An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov–Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the Kolmogorov–Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.’s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov–Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.’s in only 6 different clusters that correspond to 6 different c.p.d.f.’s.This research has been partially supported by the Spanish Consejería de Economía, Innovación y Ciencia of the Junta de Andalucía under projects TIC-6441 and P11-RNM7115, and the Spanish MEC under project ECO2011–29751

A statistically principled approach to histogram segmentation

This paper outlines a statistically principled approach to clustering one dimensional data. Given a dataset, the idea is to fit a density function that is as simple as possible, but still compatible with the data. Simplicity is measured in terms of a standard smoothness functional. Data-compatibility is given a precise meaning in terms of distribution-free statistics based on the empirical distribution function. The main advantages of this approach are that (i) it involves a single decision-parameter which has a clear statistical interpretation, and (ii) there is no need to make a priori assumptions about the number or shape of the clusters

Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure. In this paper we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained which lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.Comment: Accepted for publication in the IEEE Transactions on Geoscience and Remote Sensing journa

Nonparametric Bayesian Image Segmentation

Image segmentation algorithms partition the set of pixels of an image into a specific number of different, spatially homogeneous groups. We propose a nonparametric Bayesian model for histogram clustering which automatically determines the number of segments when spatial smoothness constraints on the class assignments are enforced by a Markov Random Field. A Dirichlet process prior controls the level of resolution which corresponds to the number of clusters in data with a unique cluster structure. The resulting posterior is efficiently sampled by a variant of a conjugate-case sampling algorithm for Dirichlet process mixture models. Experimental results are provided for real-world gray value images, synthetic aperture radar images and magnetic resonance imaging dat

Automatic Positional Accuracy Assessment of Imagery Segmentation Processes: A Case Study

There are many studies related to Imagery Segmentation (IS) in the field of Geographic Information (GI). However, none of them address the assessment of IS results from a positional perspective. In a field in which the positional aspect is critical, it seems reasonable to think that the quality associated with this aspect must be controlled. This paper presents an automatic positional accuracy assessment (PAA) method for assessing this quality component of the regions obtained by means of the application of a textural segmentation algorithm to a Very High Resolution (VHR) aerial image. This method is based on the comparison between the ideal segmentation and the computed segmentation by counting their differences. Therefore, it has the same conceptual principles as the automatic procedures used in the evaluation of the GI's positional accuracy. As in any PAA method, there are two key aspects related to the sample that were addressed: (i) its size-specifically, its influence on the uncertainty of the estimated accuracy values-and (ii) its categorization. Although the results obtained must be taken with caution, they made it clear that automatic PAA procedures, which are mainly applied to carry out the positional quality assessment of cartography, are valid for assessing the positional accuracy reached using other types of processes. Such is the case of the IS process presented in this study

Cerebral white matter status and resting state functional MRI.

White Matter (WM) is a pivotal component of the Central Nervous System (CNS), and its main role is the transmission of the neural impulses within the CNS and between CNS and Peripheral Nervous System (PNS). It is note from literature that changes in the WM affects the function of the CNS with effects on the higher neurological function, included cognition. Further, it has been theorized in the last decades that ageing-associated decline in higher neurological functions, in particular in the neurocognitive sphere, could be at least partly explained by the “disconnection” of the cortical areas of the brain due to the WM degeneration. Although standard “in-vivo” imaging biomarkers of WM integrity have not been validated yet for clinical purposes, several researches have demonstrated the correlation between different potential imaging biomarkers and WM integrity. The aim of the PhD project is to explore and better understanding the effects of WM status on the brain structure, networking and cognition. In particular, we designed three distinct explorative and cross-sectional studies; more specifically, we analyzed the effects of two Magnetic Resonance Imaging (MRI) markers of WM degeneration (the global Fractional Anisotropy (gFA) and the white matter hyperintensities burden (WMHb), respectively) on the brain activity measured with the Resting-State Functional Magnetic Resonance Imaging (rs-fMRI) technique. The project was conducted by analyzing a human population of healthy subjects extracted from the public available dataset “Leipzig Study for Mind-Body-Emotion Interactions” (LEMON). The results of these studies have been published during the PhD course on three distinct international scientific papers