Directional naive Bayes classifiers

Directional data are ubiquitous in science. These data have some special properties that rule out the use of classical statistics. Therefore, different distributions and statistics, such as the univariate von Mises and the multivariate von Mises–Fisher distributions, should be used to deal with this kind of information. We extend the naive Bayes classifier to the case where the conditional probability distributions of the predictive variables follow either of these distributions. We consider the simple scenario, where only directional predictive variables are used, and the hybrid case, where discrete, Gaussian and directional distributions are mixed. The classifier decision functions and their decision surfaces are studied at length. Artificial examples are used to illustrate the behavior of the classifiers. The proposed classifiers are then evaluated over eight datasets, showing competitive performances against other naive Bayes classifiers that use Gaussian distributions or discretization to manage directional data

Support Directional Shifting Vector: A Direction Based Machine Learning Classifier

Machine learning models have been very popular nowadays for providing rigorous solutions to complicated real-life problems. There are three main domains named supervised, unsupervised, and reinforcement. Supervised learning mainly deals with regression and classification. There exist several types of classification algorithms, and these are based on various bases. The classification performance varies based on the dataset velocity and the algorithm selection. In this article, we have focused on developing a model of angular nature that performs supervised classification. Here, we have used two shifting vectors named Support Direction Vector (SDV) and Support Origin Vector (SOV) to form a linear function. These vectors form a linear function to measure cosine-angle with both the target class data and the non-target class data. Considering target data points, the linear function takes such a position that minimizes its angle with target class data and maximizes its angle with non-target class data. The positional error of the linear function has been modelled as a loss function which is iteratively optimized using the gradient descent algorithm. In order to justify the acceptability of this method, we have implemented this model on three different standard datasets. The model showed comparable accuracy with the existing standard supervised classification algorithm. Doi: 10.28991/esj-2021-01306 Full Text: PD

Impact Learning: A Learning Method from Features Impact and Competition

Machine learning is the study of computer algorithms that can automatically improve based on data and experience. Machine learning algorithms build a model from sample data, called training data, to make predictions or judgments without being explicitly programmed to do so. A variety of wellknown machine learning algorithms have been developed for use in the field of computer science to analyze data. This paper introduced a new machine learning algorithm called impact learning. Impact learning is a supervised learning algorithm that can be consolidated in both classification and regression problems. It can furthermore manifest its superiority in analyzing competitive data. This algorithm is remarkable for learning from the competitive situation and the competition comes from the effects of autonomous features. It is prepared by the impacts of the highlights from the intrinsic rate of natural increase (RNI). We, moreover, manifest the prevalence of the impact learning over the conventional machine learning algorithm

Support directional shifting vector: A direction based machine learning classifier

Machine learning models have been very popular nowadays for providing rigorous solutions to complicated real-life problems. There are three main domains named supervised, unsupervised, and reinforcement. Supervised learning mainly deals with regression and classification. There exist several types of classification algorithms, and these are based on various bases. The classification performance varies based on the dataset velocity and the algorithm selection. In this article, we have focused on developing a model of angular nature that performs supervised classification. Here, we have used two shifting vectors named Support Direction Vector (SDV) and Support Origin Vector (SOV) to form a linear function. These vectors form a linear function to measure cosine-angle with both the target class data and the non-target class data. Considering target data points, the linear function takes such a position that minimizes its angle with target class data and maximizes its angle with non-target class data. The positional error of the linear function has been modelled as a loss function which is iteratively optimized using the gradient descent algorithm. In order to justify the acceptability of this method, we have implemented this model on three different standard datasets. The model showed comparable accuracy with the existing standard supervised classification algorithm

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Multimodal Image Fusion and Its Applications.

Image fusion integrates different modality images to provide comprehensive information of the image content, increasing interpretation capabilities and producing more reliable results. There are several advantages of combining multi-modal images, including improving geometric corrections, complementing data for improved classification, and enhancing features for analysis...etc. This thesis develops the image fusion idea in the context of two domains: material microscopy and biomedical imaging. The proposed methods include image modeling, image indexing, image segmentation, and image registration. The common theme behind all proposed methods is the use of complementary information from multi-modal images to achieve better registration, feature extraction, and detection performances. In material microscopy, we propose an anomaly-driven image fusion framework to perform the task of material microscopy image analysis and anomaly detection. This framework is based on a probabilistic model that enables us to index, process and characterize the data with systematic and well-developed statistical tools. In biomedical imaging, we focus on the multi-modal registration problem for functional MRI (fMRI) brain images which improves the performance of brain activation detection.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120701/1/yuhuic_1.pd