Mahalanobis distance

About: Mahalanobis distance is a research topic. Over the lifetime, 4616 publications have been published within this topic receiving 95294 citations.

M3GP – multiclass classification with GP

Abstract: Data classification is one of the most ubiquitous machine learning tasks in science and engineering. However, Genetic Programming is still not a popular classification methodology, partially due to its poor performance in multiclass problems. The recently proposed M2GP - Multidimensional Multiclass Genetic Programming algorithm achieved promising results in this area, by evolving mappings of the \(p\)-dimensional data into a \(d\)-dimensional space, and applying a minimum Mahalanobis distance classifier. Despite good performance, M2GP employs a greedy strategy to set the number of dimensions \(d\) for the transformed data, and fixes it at the start of the search, an approach that is prone to locally optimal solutions. This work presents the M3GP algorithm, that stands for M2GP with multidimensional populations. M3GP extends M2GP by allowing the search process to progressively search for the optimal number of new dimensions \(d\) that maximize the classification accuracy. Experimental results show that M3GP can automatically determine a good value for \(d\) depending on the problem, and achieves excellent performance when compared to state-of-the-art-methods like Random Forests, Random Subspaces and Multilayer Perceptron on several benchmark and real-world problems.

End milling tool breakage detection using lifting scheme and Mahalanobis distance

Abstract: In this paper, a novel method based on lifting scheme and Mahalanobis distance (MD) is proposed for detection of tool breakage via acoustic emission (AE) signals generated in end milling process. The method consists of three stages. First, by investigating the specialty of AE signals, a biorthogonal wavelet with impact property is constructed using lifting scheme, and wavelet transform is carried out to separate AE components from the original signals. Second, Hilbert transform is adopted to demodulate signal envelope on wavelet coefficients and salient features indicating the tool state (i.e., normal conditions, slight breakage, and serious breakage) are extracted. Finally, tool conditions are identified directly through the recognition of these features by means of MD. Practical application results on a CNC vertical milling machine tool show that the proposed method is accurate for feature extraction and efficient for condition monitoring of cutting tools in end milling process.

A note on “distance transformations in digital images

Abstract: The influence of using distinct optimization criteria for determining the coefficients of a distance transform is studied. The criteria studied are (1) minimizing the maximum of the absolute value of the difference between the distance transform and Euclidaan distance, and (2) minimizing the root-mean-square difference between the distance transform and Euclidean distance. By allowing an overall scaling factor to have other than integer values, other integer approximations of the distance transform's coefficients result as optimal. Emphasis is given to isotropy, or invariance with respect to rotation, and to the use of unbiased distance estimates.