12,236 research outputs found
Probability density estimation with tunable kernels using orthogonal forward regression
A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately
On the characterization of flowering curves using Gaussian mixture models
In this paper, we develop a statistical methodology applied to the
characterization of flowering curves using Gaussian mixture models. Our study
relies on a set of rosebushes flowering data, and Gaussian mixture models are
mainly used to quantify the reblooming properties of each one. In this regard,
we also suggest our own selection criterion to take into account the lack of
symmetry of most of the flowering curves. Three classes are created on the
basis of a principal component analysis conducted on a set of reblooming
indicators, and a subclassification is made using a longitudinal --means
algorithm which also highlights the role played by the precocity of the
flowering. In this way, we obtain an overview of the correlations between the
features we decided to retain on each curve. In particular, results suggest the
lack of correlation between reblooming and flowering precocity. The pertinent
indicators obtained in this study will be a first step towards the
comprehension of the environmental and genetic control of these biological
processes.Comment: 28 pages, 27 figure
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