Compactly supported radial basis functions: How and why?

Compactly supported basis functions are widely required and used in many applications. We explain why radial basis functions are preferred to multi-variate polynomials for scattered data approximation in high-dimensional space and give a brief description on how to construct the most commonly used compactly supported radial basis functions - the Wendland functions and the new found missing Wendland functions. One can construct a compactly supported radial basis function with required smoothness according to the procedure described here without sophisticated mathematics. Very short programs and extended tables for compactly supported radial basis functions are supplied

Application of Fredholm integral equations inverse theory to the radial basis function approximation problem

This paper reveals and examines the relationship between the solution and stability of Fredholm integral equations and radial basis function approximation or interpolation. The underlying system (kernel) matrices are shown to have a smoothing property which is dependent on the choice of kernel. Instead of using the condition number to describe the ill-conditioning, hence only looking at the largest and smallest singular values of the matrix, techniques from inverse theory, particularly the Picard condition, show that it is understanding the exponential decay of the singular values which is critical for interpreting and mitigating instability. Results on the spectra of certain classes of kernel matrices are reviewed, verifying the exponential decay of the singular values. Numerical results illustrating the application of integral equation inverse theory are also provided and demonstrate that interpolation weights may be regarded as samplings of a weighted solution of an integral equation. This is then relevant for mapping from one set of radial basis function centers to another set. Techniques for the solution of integral equations can be further exploited in future studies to find stable solutions and to reduce the impact of errors in the data

Information Splitting for Big Data Analytics

Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the \emph{observed information}--the negative Hessian matrix or the second derivative of the log-likelihood---to obtain an accurate maximum likelihood estimator according to the Newton method. When one uses the \emph{Fisher information}, the expect value of the observed information, a simpler algorithm than the Newton method is obtained as the Fisher scoring algorithm. With the advance in high-throughput technologies in the biological sciences, recommendation systems and social networks, the sizes of data sets---and the corresponding statistical models---have suddenly increased by several orders of magnitude. Neither the observed information nor the Fisher information is easy to obtained for these big data sets. This paper introduces an information splitting technique to simplify the computation. After splitting the mean of the observed information and the Fisher information, an simpler approximate Hessian matrix for the log-likelihood can be obtained. This approximated Hessian matrix can significantly reduce computations, and makes the linear mixed model applicable for big data sets. Such a spitting and simpler formulas heavily depends on matrix algebra transforms, and applicable to large scale breeding model, genetics wide association analysis.Comment: arXiv admin note: text overlap with arXiv:1605.0764

Comorbidity between neurodevelopmental disorders and childhood-onset type 1 diabetes

Childhood-onset type 1 diabetes and neurodevelopmental disorders, including attention-deficit/hyperactivity disorder (ADHD), autism spectrum disorder, and intellectual disability, globally represent substantial health challenges. Each condition places a substantial challenge on the individuals, their families, and healthcare systems. The comorbidity between these two types of disorders has been a research focus, with findings suggesting a higher prevalence of neurodevelopmental disorders among individuals with childhood-onset type 1 diabetes. However, the underlying mechanism of this comorbidity remains largely unknown, and the potential alteration in the health and socio-economic outcomes due to this comorbidity remains unexplored. This thesis aimed to elucidate the potential mechanisms behind the comorbidity between childhood-onset type 1 diabetes and neurodevelopmental disorders and explore its impact on health and education outcomes, with the goal of improving early detection, prevention, and management strategies to enhance the quality of life for the affected children and adolescents. In Study I, we examined the impact of childhood-onset type 1 diabetes and the role of glycemic control on the risk of subsequent neurodevelopmental disorders. We found that individuals with childhood-onset type 1 diabetes had a higher risk of developing neurodevelopmental disorders than the general population. Notably, this risk was highest among those with less optimal glycemic control. These findings provided insight into the role of glycemic control, a crucial diabetes-related factor, in the occurrence of comorbidity between childhood-onset type 1 diabetes and neurodevelopmental disorders. In Study II, we investigated the potential contribution from shared familial liability to the comorbidity between childhood-onset type 1 diabetes and neurodevelopmental disorders. We found that the elevated risk of neurodevelopmental disorders did not only appear in individuals with childhood-onset type 1 diabetes but also in their full-siblings. The general family co-aggregation pattern and the results of the quantitative genetic modeling, however, did not conclusively show that familial liability contributes to the comorbidity. This ambiguity underscores the need for subsequent research to further elucidate the underlying causes of this comorbidity. In Study III, we explored the impacts of neurodevelopmental disorders on long-term glycemic control and the risk of diabetic complications in individuals with childhoodonset type 1 diabetes. We found that neurodevelopmental disorders, particularly ADHD and intellectual disability, were associated with increased risk of poor glycemic control and diabetic complications such as nephropathy and retinopathy. These observations highlight that taking neurodevelopmental aspects into account can be crucial when designing interventions and follow-ups for individuals with childhood-onset type 1 diabetes. In Study IV, evaluated the interplay between childhood-onset type 1 diabetes, ADHD, and academic outcomes, spanning from compulsory education to university levels. We found that children and adolescents with both type 1 diabetes and ADHD were significantly less likely to achieve educational milestones, crossing different education levels, and had less favorable compulsory school performances compared to their peers without these conditions. These results underline the importance of providing targeted support to minimize the educational gap between the affected children and adolescents and their peers

Exploiting Image-trained CNN Architectures for Unconstrained Video Classification

We conduct an in-depth exploration of different strategies for doing event detection in videos using convolutional neural networks (CNNs) trained for image classification. We study different ways of performing spatial and temporal pooling, feature normalization, choice of CNN layers as well as choice of classifiers. Making judicious choices along these dimensions led to a very significant increase in performance over more naive approaches that have been used till now. We evaluate our approach on the challenging TRECVID MED'14 dataset with two popular CNN architectures pretrained on ImageNet. On this MED'14 dataset, our methods, based entirely on image-trained CNN features, can outperform several state-of-the-art non-CNN models. Our proposed late fusion of CNN- and motion-based features can further increase the mean average precision (mAP) on MED'14 from 34.95% to 38.74%. The fusion approach achieves the state-of-the-art classification performance on the challenging UCF-101 dataset

Device-free Localization using Received Signal Strength Measurements in Radio Frequency Network

Device-free localization (DFL) based on the received signal strength (RSS) measurements of radio frequency (RF)links is the method using RSS variation due to the presence of the target to localize the target without attaching any device. The majority of DFL methods utilize the fact the link will experience great attenuation when obstructed. Thus that localization accuracy depends on the model which describes the relationship between RSS loss caused by obstruction and the position of the target. The existing models is too rough to explain some phenomenon observed in the experiment measurements. In this paper, we propose a new model based on diffraction theory in which the target is modeled as a cylinder instead of a point mass. The proposed model can will greatly fits the experiment measurements and well explain the cases like link crossing and walking along the link line. Because the measurement model is nonlinear, particle filtering tracing is used to recursively give the approximate Bayesian estimation of the position. The posterior Cramer-Rao lower bound (PCRLB) of proposed tracking method is also derived. The results of field experiments with 8 radio sensors and a monitored area of 3.5m 3.5m show that the tracking error of proposed model is improved by at least 36 percent in the single target case and 25 percent in the two targets case compared to other models.Comment: This paper has been withdrawn by the author due to some mistake