Mises-Fisher Distribution Research Articles

A long-term joint probability model for metocean circular and linear characteristics

Structural performance analysis of offshore structures extremely depends on the smart selection of design environment. In this paper, a joint probability model is developed to provide the designers with the joint probability of occurrence of all possible sea states including their circular and linear variables. The presented Joint PDF consists of a marginal PDF for circular variable and two conditional PDFs for linear variables. The marginal PDF for wave direction as a circular variable is a mixture of von-Mises Fisher distribution and the conditional PDFs are assumed to be a conditional Weibull distribution for wave height and a conditional lognormal distribution for wave period. An extreme value analysis is also applied to make sure that the model covers all possible ranges of wave circular and linear parameters in the desired lifetime. Design scenarios can be chosen from the highest probable combinations of wave height, period and direction. The proposed method was applied on Caspian Sea 45-years and Persian Gulf 11-years hindcast data. The results indicate the acceptable accuracy and practicality of this methodology for the directionality dependent design approaches.

A longitudinal model for shapes through triangulation

It is known that the shapes of planar triangles can be represented by a set of points on the surface of the unit sphere. On the other hand, most of the objects can easily be triangulated and so each triangle can accordingly be treated in the context of shape analysis. There is a growing interest to fit a smooth path going through the cloud of shape data available in some time instances. To tackle this problem, we propose a longitudinal model through a triangulation procedure for the shape data. In fact, our strategy initially relies on a spherical regression model for triangles, but is extended to shape data via triangulation. Regarding modeling of directional data, we use the bivariate von Mises–Fisher distribution for density of the errors. Various forms of the composite likelihood functions, constructed by altering the assumptions considered for the angles defined for each triangle, are invoked. The proposed regression model is applied to rat skull data. Also, some simulations results are presented along with the real data results.

Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations

We suggest a new efficient and reliable random walk method, continuous both in space and time, for solving high-dimensional diffusion–advection–reaction equations. It is based on a discovered intrinsic relation between the von Mises–Fisher distribution on a sphere with this type of equations. It can be formulated as follows: the von Mises–Fisher distribution uniquely defines the solution of a diffusion–advection equation in any bounded or unbounded domain if the relevant boundary value problem for this equation satisfies regular existence and uniqueness conditions. Both two- and three-dimensional transient equations are included in our considerations. The accuracy and the cost of the suggested random walk on spheres method are estimated.

A Novel 3D Non-Stationary Vehicle-to-Vehicle Channel Model and its Spatial-Temporal Correlation Properties

In this paper, a new non-stationary Vehicle-to-Vehicle (V2V) channel model is proposed. It could generate more smooth fading phase between the adjacent channel states and guarantee more accurate Doppler frequency, which is a great improvement comparing with those of the existing non-stationary geometry-based stochastic models (GBSMs) for V2V channels. Meanwhile, the spatial–temporal correlation function (STCF) as well as a temporal correlation function (TCF) and a spatial correlation function (SCF) are derived in details based on the power angle spectrums of both the mobile transmitter (MT) and mobile receiver (MR) following the Von Mises Fisher (VMF) distribution. Simulation results have demonstrated that the time-variant correlation properties of our proposed channel model have an excellent agreement with the theoretical results, which verifies the correctness of theoretical derivations and simulations. Finally, the TCF and stationary interval of the proposed model are verified by the measured results.

A Spherical Probability Distribution Model of the User-Induced Mobile Phone Orientation

This paper presents a statistical modeling approach of the real-life user-induced randomness due to mobile phone orientations for different phone usage types. As well-known, the radiated performance of a wireless device depends on its orientation and position relative to the user. Therefore, realistic handset usage models will lead to more accurate over-the-air characterization measurements for antennas and wireless devices in general. We introduce a phone usage classification based on the network access modes, e.g., voice (circuit switched) or non-voice (packet switched) services, and the use of accessories, such as wired or Bluetooth handsets, or a speaker-phone during the network access session. The random phone orientation is then modeled by the spherical von Mises-Fisher distribution for each of the identified phone usage types. A finite mixture model based on the individual probability distribution functions and heuristic weights is also presented. The models are based on data collected from built-in accelerometer measurements. Our approach offers a straightforward modeling of the user-induced random orientation for different phone usage types. The models can be used in the design of better handsets and antenna systems as well as for the design and optimization of wireless networks.

Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions

Background:In the statistical analysis of directional data, the von Mises-Fisher distribution plays an important role to model unit vectors. The estimation of the parameters of a mixture of von Mises-Fisher distributions can be done through the Estimation-Maximization algorithm.Objective:In this paper we propose a dynamic clusters type algorithm based on the estimation of the parameters of a mixture of von Mises-Fisher distributions for clustering directions, and we compare this algorithm with the Estimation-Maximization algorithm. We also define the between-groups and within-groups variability measures to compare the solutions obtained with the algorithms through these measures.Results:The comparison of the clusters obtained with both algorithms is provided for a simulation study based on samples generated from a mixture of two Fisher distributions and for an illustrative example with spherical data.

Multivariate saddlepoint tests on the mean direction of the von Mises–Fisher distribution

This article provides P values for two new tests on the mean direction of the von Mises–Fisher distribution. The test statistics are obtained from the exponent of the saddlepoint approximation to the density of M-estimators, as suggested by Robinson et al. (Ann Stat 31:1154–1169, 2003). These test statistics are chi-square distributed with asymptotically small relative errors. Despite the high dimensionality of the problem, the proposed P values are accurate and simple to compute. The numerical precision of the P values of the new tests is illustrated by some simulation studies.

3-D MIMO Parametric Stochastic Channel Model for Urban Macrocell Scenario

For the design, performance evaluation, and optimization of potential 3-D multiple input and multiple output (3-D MIMO) algorithms, an accurate stochastic channel model is indispensable. Simultaneously, it is desirable for the new 3-D MIMO channel model to be a further expansion of already well developed 2-D MIMO channel models to allow easy implementation and facilitate possible $3^{rd}$ generation partnership project standardization. This paper first shows our recent outfield channel measurement campaigns in urban macrocell scenarios with a planar antenna array and a crown-shaped antenna array installed on the base station and the user sides, respectively. A comprehensive methodology from the statistical analysis perspective to characterize the 3-D MIMO channel, particularly, in the elevation domain, is then elaborated upon. The framework of the new approach coincides with mainstream parametric stochastic models. Moreover, it is observed that, by recalculating the statistics of the large scale parameters as well as their cross-correlation matrix to rectify existent non-positive definite problem, adding distance dependent elevation angular spread and introducing a mixture of Von Mises Fisher distributions to describe the interdependence between azimuth and elevation, the accuracy of current standardized 3-D channel models can be improved upon. Finally, numerical results verify the validity of our proposal.

Learning-based EM clustering for data on the unit hypersphere with application to exoplanet data

This study focuses on clustering algorithms for data on the unit hypersphere. This type of directional data lain on the surface of a unit hypersphere is used in geology, biology, meteorology, medicine and oceanography. The EM algorithm with mixtures of von Mises-Fisher distributions is often used for model-based clustering for data on the unit hypersphere. However, the EM algorithm is sensitive to initial values and outliers and a number of clusters must be assigned a priori. In this paper, we propose an effective approach, called a learning-based EM algorithm with von Mises-Fisher distributions, to cluster this type of hyper-spherical data. The proposed clustering method is robust to outliers, without the need for initialization, and automatically determines the number of clusters. Thus, it becomes a fully-unsupervised model-based clustering method for data on the unit hypersphere. Some numerical and real examples with comparisons are given to demonstrate the effectiveness and superiority of the proposed method. We also apply the proposed learning-based EM algorithm to cluster exoplanet data in extrasolar planets. The clustering results have several important implications for exoplanet data and allow an interpretation of exoplanet migration.

The Analysis of Ranking Data Using Score Functions and Penalized Likelihood

In this paper, we consider different score functions in order summarize certain characteristics for one and two sample ranking data sets. Our approach is flexible and is based on embedding the nonparametric problem in a parametric framework. We make use of the von Mises-Fisher distribution to approximate the normalizing constant in our model. In order to gain further insight in the data, we make use of penalized likelihood to narrow down the number of items where the rankers differ. We applied our method on various real life data sets and we conclude that our methodology is consistent with the data.

Saddlepoint approximations to the distribution of the total distance of the multivariate isotropic and von Mises–Fisher random walks

This article considers the random walk over Rp, with p ≥ 2, where the directions taken by the individual steps follow either the isotropic or the vonMises–Fisher distributions. Saddlepoint approximations to the density and to upper tail probabilities of the total distance covered by the random walk, i.e., of the length of the resultant, are derived. The saddlepoint approximations are onedimensional and simple to compute, even though the initial problem is p-dimensional. Numerical illustrations of the high accuracy of the proposed approximations are provided.

