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Loss function plays an important role in data classification. Manyloss functions have been proposed and applied to differentclassification problems. This paper proposes a new so called thesmoothed 0-1 loss function, that could be considered as anapproximation of the classical 0-1 loss function. Due to thenon-convexity property of the proposed loss function, globaloptimization methods are required to solve the correspondingoptimization problems. Together with the proposed loss function, wecompare the performance of several existing loss functions in theclassification of noisy data sets. In this comparison, differentoptimization problems are considered in regards to the convexity andsmoothness of different loss functions. The experimental resultsshow that the proposed smoothed 0-1 loss function works better ondata sets with noisy labels, noisy features, and outliers. [ABSTRACT FROM AUTHOR]

The Naive Bayes classifier is a popular classification technique for data mining and machine learning. It has been shown to be very effective on a variety of data classification problems. However, the strong assumption that all attributes are conditionally independent given the class is often violated in real-world applications. Numerous methods have been proposed in order to improve the performance of the Naive Bayes classifier by alleviating the attribute independence assumption. However, violation of the independence assumption can increase the expected error. Another alternative is assigning the weights for attributes. In this paper, we propose a novel attribute weighted Naive Bayes classifier by considering weights to the conditional probabilities. An objective function is modeled and taken into account, which is based on the structure of the Naive Bayes classifier and the attribute weights. The optimal weights are determined by a local optimization method using the quasisecant method. In the proposed approach, the Naive Bayes classifier is taken as a starting point. We report the results of numerical experiments on several real-world data sets in binary classification, which show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The Knowledge Discovery from Databases (KDD) technique called 'association rules' is applied to a large data set representing applicants for government-funded legal aid. Results indicate that KDD can be an invaluable tool for legal analysts. Association rules discovered identify associations between variables that are present in the data set though are not necessarily causal. Interesting rules can prompt analysts to formulate hypotheses for further investigation. The identification of interesting rules is typically performed using an objective measure of 'interesting' although this measure is often not sufficiently accurate to eliminate all uninteresting rules. In this article, a subjective measure of interestingness is adopted in conjunction with the objective measures. This leads to the ability to focus more accurately on those rules that surprise the analyst and are therefore more likely to be interesting. In general, KDD techniques have not been applied to law despite possible benefits because data is often stored in narrative form rather than in structured databases. However, the impending introduction of data warehouses that collect data from a number of organizations across a legal system presents invaluable opportunities for analysts using KDD. [ABSTRACT FROM AUTHOR]

Abstract: The endomorphism monoids of graphs have been actively investigated. They are convenient tools expressing asymmetries of the graphs. One of the most important classes of graphs considered in this framework is that of Cayley graphs. Our paper proposes a new method of using Cayley graphs for classification of data. We give a survey of recent results devoted to the Cayley graphs also involving their endomorphism monoids. [Copyright &y& Elsevier]