85,813 research outputs found
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
Mixtures of Regression Models for Time-Course Gene Expression Data: Evaluation of Initialization and Random Effects
Finite mixture models are routinely applied to time course microarray data.
Due to the complexity and size of this type of data the choice of good starting values plays
an important role. So far initialization strategies have only been investigated for data
from a mixture of multivariate normal distributions. In this work several initialization
procedures are evaluated for mixtures of regression models with and without random
effects in an extensive simulation study on different artificial datasets. Finally these
procedures are also applied to a real dataset from E. coli
From here to infinity - sparse finite versus Dirichlet process mixtures in model-based clustering
In model-based-clustering mixture models are used to group data points into
clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli
et al (2016) are sparse finite mixtures, where the prior distribution on the
weight distribution of a mixture with components is chosen in such a way
that a priori the number of clusters in the data is random and is allowed to be
smaller than with high probability. The number of cluster is then inferred
a posteriori from the data.
The present paper makes the following contributions in the context of sparse
finite mixture modelling. First, it is illustrated that the concept of sparse
finite mixture is very generic and easily extended to cluster various types of
non-Gaussian data, in particular discrete data and continuous multivariate data
arising from non-Gaussian clusters. Second, sparse finite mixtures are compared
to Dirichlet process mixtures with respect to their ability to identify the
number of clusters. For both model classes, a random hyper prior is considered
for the parameters determining the weight distribution. By suitable matching of
these priors, it is shown that the choice of this hyper prior is far more
influential on the cluster solution than whether a sparse finite mixture or a
Dirichlet process mixture is taken into consideration.Comment: Accepted versio
Functional Mixture Discriminant Analysis with hidden process regression for curve classification
We present a new mixture model-based discriminant analysis approach for
functional data using a specific hidden process regression model. The approach
allows for fitting flexible curve-models to each class of complex-shaped curves
presenting regime changes. The model parameters are learned by maximizing the
observed-data log-likelihood for each class by using a dedicated
expectation-maximization (EM) algorithm. Comparisons on simulated data with
alternative approaches show that the proposed approach provides better results.Comment: In Proceedings of the XXth European Symposium on Artificial Neural
Networks, Computational Intelligence and Machine Learning (ESANN), Pages
281-286, 2012, Bruges, Belgiu
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