Structure-From-Motion in Spherical Video Using the von Mises-Fisher Distribution.

In this paper, we present a complete pipeline for computing structure-from-motion from the sequences of spherical images. We revisit problems from multiview geometry in the context of spherical images. In particular, we propose methods suited to spherical camera geometry for the spherical-n-point problem (estimating camera pose for a spherical image) and calibrated spherical reconstruction (estimating the position of a 3-D point from multiple spherical images). We introduce a new probabilistic interpretation of spherical structure-from-motion which uses the von Mises-Fisher distribution to model noise in spherical feature point positions. This model provides an alternate objective function that we use in bundle adjustment. We evaluate our methods quantitatively and qualitatively on both synthetic and real world data and show that our methods developed for spherical images outperform straightforward adaptations of methods developed for perspective images. As an application of our method, we use the structure-from-motion output to stabilise the viewing direction in fully spherical video.

Ligand Release Pathways Obtained with WExplore: Residence Times and Mechanisms.

The binding of ligands with their molecular receptors is of tremendous importance in biology. Although much emphasis has been placed on characterizing binding sites and bound poses that determine the binding thermodynamics, the pathway by which a ligand binds importantly determines the binding kinetics. The computational study of entire unbiased ligand binding and release pathways is still an emerging field, made possible only recently by advances in computational hardware and sampling methodologies. We have developed one such method (WExplore) that is based on a weighted ensemble of trajectories, which we apply to ligand release for the first time, using a set of three previously characterized interactions between low-affinity ligands and the protein FKBP-12 (FK-506 binding protein). WExplore is found to be more efficient that conventional sampling, even for the nanosecond-scale unbinding events observed here. From a nonequilibrium ensemble of unbinding trajectories, we obtain ligand residence times and release pathways without using biasing forces or a Markovian assumption of transitions between regions. We introduce a set of analysis tools for unbinding transition pathways, including using von Mises-Fisher distributions to model clouds of ligand exit points, which provide a quantitative proxy for ligand surface diffusion. Differences between the transition pathway ensembles of the three ligands are identified and discussed.

Asymmetric biclustering with constrained von Mises-Fisher models

As a probability distribution on the high-dimensional sphere, the von Mises-Fisher (vMF) distribution is widely used for directional statistics and data analysis methods based on correlation. We consider a constrained vMF distribution for block modeling, which provides a probabilistic model of an asymmetric biclustering method that uses correlation as the similarity measure of data features. We derive the variational Bayesian inference algorithm for the mixture of the constrained vMF distributions. It is applied to a multivariate data visualization method implemented with enhanced parallel coordinate plots.

Nonparametric Spherical Topic Modeling with Word Embeddings.

Traditional topic models do not account for semantic regularities in language. Recent distributional representations of words exhibit semantic consistency over directional metrics such as cosine similarity. However, neither categorical nor Gaussian observational distributions used in existing topic models are appropriate to leverage such correlations. In this paper, we propose to use the von Mises-Fisher distribution to model the density of words over a unit sphere. Such a representation is well-suited for directional data. We use a Hierarchical Dirichlet Process for our base topic model and propose an efficient inference algorithm based on Stochastic Variational Inference. This model enables us to naturally exploit the semantic structures of word embeddings while flexibly discovering the number of topics. Experiments demonstrate that our method outperforms competitive approaches in terms of topic coherence on two different text corpora while offering efficient inference.

3D Wideband Non-Stationary Geometry-Based Stochastic Models for Non-Isotropic MIMO Vehicle-to-Vehicle Channels

