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Register a new userDepth and depth-based classification with R-package ddalpha
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Added by
Pavlo Mozharovskyi
Publication date
2016
fields
Mathematical Statistics
and research's language is
English
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Following the seminal idea of Tukey, data depth is a function that measures how close an arbitrary point of the space is located to an implicitly defined center of a data cloud. Having undergone theoretical and computational developments, it is now employed in numerous applications with classification being the most popular one. The R-package ddalpha is a software directed to fuse experience of the applicant with recent achievements in the area of data depth and depth-based classification. ddalpha provides an implementation for exact and approximate computation of most reasonable and widely applied notions of data depth. These can be further used in the depth-based multivariate and functional classifiers implemented in the package, where the $DDalpha$-procedure is in the main focus. The package is expandable with user-defined custom depth methods and separators. The implemented functions for depth visualization and the built-in benchmark procedures may also serve to provide insights into the geometry of the data and the quality of pattern recognition.
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Prediction rule ensembles (PREs) are sparse collections of rules, offering highly interpretable regression and classification models. This paper presents the R package pre, which derives PREs through the methodology of Friedman and Popescu (2008). The implementation and functionality of package pre is described and illustrated through application on a dataset on the prediction of depression. Furthermore, accuracy and sparsity of PREs is compared with that of single trees, random forest and lasso regression in four benchmark datasets. Results indicate that pre derives ensembles with predictive accuracy comparable to that of random forests, while using a smaller number of variables for prediction.
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A new procedure, called DDa-procedure, is developed to solve the problem of classifying d-dimensional objects into q >= 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0,1]^q. Specifically, the depth is the zonoid depth, and the algorithm is the alpha-procedure. In case of more than two classes several binary classifications are performed and a majority rule is applied. Special treatments are discussed for outsiders, that is, data having zero depth vector. The DDa-classifier is applied to simulated as well as real data, and the results are compared with those of similar procedures that have been recently proposed. In most cases the new procedure has comparable error rates, but is much faster than other classification approaches, including the SVM.
Fingerprint classification is an effective technique for reducing the candidate numbers of fingerprints in the stage of matching in automatic fingerprint identification system (AFIS). In recent years, deep learning is an emerging technology which has achieved great success in many fields, such as image processing, natural language processing and so on. In this paper, we only choose the orientation field as the input feature and adopt a new method (stacked sparse autoencoders) based on depth neural network for fingerprint classification. For the four-class problem, we achieve a classification of 93.1 percent using the depth network structure which has three hidden layers (with 1.8% rejection) in the NIST-DB4 database. And then we propose a novel method using two classification probabilities for fuzzy classification which can effectively enhance the accuracy of classification. By only adjusting the probability threshold, we get the accuracy of classification is 96.1% (setting threshold is 0.85), 97.2% (setting threshold is 0.90) and 98.0% (setting threshold is 0.95). Using the fuzzy method, we obtain higher accuracy than other methods.
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