Narrow Results

This work proposes and studies the concept of Functional Data Analysis transform, applying it to the performance improving of volumetric Bouligand–Minkowski fractal descriptors. The proposed transform consists essentially in changing the descriptors originally defined in the space of the calculus of fractal dimension into the space of coefficients used in the functional data representation of these descriptors. The transformed descriptors are used here in texture classification problems. The enhancement provided by the FDA transform is measured by comparing the transformed to the original descriptors in terms of the correctness rate in the classification of well known datasets.

This paper studies the relationship between monthly economic uncertainty of 20 advanced and emerging markets, and two daily covariates, i.e., exchange rate and stock index, with particular emphasis on the relationship between the variables in response to the Brexit vote. We use a functional data approach supplemented with a point of impact structure to conduct a mixed-frequency analysis. We find that incorporating the point of impact, in this case the Brexit shock, is marginally important relative to models that ignore it. We also find that the exchange rate played a more important role than the equity market in transmitting the Brexit shock to cause heightened uncertainty in the 20 countries considered. Our results have important policy implications.

The structural dependence of nonlinear optical properties associated with ADP-doped PVA/PVP polymer composites is discussed in this work. Polymer composites are fabricated using the solution casting method. X-ray diffraction (XRD) was used to perform structural analysis on these samples whose average crystallite size increases with an increase in dopant concentration. Results from UV–Vis–NIR spectra show that the samples are transparent in the IR region. The Z-scan technique was established by following the method described by Sheik-Bahae et al. The shape of the open aperture plot suggests that the samples exhibit two-photon absorption. The NLO properties such as nonlinear absorption coefficient ($\beta )$, two-photon absorption cross-section (${\sigma }_2)$ and the imaginary part of third-order nonlinear susceptibility $({\chi }^{(3)})$ were investigated at 1064 nm and these values were found to be in the order of $\sim {10}^{-7}$W/cm, $\sim {10}^{-20}$cm⁴/GW and $\sim {10}^{-14}$esu, respectively. The open aperture Z-scan method yielded optical limiting data, from which the optical limiting threshold was calculated to be in the order of $\sim {10}^{13}$W/m². Functional data analysis uses a suitable basis representation to assess the functional correlation between global and local variables.

This work presents a novel approach in order to increase the recognition power of Multiscale Fractal Dimension (MFD) techniques, when applied to image classification. The proposal uses Functional Data Analysis (FDA) with the aim of enhancing the MFD technique precision achieving a more representative descriptors vector, capable of recognizing and characterizing more precisely objects in an image. FDA is applied to signatures extracted by using the Bouligand–Minkowsky MFD technique in the generation of a descriptors vector from them. For the evaluation of the obtained improvement, an experiment using two datasets of objects was carried out. A dataset was used of characters shapes (26 characters of the Latin alphabet) carrying different levels of controlled noise and a dataset of fish images contours. A comparison with the use of the well-known methods of Fourier and wavelets descriptors was performed with the aim of verifying the performance of FDA method. The descriptor vectors were submitted to Linear Discriminant Analysis (LDA) classification method and we compared the correctness rate in the classification process among the descriptors methods. The results demonstrate that FDA overcomes the literature methods (Fourier and wavelets) in the processing of information extracted from the MFD signature. In this way, the proposed method can be considered as an interesting choice for pattern recognition and image classification using fractal analysis.

Assuming a Parametric Family of Functional Data, the problem of computing summary statistics of the same functional form is investigated. The central idea is to compile the statistics on the parameters instead of on the functions themselves. With the hypothesis of a monotonic dependence from parameters, we highlight the special features of this statistics.

In functional data analysis, linear prediction problems have been widely studied based on the functional linear regression model. However, restrictive condition is needed to ensure the existence of the coefficient function. In this paper, a general linear prediction model is considered on the framework of reproducing kernel Hilbert space, which includes both the functional linear regression model and the point impact model. We show that from the point view of prediction, this general model works as well even the coefficient function does not exist. Moreover, under mild conditions, the minimax optimal rate of convergence is established for the prediction under the integrated mean squared prediction error. In particular, the rate reduces to the existing result when the coefficient function exists.

The study of regularized learning algorithms is a very important issue and functional data analysis extends classical methods. We establish the learning rates of the least square regularized regression algorithm in reproducing kernel Hilbert space for functional data. With the iteration method, we obtain fast learning rate for functional data. Our result is a natural extension for least square regularized regression algorithm when the dimension of input data is finite.

This paper investigates the use of functional principal component analysis (FPCA) for automatic recognition of dynamic human arm gestures and robot imitation. FPCA is a statistical technique of functional data analysis that generalizes standard multivariate principal component analysis. Functional data analysis signals (e.g., gestures) are functions that are considered as observations of a random variable on a functional space. In particular, FPCA reduces the dimensionality of the input data by projecting them onto a finite-dimensional space spanned by a few prominent eigenfunctions. The main contribution of this work is the proposal of a novel technique for unsupervised clustering of training data and dynamic gesture recognition based on FPCA. FPCA has not been considered in previous studies on humanoid learning. The proposed approach has been evaluated in two experimental settings for motion capture. In the first setup single arm gestures are recognized from inertial sensors attached to the arm of the user. In the second setup the method is extended to two-arm gestures acquired from a range sensor. Recognized gestures are reproduced by a small humanoid robot. The FPCA method has also been compared to a high performance algorithm for gesture classification based on dynamic time warping (DTW). The FPCA algorithm achieves comparable results in both recognition rate and robustness to missing data, while it outperforms DTW in terms of efficiency in execution time.

Inference methods are proposed for the bivariate mean function of a continuous stochastic process with a two-dimensional domain. Nonparametric bivariate estimation is facilitated by thresholded projection estimators. Estimators adapt to the sparsity of the bivariate function. Oracle inequality results are developed to describe the adaptive inference methods. The construction of nonparametric bivariate confidence bands is presented. Implementation results show the applicability of the methods in practice.

One of the open problems in systems biology is to infer dynamic gene networks describing the underlying biological process with mathematical, statistical and computational methods. The first-order difference equation-based models such as dynamic Bayesian networks and vector autoregressive models were used to infer time-lagged relationships between genes from time-series microarray data. However, two primary problems greatly reduce the effectiveness of current approaches. The first problem is the tacit assumption that time lag is stationary. The second is the inseparability between measurement noise and process noise (unmeasured disturbances that pass through time process).

To address these problems, we propose a stochastic differential equation model for inferring continuous-time dynamic gene networks under the situation in which both of the process noise and the observation noise exist. We present a collocation-based sparse estimation for simultaneous parameter estimation and model selection in the model. The collocation-based approach requires considerably less computational effort than traditional methods in ordinary stochastic differential equation models. We also incorporate various biological knowledge easily to refine the estimation accuracy with the proposed method. The results using simulated data and real time-series expression data of human primary small airway epithelial cells demonstrate that the proposed approach outperforms competing approaches and can provide significant genes influenced by gefitinib.

Probability distributions are central tools for probabilistic modeling in data mining. In functional data analysis (FDA) they are weakly studied in the general case. In this paper we discuss a probability distribution law for functional data considered as stochastic process. We define first a new kind of stationarity linked to the Archimedean copulas, and then we build a probability distribution using jointly the Quasi-arithmetic means and the generators of Archimedean copulas. We also study some properties of this new mathematical tool.