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Graph-based semi-supervised learning for classification endorses a nice interpretation in terms of diffusive random walks, where the regularisation factor in the original optimisation formulation plays the role of a restarting probability. Recently, a new type of biased random walks for characterising certain dynamics on networks have been defined and rely on the γ-th power of the standard Laplacian...
Multifractal analysis of cardiovascular variability series is an effective tool for the characterization of pathological states associated with congestive heart failure (CHF). Consequently, variations of heartbeat scaling properties have been associated with the dynamical balancing of nonlinear sympathetic/vagal activity. Nevertheless, whether vagal dynamics has multifractal properties yet alone is...
Among many research efforts devoted to automated art investigations, the problem of quantification of literary style remains current. Meanwhile, linguists and computer scientists have tried to sort out texts according to their types or authors. We use the recently-introduced p-leader multifractal formalism to analyze a corpus of novels written for adults and young adults, with the goal of assessing...
Scale-free dynamics commonly appear in individual components of multivariate data. Yet, while the behavior of cross-components is crucial in modeling real-world multivariate data, their examination often suggests departures from exact multivariate self-similarity (also termed fractal connectivity). The present paper introduces a multivariate Gaussian stochastic process with Hadamard (i.e., entry-wise)...
Wove paper, made on a papermaking screen or mold having a surface of smooth tightly woven wires, was the predominant paper type used for printing in the twentieth century. To aid in the study and classification of fine art prints on wove paper, the present work compares the results of five different image processing approaches for characterizing surface texture. Using a collection of popular wove...
Scale invariance has proven a crucial concept in texture modeling and analysis. Isotropic and self-similar fractional Brownian fields (2D-fBf) are often used as the natural reference process to model scale free textures. Its analysis is standardly conducted using the 2D discrete wavelet transform. Generalizations of 2D-fBf were considered independently in two respects: Anisotropy in the texture is...
Texture analysis can be embedded in the mathematical framework of multifractal (MF) analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, wavelet leaders. A statistical model for leaders was proposed permitting Bayesian estimation of MF parameters for images yielding improved estimation quality over linear regression based...
Multifractal analysis (MF) is a widely used signal processing tool that enables the study of scale invariance models. Classical MF assumes homogeneous MF properties, which cannot always be guaranteed in practice. Yet, the local estimation of MF parameters has barely been considered due to the challenging statistical nature of MF processes (non-Gaussian, intricate dependence), requiring large sample...
So far considered as noise in neuroscience, irregular arrhythmic field potential activity accounts for the majority of the signal power recorded in EEG or MEG [1,2]. This brain activity follows a power law spectrum P (f) ∼ 1/fβ in the limit of low frequencies, which is a hallmark of scale invariance. Recently, several studies [1, 3-6] have shown that the slope β (or equivalently Hurst exponent H)...
Texture analysis can be conducted within the mathematical framework of multifractal analysis (MFA) via the study of the regularity fluctuations of image amplitudes. Successfully used in various applications, however MFA remains limited to the independent analysis of single images while, in an increasing number of applications, data are multi-temporal. The present contribution addresses this limitation...
Multifractal (MF) analysis enables the theoretical study of scale invariance models and their practical assessment via wavelet leaders. Yet, the accurate estimation of MF parameters remains a challenging task. For a range of applications, notably biomedical, the performance can potentially be improved by taking advantage of the multivariate nature of data. However, this has barely been considered...
Texture analysis is an image processing task that can be conducted using the mathematical framework of multifractal analysis to study the regularity fluctuations of image intensity and the practical tools for their assessment, such as (wavelet) leaders. A recently introduced statistical model for leaders enables the Bayesian estimation of multifractal parameters. It significantly improves performance...
Texture characterization of photographic papers is likely to provide scholars with valuable information regarding artistic practices. Currently, texture assessment remains mostly based on visual and manual inspections, implying long repetitive tasks prone to inter- and even intra-observer variability. Automated texture characterization and classification procedures are thus important tasks in historical...
Multiscale analysis of human heartbeat dynamics has been proved effective in characterizeing cardiovascular control physiology in health and disease. However, estimation of multiscale properties can be affected by the interpolation procedure used to preprocess the unevenly sampled R-R intervals derived from the ECG. To this extent, in this study we propose the estimation of wavelet coefficients and...
Intrapartum fetal heart rate (FHR) constitutes a prominent source of information for the assessment of fetal reactions to stress events during delivery. Yet, early detection of fetal acidosis remains a challenging signal processing task. The originality of the present contribution are three-fold: multiscale representations and wavelet leader based multifractal analysis are used to quantify FHR variability...
Interpretation and analysis of intrapartum fetal heart rate, enabling early detection of fetal acidosis, remains a challenging signal processing task. Among the many strategies that were used to tackle this problem, scale-invariance and multifractal analysis stand out. Recently, a new and promising variant of multifractal analysis, based on p-leaders, has been proposed. In this contribution, we use...
Texture analysis is central in many image processing problems. It can be conducted by studying the local regularity fluctuations of image amplitudes, and multifractal analysis provides a theoretical and practical framework for such a characterization. Yet, due to the non Gaussian nature and intricate dependence structure of multifractal models, accurate parameter estimation is challenging: standard...
We present a new anomaly detector for data traffic, ‘SMS’, based on combining random projections (sketches) with multiscale analysis, which has low computational complexity. The sketches allow ‘normal’ traffic to be automatically and robustly extracted, and anomalies detected, without the need for training data. The multiscale analysis extracts statistical descriptors, using wavelet leader tools developed...
Multifractal analysis is a powerful tool used in signal processing. Multifractal models are essentially characterized by two parameters, the multifractality parameter c2 and the integral scale A (the time scale beyond which multifractal properties vanish). Yet, most applications concentrate on estimating c2 while the estimation of A is in general overlooked, despite the fact that A potentially conveys...
In transport networks, Origin-Destination matrices (ODM) are classically estimated from road traffic counts whereas recent technologies grant also access to sample car trajectories. One example is the deployment in cities of Bluetooth scanners that measure the trajectories of Bluetooth equipped cars. Exploiting such sample trajectory information, the classical ODM estimation problem is here extended...
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