Search results for "Density estimation"
showing 10 items of 61 documents
CENTRAL LIMIT THEOREM FOR KERNEL ESTIMATOR OF INVARIANT DENSITY IN BIFURCATING MARKOV CHAINS MODELS
2021
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. Motivated by the functional estimation of the density of the invariant probability measure which appears as the asymptotic distribution of the trait, we prove the consistence and the Gaussian fluctuations for a kernel estimator of this density based on late generations. In this setting, it is interesting to note that the distinction of the three regimes on the ergodic rate identified in a previous work (for fluctuations of average over large generations) disappears. This result is a first step to go beyond the thresh…
CENTRAL LIMIT THEOREM FOR BIFURCATING MARKOV CHAINS
2020
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We first provide a central limit theorem for general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (2007), where the considered additive functionals are sums of martingale increments, and only one regime appears. Our first result can be seen as a discrete time version, but with general trait evoluti…
Observations of land use transformations during the Neolithic using exploratory spatial data analysis: contributions and limitations
2010
International audience; The settlement pattern analysis in archaeology implies some methodological questions. In this paper, we question some issues about the use of geostatistical methods for the observation of land use transformations during the Neolithic. We have developed two examples in Burgundy (France): the first one on a regional scale and the second one on a micro-regional scale. Using different ESDA approaches (Ripley’K function, Nearest Neighbour Distance, Kernel Density Estimation), we would like to underline what the methodological and archaeological contributions and their limits are. Both experiences point out that the results obtained depend not only on the analytical scale,…
Models and tools for territorial dynamic studies (chapter 1)
2012
As part of the ArchaeDyn project, a workgroup was formed to coordinate the development, implementation and application of methods and tools for spatial analysis. The workgroup's activities were directed at various problems. The first was to construct a grid common to all the workgroups and to homogenize the study areas used by the different workgroups in their databases. The 'confidence maps' method was suggested for assessing the quality and quantity of information inventoried in the databases. Confidence maps are produced from representation and reliability maps by simple map algebra and they can be considered as 'masks' for interpreting spatial analysis results. Finally, the research tea…
Spectral clustering with the probabilistic cluster kernel
2015
Abstract This letter introduces a probabilistic cluster kernel for data clustering. The proposed kernel is computed with the composition of dot products between the posterior probabilities obtained via GMM clustering. The kernel is directly learned from the data, is parameter-free, and captures the data manifold structure at different scales. The projections in the kernel space induced by this kernel are useful for general feature extraction purposes and are here exploited in spectral clustering with the canonical k-means. The kernel structure, informative content and optimality are studied. Analysis and performance are illustrated in several real datasets.
Semisupervised kernel orthonormalized partial least squares
2012
This paper presents a semisupervised kernel orthonormalized partial least squares (SS-KOPLS) algorithm for non-linear feature extraction. The proposed method finds projections that minimize the least squares regression error in Hilbert spaces and incorporates the wealth of unlabeled information to deal with small size labeled datasets. The method relies on combining a standard RBF kernel using labeled information, and a generative kernel learned by clustering all available data. The positive definiteness of the kernels is proven, and the structure and information content of the derived kernels is studied. The effectiveness of the proposed method is successfully illustrated in standard UCI d…
Semisupervised Kernel Feature Extraction for Remote Sensing Image Analysis
2014
This paper presents a novel semisupervised kernel partial least squares (KPLS) algorithm for nonlinear feature extraction to tackle both land-cover classification and biophysical parameter retrieval problems. The proposed method finds projections of the original input data that align with the target variable (labels) and incorporates the wealth of unlabeled information to deal with low-sized or underrepresented data sets. The method relies on combining two kernel functions: the standard radial-basis-function kernel based on labeled information and a generative, i.e., probabilistic, kernel directly learned by clustering the data many times and at different scales across the data manifold. Th…
A family of kernel anomaly change detectors
2014
This paper introduces the nonlinear extension of the anomaly change detection algorithms in [1] based on the theory of reproducing kernels. The presented methods generalize their linear counterparts, under both the Gaussian and elliptically-contoured assumptions, and produce both improved detection accuracies and reduced false alarm rates. We study the Gaussianity of the data in Hilbert spaces with kernel dependence estimates, provide low-rank kernel versions to cope with the high computational cost of the methods, and give prescriptions about the selection of the kernel functions and their parameters. We illustrate the performance of the introduced kernel methods in both pervasive and anom…
Semi-Supervised Remote Sensing Image Classification based on Clustering and the Mean Map Kernel
2008
This paper presents a semi-supervised classifier based on the combination of the expectation-maximization (EM) algorithm for Gaussian mixture models (GMM) and the mean map kernel. The proposed method uses the most reliable samples in terms of maximum likelihood to compute a kernel function that accurately reflects the similarity between clusters in the kernel space. The proposed method improves classification accuracy in situations where the available labeled information does not properly describe the classes in the test image.
Central limit theorem for bifurcating Markov chains under L 2 -ergodic conditions
2021
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMC under L 2-ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As application, we study the elementary case of symmetric bifurcating autoregressive process, which justify the non-trivial hypothesis considered on the kernel transition of the BMC. We illustrate in this example the phase transition observed in the fluctuations.