Actual vehicle-to-vehicle (V2V) channel measurements have shown that the wide-sense stationary (WSS) modeling assumption is valid only for very short time intervals. This fact motivates us to develop non-WSS V2V channel models. In this paper, we propose a novel three-dimensional (3D) theoretical non-WSS regular-shaped geometry-based stochastic model (RS-GBSM) and the corresponding sum-of-sinusoids (SoS) simulation model for non-isotropic scattering wideband multiple-input multiple-output (MIMO) V2V fading channels. The movements of the transmitter (Tx), scatterers, and receiver (Rx) result in the time-varying angles of departure (AoDs) and angles of arrival (AoAs) that make our models non-stationary. The proposed RS-GBSMs, combining line-of-sight (LoS) components, a two-sphere model, and multiple confocal elliptic-cylinder models, have the ability to study the impacts of vehicular traffic density (VTD) and non-stationarity on channel statistics, and jointly consider the azimuth and elevation angles by using the von Mises Fisher (VMF) distribution. The proposed RS-GBSMs are sufficiently generic and adaptable to model various V2V scenarios. Based on the proposed 3D non-WSS RS-GBSMs, important local channel statistical properties are derived and thoroughly investigated. The impacts of VTD and non-stationarity on these channel statistical properties are investigated by comparing them with those of the corresponding WSS model. The proposed non-WSS RS-GBSMs are validated by measurements in terms of the channel stationary time. Finally, numerical and simulation results demonstrate that the 3D non-WSS model is more practical to characterize real V2V channels.

Spatially Robust Far-field Beamforming Using the von Mises(-Fisher) Distribution

This paper presents spatially robust far-field microphone beamformers and nullformers derived using the von Mises and von Mises-Fisher distributions to model the expected direction of arrival. Simple analytic expressions are presented for 2D and 3D far-field correlation functions and used to design spatially robust beamformers and nullformers. It is demonstrated that the spatially robust beamformers show a modest improvement in tolerating uncertainty in the target direction of arrival without incurring a significant penalty in terms of SINR performance compared with the MVDR beamformer. In addition, the spatially robust formulation shows significantly improved numerical robustness, indicating improved ability in tolerating intrinsic array errors.

Performance Analysis of Two‐Dimensional Massive Antenna Arrays for Future Mobile Networks

In this paper, the performance of a massive multiple-antenna system under the pilot contamination effect is studied. A 2-D massive antenna array with a uniform circular array (UCA) topology at base stations (BSs) is considered. A 3-D spatial channel model with Von Mises Fisher (VMF) distribution is applied. It is shown that the interfering channels tend to fall into the null space of the desired user's covariance matrix. The pilot contamination can be mitigated if the angle-of-arrival (AoA) pairs of the interfering users have a nonoverlapping region with the AoA of the desired user. The impact of the AoA distribution on the beam pattern is studied as well. Numerical results confirm the analysis and show that the mitigation of pilot contamination depends on the directional dispersion of the multipath AoA distribution.

A discriminative approach to perspective shape from shading in uncalibrated illumination

Estimating surface normals from a single image alone is a challenging problem. Previous work made various simplifications and focused on special cases, such as having directional lighting, known reflectance maps, etc. This is problematic, however, as shape from shading becomes impractical outside the lab. We argue that addressing more realistic settings requires multiple shading cues to be combined as well as generalized to natural illumination. However, this requires coping with an increased complexity of the approach and more parameters to be adjusted. Starting from a novel large-scale dataset for training and analysis, we pursue a discriminative learning approach to shape from shading. Regression forests enable efficient pixel-independent prediction and fast learning. The regression trees are adapted to predicting surface normals by using von Mises–Fisher distributions in the leaves. Spatial regularity of the normals is achieved through a combination of spatial features, including texton as well as novel silhouette features. The proposed silhouette features leverage the occluding contours of the surface and yield scale-invariant context. Their benefits include computational efficiency and good generalization to unseen data. Importantly, they allow estimating the reflectance map robustly, thus addressing the uncalibrated setting. Our method can also be extended to handle perspective projection. Experiments show that our discriminative approach outperforms the state of the art on various synthetic and real-world datasets.

Modeling a Multi-modal Distribution of Wind Direction Data in Kudat, Malaysia

Wind direction is the direction from which the wind is blowing. It is expressed in terms of degrees measured clockwise from geographical direction. The knowledge of the wind direction can be used to obtain information about the wind energy potential, dispersion of particulate matter in the air, the effects of engineering structures on the building, maritime study, and etc. This study provides a suitable model for the wind direction that indicates multi-modal distributional properties. A case study involves with a data from Kudat, Malaysia has been analysed. The statistical models known as a Finite Mixture of von Mises Fisher (mvMF) and Circular Distribution based on Nonnegative Trigonometric Sums (NNTS) has been fitted to the data. Then, the suitability of mvMF and NNTS models were judged based on a graphical representation and goodness-of-fit statistics. The results found that the mvMF model with components is sufficient to provide a best model.