On the influence of imputation in classification: practical issues

The substitution of missing values, also called imputation, is an important data preparation task for many domains. Ideally, the substitution of missing values should not insert biases into the dataset. This aspect has been usually assessed by some measures of the prediction capability of imputation methods. Such measures assume the simulation of missing entries for some attributes whose values are actually known. These artificially missing values are imputed and then compared with the original values. Although this evaluation is useful, it does not allow the influence of imputed values in the ultimate modelling task (e.g. in classification) to be inferred. We argue that imputation cannot be properly evaluated apart from the modelling task. Thus, alternative approaches are needed. This article elaborates on the influence of imputed values in classification. In particular, a practical procedure for estimating the inserted bias is described. As an additional contribution, we have used such a procedure to empirically illustrate the performance of three imputation methods (majority, naive Bayes and Bayesian networks) in three datasets. Three classifiers (decision tree, naive Bayes and nearest neighbours) have been used as modelling tools in our experiments. The achieved results illustrate a variety of situations that can take place in the data preparation practice.

Quality indices for (practical) clustering evaluation

Clustering quality or validation indices allow the evaluation of the quality of clustering in order to support the selection of a specific partition or clustering structure in its natural unsupervised environment, where the real solution is unknown or not available. In this paper, we investigate the use of quality indices mostly based on the concepts of clusters` compactness and separation, for the evaluation of clustering results (partitions in particular). This work intends to offer a general perspective regarding the appropriate use of quality indices for the purpose of clustering evaluation. After presenting some commonly used indices, as well as indices recently proposed in the literature, key issues regarding the practical use of quality indices are addressed. A general methodological approach is presented which considers the identification of appropriate indices thresholds. This general approach is compared with the simple use of quality indices for evaluating a clustering solution.

A note on a practical relationship between filter coefficients and scaling and wavelet functions of Discrete Wavelet Transforms

In this paper, the relationship between the filter coefficients and the scaling and wavelet functions of the Discrete Wavelet Transform is presented and exemplified from a practical point-of-view. The explanations complement the wavelet theory, that is well documented in the literature, being important for researchers who work with this tool for time-frequency analysis. (c) 2011 Elsevier Ltd. All rights reserved.

An algorithm for automatic checking of exercises in a dynamic geometry system: iGeom

One of the key issues in e-learning environments is the possibility of creating and evaluating exercises. However, the lack of tools supporting the authoring and automatic checking of exercises for specifics topics (e.g., geometry) drastically reduces advantages in the use of e-learning environments on a larger scale, as usually happens in Brazil. This paper describes an algorithm, and a tool based on it, designed for the authoring and automatic checking of geometry exercises. The algorithm dynamically compares the distances between the geometric objects of the student`s solution and the template`s solution, provided by the author of the exercise. Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output). Thus, for a given problem, if we know one function (construction) that solves the problem, we can compare it to any other function to check whether they are equivalent or not. Two functions are equivalent if, and only if, they have the same output when the same input is applied. If the student`s solution is equivalent to the template`s solution, then we consider the student`s solution as a correct solution. Our software utility provides both authoring and checking tools to work directly on the Internet, together with learning management systems. These tools are implemented using the dynamic geometry software, iGeom, which has been used in a geometry course since 2004 and has a successful track record in the classroom. Empowered with these new features, iGeom simplifies teachers` tasks, solves non-trivial problems in student solutions and helps to increase student motivation by providing feedback in real time. (c) 2008 Elsevier Ltd. All rights reserved.

Practical synthesis of chiral beta-telluro amines by ring-opening reaction of aziridines

A set of chiral beta-tellurium amines and their selenium and sulfur-containing derivatives have been efficiently synthesized in good to excellent yields via the ring-opening reaction of chiral aziridines by chalcogen nucleophilic species. (C) 2008 Elsevier B.V. All rights reserved.

Grafisk profilering med praktisk tillämpning på PZ hair : Graphic profiling with a practical application on PZ hair

Design, Grafiskt program, Symbol, Hair