Сравнение критериев выбора модели в задачах аппроксимации с естественным базисом

Проведен сравнительный анализ критериев выбора линейной модели на примере задачи определения содержания радионуклидов в объектах окружающей среды. В качестве базисных функций использованы функции отклика детектора на воздействие гамма-квантов с определенной энергией. Исследована зависимость сложности и адекватности (качества) моделей от уровня шума для разных критериев выбора модели.Проведено порівняльний аналіз критеріїв вибору лінійної моделі на прикладі задачі визначення складу радіонуклідів в об'єктах навколишнього середовища. За базисні функції було взято функції відгуку детектора на вплив гамма-квантів з визначеною енергією. Досліджено залежність складності й адекватності (якості) моделей від рівня шуму для різних критеріїв вибору моделі.A comparative analysis of linear model selection criteria applied to the problem of assessing the radionuclide content in environmental objects is performed. Detector outputs obtained for gamma-quanta of particular energy are used as basis functions. Complexity and quality of models vs noise level for various model selection criteria is investigated

Representing functional data in reproducing Kernel Hilbert Spaces with applications to clustering and classification

Functional data are difficult to manage for many traditional statistical techniques given their very high (or intrinsically infinite) dimensionality. The reason is that functional data are essentially functions and most algorithms are designed to work with (low) finite-dimensional vectors. Within this context we propose techniques to obtain finitedimensional representations of functional data. The key idea is to consider each functional curve as a point in a general function space and then project these points onto a Reproducing Kernel Hilbert Space with the aid of Regularization theory. In this work we describe the projection method, analyze its theoretical properties and propose a model selection procedure to select appropriate Reproducing Kernel Hilbert spaces to project the functional data.Functional data, Reproducing, Kernel Hilbert Spaces, Regularization theory

Representing functional data in reproducing Kernel Hilbert Spaces with applications to clustering and classification

Functional data are difficult to manage for many traditional statistical techniques given their very high (or intrinsically infinite) dimensionality. The reason is that functional data are essentially functions and most algorithms are designed to work with (low) finite-dimensional vectors. Within this context we propose techniques to obtain finitedimensional representations of functional data. The key idea is to consider each functional curve as a point in a general function space and then project these points onto a Reproducing Kernel Hilbert Space with the aid of Regularization theory. In this work we describe the projection method, analyze its theoretical properties and propose a model selection procedure to select appropriate Reproducing Kernel Hilbert spaces to project the functional data

Stability Selection of the Number of Clusters

Selecting the number of clusters is one of the greatest challenges in clustering analysis. In this thesis, we propose a variety of stability selection criteria based on cross validation for determining the number of clusters. Clustering stability measures the agreement of clusterings obtained by applying the same clustering algorithm on multiple independent and identically distributed samples. We propose to measure the clustering stability by the correlation between two clustering functions. These criteria are motivated by the concept of clustering instability proposed by Wang (2010), which is based on a form of clustering distance. In addition, the effectiveness and robustness of the proposed methods are numerically demonstrated on a variety of simulated and real world samples