Directional naive Bayes classifiers

López-Cruz, Pedro L.; Bielza, Concha; Larrañaga, Pedro

doi:10.1007/s10044-013-0340-z

Cited by 25 publications

(30 citation statements)

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“…Several phenomena and concepts in real life applications are represented by angular data or, as is referred in the literature, directional data. Some examples of directional information are the wind direction as analyzed by meteorologists, magnetic fields in rocks studied by geologists, geographic coordinates, among others [1]. Also, some entities are usually referenced in an angular manner; gynecologists denote the location to perform a biopsy, when performing a colposcopic screening, using the angle formed by the vertical axis of the cervix.…”

Section: Introductionmentioning

confidence: 99%

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Discriminative directional classifiers

Fernandes

Cardoso

2016

Neurocomputing

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a b s t r a c tIn different areas of knowledge, phenomena are represented by directional-angular or periodic-data; from wind direction and geographical coordinates to time references like days of the week or months of the calendar. These values are usually represented in a linear scale, and restricted to a given range (e.g. ½0; 2πÞ), hiding the real nature of this information. Therefore, dealing with directional data requires special methods. So far, the design of classifiers for periodic variables adopts a generative approach based on the usage of the von Mises distribution or variants. Since for non-periodic variables state of the art approaches are based on non-generative methods, it is pertinent to investigate the suitability of other approaches for periodic variables. We propose a discriminative Directional Logistic Regression model able to deal with angular data, which does not make any assumption on the data distribution. Also, we study the expressiveness of this model for any number of features. Finally, we validate our model against the previously proposed directional naïve Bayes approach and against a Support Vector Machine with a directional Radial Basis Function kernel with synthetic and real data obtaining competitive results.

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Section: Introductionmentioning

confidence: 99%

“…Working effectively with directional data requires dealing with techniques that are aware of the angular nature of the information [1]. For example, 0 and 2π are indeed the same angle and their average is not π but 0.…”

Section: Introductionmentioning

confidence: 99%

Discriminative directional classifiers

Fernandes

Cardoso

2016

Neurocomputing

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“…Wrapped Cauchy selective naive Bayes (wCsNB) is a classification model with a structure similar to that of wCNB, but not all the variables are necessarily used by the classifier. FSS techniques were previously employed in a circular classification model with von Mises and von Mises-Fisher distributions in [28], where a filter-wrapper algorithm is applied to rank the variables according to the mutual information between them and the class, and therefore, using the ranking provided by the filter step, the variables are selected to induce a new classifier until the best model is achieved.…”

Section: Wrapped Cauchy Selective Naive Bayesmentioning

confidence: 99%

“…There is no equation to compute the MI between circular variables and discrete variables. Therefore, we approach the problem using Monte Carlo methods, as in [28]; we model the conditional density functions of | = as wrapped Cauchy distributions. Hence…”

Section: Wrapped Cauchy Selective Naive Bayesmentioning

confidence: 99%

Circular Bayesian classifiers using wrapped Cauchy distributions

Leguey

Bielza

Larrañaga

2019

Data & Knowledge Engineering

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A B S T R A C TCapturing the dependences among circular variables within supervised classification models is a challenging task. In this paper, we propose four different supervised Bayesian classification algorithms where the predictor variables follow all circular wrapped Cauchy distributions. For this purpose, we introduce four wrapped Cauchy classifiers. The bivariate wrapped Cauchy distribution is the only bivariate circular distribution whose marginals and conditionals are also wrapped Cauchy distributions, a property that makes it possible to define these models easily. Furthermore, the wrapped Cauchy tree-augmented naive Bayes classifier requires the definition of a conditional circular mutual information measure between variables that follow wrapped Cauchy distributions. Synthetic data is used to illustrate, compare and evaluate the classification algorithms (including a comparison with the Gaussian TAN classifier, decision tree, random forest, multinomial logistic regression, support vector machine and simple neural network), leading to satisfactory predictive results. We also use a real neuromorphological dataset obtained from juvenile rat somatosensory cortex cells, where we measure the bifurcation angles of the dendritic basal arbors.characteristic that each variable is conditionally independent of those that are non-descendants in the graph given the value of their parents. Therefore the joint probability distribution is expressed as the product of the local distributions conditioned to their parents. For these reasons, Bayesian networks can deal efficiently with supervised classification i.e., the Bayesian network classifiers [13] and offer an explicit, graphical and interpretable representation of uncertain knowledge, which has made it possible to successfully apply them to real-world problems.Supervised classification [19] deals with the problem of assigning a label to an instance, based on a set of variables that characterize it. Yet circular data has been commonly treated as linear data in supervised classification tasks. Only a few circular classifiers exist, and almost none of them are based on the principles of Bayesian networks, capable of capturing multivariate relationships among variables. Most of them focus on discriminant analysis and assume several circular distributions such as the von Mises distribution [20], later extended to the von Mises-Fisher distribution [21]. There are also circular discriminant analysis studies for the Watson, Selby and Arnold distributions on the sphere [22,23]. SenGupta and Roy [24] used a classification discriminant rule based on the mean chord-length to classify a new observation into one of two different circular populations that are von Mises, when training samples are available for each of them. Also a likelihood ratio test based on a bootstrapping approach for classifying into two populations was proposed for linear and circular data [25]. Kirby and Miranda [26] proposed a variation of a neural network, including a circular node, which was able to ke...

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“…The von Mises distribution has received undisputed attention in the field of directional statistics (Jupp and Mardia (1989)) and in other areas like supervised classification (Lopez-Cruz et al (2013)). Thanks to desirable properties such as its symmetry, mathematical tractability and convergence to the wrapped normal distribution (Mardia and Jupp (2000)) for high concentrations, it is a viable option for many statistical analyses.…”

Section: Introductionmentioning

confidence: 99%

Univariate and bivariate truncated von Mises distributions

2017

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In this article we study the univariate and bivariate truncated von Mises distribution, as a generalization of the von Mises distribution (Jupp and Mardia (1989)), (Mardia and Jupp (2000)). This implies the addition of two or four new truncation parameters in the univariate and, bivariate cases, respectively. The results include the definition, properties of the distribution and maximum likelihood estimators for the univariate and bivariate cases. Additionally, the analysis of the bivariate case shows how the conditional distribution is a truncated von Mises distribution, whereas the marginal distribution that generalizes the distribution introduced in Singh (2002). From the viewpoint of applications, we test the distribution with simulated data, as well as with data regarding leaf inclination angles (Bowyer and Danson. (2005)) and dihedral angles in protein chains (Murzin AG (1995)).This research aims to assert this probability distribution as a potential option for modelling or simulating any kind of phenomena where circular distributions are applicable.

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Directional naive Bayes classifiers

Cited by 25 publications

References 50 publications

Discriminative directional classifiers

Discriminative directional classifiers

Circular Bayesian classifiers using wrapped Cauchy distributions

Univariate and bivariate truncated von Mises distributions

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