The proposed solution is capable of providing a signal-to-noise ratio gain in excess of 8 dB against the powerfull linear minimum bit error rate benchmarker, when supporting five users with the aid of three receive antennas.

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Arrhythmia constitutes a problem with the rate or rhythm of the heartbeat, and an early diagnosis is essential for the timely inception of successful treatment. We have jointly optimized the entire multi-stage arrhythmia **classification** scheme based on 12-lead surface ECGs that attains the accuracy performance level of professional cardiologists. The new approach is comprised of a three-step noise reduction stage, a novel feature extraction method and an **optimal** **classification** model with finely tuned hyperparameters. We carried out an exhaustive study comparing thousands of competing **classification** algorithms that were trained on our proprietary, large and expertly labeled dataset consisting of 12-lead ECGs from 40,258 patients with four arrhythmia classes: atrial fibrillation, general supraventricular tachycardia, sinus bradycardia and sinus rhythm including sinus irregularity rhythm. Our results show that the **optimal** approach consisted of Low Band Pass filter, Robust LOESS, Non Local Means smoothing, a proprietary feature extraction method based on percentiles of the empirical distribution of ratios of interval lengths and magnitudes of peaks and valleys, and Extreme Gradient Boosting Tree classifier, achieved an F 1 -Score of 0.988 on patients without additional cardiac conditions.

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Abstract— Network traffic **classification** is a difficult yet important task in analyzing and avoiding the overheads occurred in the network traffic to optimize the internet flow. But there are very rare cases of research that have been carried out in the field of optimizing the internet traffic and also **classification** of internet traffic. Many existing approaches try to minimize the over head occurred and they are yet not **optimal**. In this project we propose an optimized **classification** approach of internet traffic. It analyzed the behavior of nodes and take decision by allowing or disallowing the connection of the incoming node. We focused on this by **optimal** **classification** approach i.e., Naïve Bayes **Classification**/Prediction for internet traffic to analyze the behavior of nodes and also for computing the posterior probabilities with respect to each node. Though there are many other approaches at present, this proposed approach is found to be suitable and efficient in classifying the network behavior.

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In searching for the **optimal** **classification** system, it is crucially important that in- surers not neglect to take into consideration underwriting risk costs, i.e., the risk that insureds are assigned to inappropriate risk classes. For example, if policyholders are assumed to belong to a risk class with higher average mortality than they actually have, the true cost of one unit of annuity will be underestimated. If, based on this erroneous assignment to risk class, the insurer charges a relatively low price for the annuity, demand will increase, and thus the original error compounds itself, as an increasing number of people who will live longer than expected are paying less than is necessary for the insurer to make a profit; in the worst case, the insurer will cer- tainly lose money. This is what is known as underwriting risk and fully taking it into consideration will have a large impact on the insurer’s **optimal** **classification** system. Insufficient risk assessment (e.g., underwriting risk) is one of the greatest hazards for insurers in the issuance of enhanced annuities. Thus, it is vital to consider under- writing risk costs in the optimization problem. Underwriting risk can be integrated by means of underwriting error probabilities, which reflect the frequency with which an insured is classified into a risk class with higher average mortality than is appropriate for that individual. A comprehensive formal description of how to include underwrit- ing risk in the optimization problem can be found in the underlying working paper by Gatzert et al. (2008).

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In the framework of supervised **classification** (discrimination) for functional data, it is shown that the **optimal** **classification** rule can be explicitly obtained for a class of Gaussian processes with “triangular” covariance functions. This explicit knowledge has two practical consequences. First, the consistency of the well- known nearest neighbors classifier (which is not guaranteed in the problems with functional data) is established for the indicated class of processes. Second, and more important, parametric and nonparametric plug-in classifiers can be obtained by estimating the unknown elements in the **optimal** rule.

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The predictive performance of a random forest ensemble is highly associated with the strength of individual trees and their diversity. Ensemble of a small number of accurate and diverse trees, if prediction accuracy is not compromised, will also reduce computational burden. We investigate the idea of integrating trees that are accurate and diverse. For this purpose, we utilize out-of-bag observations as a validation sample from the training bootstrap samples, to choose the best trees based on their individual performance and then assess these trees for diversity using the Brier score on an independent validation sample. Starting from the first best tree, a tree is selected for the final ensemble if its addition to the forest reduces error of the trees that have already been added. Our approach does not use an implicit dimension reduction for each tree as random project ensemble **classification**. A total of 35 bench mark problems on **classification** and regression are used to assess the performance of the proposed method and compare it with random forest, random projection ensemble, node harvest, support vector machine, kNN and **classification** and regression tree. We compute unexplained variances or **classification** error rates for all the methods on the corresponding data sets. Our experiments reveal that the size of the ensemble is reduced significantly and better results are obtained in most of the cases. Results of a simulation study are also given where four tree style scenarios are considered to generate data sets with several structures.

