Search results for "correlation"
showing 10 items of 2282 documents
Diffusion map for clustering fMRI spatial maps extracted by Indipendent Component Analysis
2013
Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Clustering of the spatial maps is usually based on correlation matrices. This usually works well, although such a similarity matrix inherently can explain only a certain amount of the total variance contained in the high-dimensional data where n is relatively small but p is large. For high-dimensional space, it is reasonable to perform dimensionality reduction before clustering.…
Gaussianizing the Earth: Multidimensional Information Measures for Earth Data Analysis
2021
Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is challenging because spatio-temporal data is high-dimensional, heterogeneous and has non-linear characteristics. In this paper, we apply multivariate Gaussianization for probability density estimation which is robust to dimensionality, comes with statistical guarantees, and is easy to apply. In addition, this methodology allows us to estimate information-theoretic measures to characterize multivariate densities: information, entropy, total correlation, and mutual in…
Microstructure reconstruction using entropic descriptors
2009
A multi-scale approach to the inverse reconstruction of a pattern's microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for stochastic optimization method. The first of them measures a spatial inhomogeneity, for a binary pattern, or compositional one, for a greyscale image. The second one quantifies a spatial or compositional statistical complexity. The EDs reveal structural information that is dissimilar, at least in part, to that given by correlation functions at almost all of discrete length scales. The method is tested on a few digitized binary and greyscale images. In each of the cases, the persuasive reconstruction of the mic…
Local inhomogeneous weighted summary statistics for marked point processes
2023
We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture different kinds of local dependence structures. We first derive some basic properties and show how these new statistical tools can be used to construct most existing summary statistics for (marked) point processes. We then propose a local test of random labelling. This procedure allows us to identify points, and consequently regions, where the random labelling assumption does not hold, e.g.~when the (functional) marks are spatially dependent. Through a simulatio…
Bootstrap validation of links of a minimum spanning tree
2018
We describe two different bootstrap methods applied to the detection of a minimum spanning tree obtained from a set of multivariate variables. We show that two different bootstrap procedures provide partly distinct information that can be highly informative about the investigated complex system. Our case study, based on the investigation of daily returns of a portfolio of stocks traded in the US equity markets, shows the degree of robustness and completeness of the information extracted with popular information filtering methods such as the minimum spanning tree and the planar maximally filtered graph. The first method performs a "row bootstrap" whereas the second method performs a "pair bo…
On the origin of power law tails in price fluctuations
2003
In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly -1.5, are modulated by the average market impact function, which describes the response of prices to transactions. They argue that the average market impact function follows a square root law, which gives power law tails for prices with exponent roughly -3. We demonstrate that the long-memory nature of order flow invalidates their statistical analysis of market impact, and present a more careful analysis that properly takes this into account. This makes i…
Single chain structure in thin polymer films: Corrections to Flory's and Silberberg's hypotheses
2005
Conformational properties of polymer melts confined between two hard structureless walls are investigated by Monte Carlo simulation of the bond-fluctuation model. Parallel and perpendicular components of chain extension, bond-bond correlation function and structure factor are computed and compared with recent theoretical approaches attempting to go beyond Flory's and Silberberg's hypotheses. We demonstrate that for ultrathin films where the thickness, $H$, is smaller than the excluded volume screening length (blob size), $\xi$, the chain size parallel to the walls diverges logarithmically, $R^2/2N \approx b^2 + c \log(N)$ with $c \sim 1/H$. The corresponding bond-bond correlation function d…
Fair Pairwise Learning to Rank
2020
Ranking algorithms based on Neural Networks have been a topic of recent research. Ranking is employed in everyday applications like product recommendations, search results, or even in finding good candidates for hiring. However, Neural Networks are mostly opaque tools, and it is hard to evaluate why a specific candidate, for instance, was not considered. Therefore, for neural-based ranking methods to be trustworthy, it is crucial to guarantee that the outcome is fair and that the decisions are not discriminating people according to sensitive attributes such as gender, sexual orientation, or ethnicity.In this work we present a family of fair pairwise learning to rank approaches based on Neur…
Ammonite faunas from condensed Cenomanian-Turonian sections (‘Tourtias’) in southern Belgium and northern France
2011
AbstractIn southern Belgium (Mons Basin and Tournai region) and northern France (area between Lille, Valenciennes and Maubeuge), condensed sequences have been referred to as ‘tourtias’ since the start of the nineteenth century. These levels correspond to a succession of trangressive systems tracts and generally appear as dark green, glauconitic and microconglomeratic facies. They are distributed all along the base of the more important transgressive systems tracts of the Cenomanian and basal Turonian from the Boulonnais (northwest France) to the Mons Basin (southern Belgium), through the Artois and Douaisis. Their age can now be determined more accurately by identification of their ammonite…
Classification of Heart Sounds Using Convolutional Neural Network
2020
Heart sounds play an important role in the diagnosis of cardiac conditions. Due to the low signal-to-noise ratio (SNR), it is problematic and time-consuming for experts to discriminate different kinds of heart sounds. Thus, objective classification of heart sounds is essential. In this study, we combined a conventional feature engineering method with deep learning algorithms to automatically classify normal and abnormal heart sounds. First, 497 features were extracted from eight domains. Then, we fed these features into the designed convolutional neural network (CNN), in which the fully connected layers that are usually used before the classification layer were replaced with a global averag…