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Artificial Neural Network (ANN) is an information processing paradigm motivated by biological nervous systems. The human learning process may be partially automated with ANNs, which can be constructed for a specific application such as pattern recognition or data **classification**, through a learning process (Mokhlessi & Rad, 2010). ANNs and their techniques have become increasingly important for modeling and optimization in many areas of science and engineering, and this assertion is largely attributed to their ability to exploit the tolerance for imprecision and uncertainty in real-world problems, coupled with their robustness and parallelism (Nicoletti, 1999). Artificial Neural Networks (ANNs) have been implemented for a variety of **classification** and learning tasks (Bhuiyan, 2009). As such, the reason for using ANNs rest solely on its several inhibitory properties such as the generalization and the capability of learning from training data, even where the rules are not known a-priori (Penedo et al., 1998).

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It mostly used for text categorisation because it is more efficient and easily understandable [10], [11], [15]. For reducing features we add some pre-processing steps in naive Bayes .It provide competitive performance compared to other data driven **classification** methods. Sometimes result of naive Bayes get poor because of some unrealistic assumptions. It applies Bayes theorem with the naive assumption it means any pair of features are independent for class. Maximum posteriori take decision in naive Bayes. It is used in many data mining application. It contain three model first Bernoulli model second is Multinomial it shows real-life benchmark[21], [22]and third is land position model and its framework result is Bernoulli naive Bayes, Multinomial naive Bayes and Position naive Bayes. Is old method for selecting feature. The feature selection is like logistic regression. It can done two measure task **classification** and clustering. **Classification** is done on previously define classes on that basis we can introduce new classes. Some algorithms can use in machine learning KNN [3] k is user define parameter it is the feature space. Feature can extract from dataset. **Classification** is done according to KNN[5] and SVM [7]. For new class instance is define according to the place of feature space related to hyper surfaces. SNM mention two properties that space between different classes the algorithm place on hyper surface in cantered as possible as and mount data instances into multi-dimensional space, so it will classify into different classes from each other. Clustering is nothing but finding groups of data instances so that data in one cluster belowthat cluster characteristics. K-mean [8]. Cluster representative name as centroid it show the characteristics of that cluster.

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There are methods available to determine the performance of a **classification** system requiring more than two outcomes. Many of these methods use extensions of receiver operating characteristic (ROC) curve theory for comparing **classification** systems on their abilities to correctly classify objects [16, 17, 20, 28, 29]. However, the number of possible outcomes is not the only concern when choosing a **classification** system. The prevalence of the di ff erent classes as well as the costs associated with making the correct (or incorrect) decision should also be considered [30, 42, 58, 65]. For example, in HIV diagnosis, different misclassifications may be considered more or less significant. A person who is misdiagnosed as the non-diseased state when they are actually HIV- positive may be considered much worse than the opposite error occurring (a non-diseased person who is diagnosed as HIV-positive). In the first scenario, a person will not receive necessary medical intervention and may now put others at risk since they are unaware of their HIV-positive status. Clearly though, the latter misdiagnosis presents its own cost in that an individual may begin treatment or otherwise suffer with a diagnosis that is incorrect.

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1 I NTRODUCTION In last decades, Computer Aided Diagnosis (CAD) techniques have been applied widely in medical domain. The Medicinal analysis is referred as subjective as it is based on doctor's practical knowledge regarding the available information. For doctor's diagnosing purpose [1, 2], it urges that system conversion would grasp the portions of solutions. In order to create CAD systems, a novel method named as Machine Learning (ML) has been proposed. The ML models are most significant and applied in several domains since it is highly capable of retrieving complex association of data in biomedical region [3,4]. The data analysis could be performed by applying maximum amount of medicinal information by integrating with various applicable techniques in **classification** process. Therefore, it assumed to be a major challenging issue in accuracy where **classification** model has been used in examining the anomalies of individual. Here, diverse type of information from medical field is composed with maximum dimensionality [5, 6]. Generally, high definition data requires the mining process with descriptive features which must be selected whereas dataset directional should be declined [7]. For avoiding the irrelevant attributes from dataset [8, 9], reducing dimension might be considered as major action while analyzing the system. By removing the number of unwanted attributes tends to execute a satisfied technique where the screen is sampled in a rapid manner with lower expense. Additionally, there is a point of enhancing the accuracy from diagnosing process, the current research work focus on determining best feature subset for lymphography dataset .

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It can be seen here that the **classification** accuracies are not as high as the ones qouted in our previous work [4]. The reason for this is that rather than only applying contrast feature (**optimal** overall accuracy of 82%), four GLCM based features are used for **classification**. They bring robustness to our analysis by improving accuracies over all the different meningioma subtypes but bring down the overall **classification** accuracy. The objective of this paper is to analyze the effect of various filters on **classification** accuracy inorder to acquire the best wavelet. The table shows that wavelet filters with certain characteristics are more useful for **classification** than others. From our results it could be safely concluded that regularity and orthogonal analysis are useful wavelet properties for image analysis and **classification**. Mojsilovic et. al. [14] in their analysis with the simple wavelet transform found biorthogonality and higher number of vanishing moments useful properties. Symmetry is not an important property as far as **classification** is concerned. In our analysis, assymetrical filters such as Daubechies 4 provides the best overall **classification** accuracy of 78%. Symmetrical wavelet coiflet 2 performs equally well with providing high **classification** accuracies for meningiotheliamatous which is one of the more difficult textures to classify. This paper dealt with mainly the effect of the use of different wavelets on **classification** accuracies. Comparison of wavelets with other techniques will be the subject of our future work.

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motor functions. An electroencephalogram (EEG) is the basic building block for Brain-Computer Interfaces. EEG is used to measure the brain signals pertaining to various activities like imagining hand movements, leg movement etc. The EEG recognition procedure mainly involves feature extraction from EEG and **classification** of mental task. The useful EEG signals contain huge data of brain signals. Numerous methods have been used to extract feature vectors from the EEG. In this study features are extracted by PSD using Welch Periodogram Method. The extracted features contains a feature vector of large dimension. The study is to reduce the dimension of feature vector at the cost of improving the accuracy of the classifier. For this purpose a good feature selection technique is required. Genetic Algorithm is one such technique which helps to select the **optimal** features .These selected features are then fed to the classifier for **classification**. Three layer feed forward neural network is used in the study to classify these tasks.

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The robustness of a k-**optimal** rule set for k > 0 is due to that it preserves more potentially predictive rules in case that some rules are paralyzed by missing values in a data set. Usually, a traditional **classification** rule set is smaller than a min-**optimal** rule set, since most traditional classifi- cation systems postprune the final rule set to a small size. From our observations, most traditional **classification** rule sets are subsets of min-**optimal** rule sets. For example, the rule set from ID3 in Example 1 is a subset of the min- **optimal** rule set in Example 3 and is less robust than the min-**optimal** rule set. Experimental results will show this.

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contaminated phasor constellation becomes linearly nonsep- arable [6],[7]. Even if it remains linearly separable, the pha- sor constellation points may be close to the decision bound- ary and hence nonlinear receivers [12] are typically capable of providing a better performance than their linear counter- parts, although at the cost of an increased complexity. These considerations motivate this study on a nonlinear beamform- ing technique. We derive the **optimal** nonlinear beamformer, which is referred to as the Bayesian beamforming solution. It is shown that this Bayesian solution has an identical form to a radial basis function (RBF) network. A block-data based adaptive RBF beamformer is proposed, which employs the relevance vector machine (RVM) principle for **classification** [8],[9]. For adaptive sample-by-sample based weight adap- tation an enhanced κ-means clustering technique and the re- cursive least squares (CRLS) algorithm [10],[11] are consid- ered.

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To identify the **optimal** initial time date, however, the period of time is critical to the appearance of the new load situation. Any measure can be evaluated by those response times. This response time is made up of a procurement and installation time. The procurement time is the time until the action is available, while the installation time represents the time taken until this availability is fully usable. The specific procurement time for the recruitment of other staff as well as the subsequent person-dependent learning curve can exemplify that. These variables are to be assessed for each measure. With the following equation it is possible to determinate its initial time date:

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Abstract. In this paper, we are concerned with a hybrid hyperbolic dynamic system formulated by partial dif- ferential equations with initial and boundary conditions. An **optimal** energy control of the system is investigated. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and then semigroup generation of the system operator is discussed. Finally, an **optimal** energy control problem is proposed and it is shown that an **optimal** energy control can be obtained by a finite dimensional approximation.

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In this study measures that consider prediction accuracy for both classes were used, the Receiver Operating Characteristic (ROC) and corresponding area under the ROC Curve (AUC), as well as geometric mean of the true rates (GM). The two measures represent different types of performance indicators and assess the predictive performance of the classifier from different angles. ROC is one of the most frequently used measures. AUC represents the probability that a randomly chosen positive case (a defaulted client) will be ranked higher than a randomly chosen negative case (a non defaulted client) [7]. It visualizes the trade-off between sensitivity and 1-specificity [32]. An algorithm that classifies all cases correctly would include point (0, 1) and a random algorithm point (0.5, 0.5). The geometric mean of the true rates measure (GM) on the other hand combines measures of correctness of the binary **classification** predictions, allowing for simultaneous maximization of the prediction accuracy for both classes. It is defined as follows [31]:

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