Related papers: Analytical Identification of Design and Multidimen…
A new procedure, called DDa-procedure, is developed to solve the problem of classifying d-dimensional objects into q >= 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm…
Random field models have been widely employed to develop a predictor of an expensive function based on observations from an experiment. The traditional framework for developing a predictor with random field models can fail due to the…
Discrete Choice Experiments (DCEs) are widely used to elicit preferences for products or services by analyzing choices among alternatives described by their attributes. The quality of the insights obtained from a DCE heavily depends on the…
In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…
We present a new supervised image classification method applicable to a broad class of image deformation models. The method makes use of the previously described Radon Cumulative Distribution Transform (R-CDT) for image data, whose…
Data-driven intelligent computational design (DICD) is a research hotspot emerged under the context of fast-developing artificial intelligence. It emphasizes on utilizing deep learning algorithms to extract and represent the design features…
We aim to detect all instances of a category in an image and, for each instance, mark the pixels that belong to it. We call this task Simultaneous Detection and Segmentation (SDS). Unlike classical bounding box detection, SDS requires a…
Discovering patterns of the complex high-dimensional data is a long-standing problem. Dimension Reduction (DR) and Intrinsic Dimension Estimation (IDE) are two fundamental thematic programs that facilitate geometric understanding of the…
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…
Irrespective of the fact that Machine learning has produced groundbreaking results, it demands an enormous amount of data in order to perform so. Even though data production has been in its all-time high, almost all the data is unlabelled,…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
Repeated-measure designs allow comparisons within a group as well as between groups, and are commonly referred to as split-plot designs. While originating in agricultural experiments, they are now widely used in medical research,…
Nonlinear dimension reduction methods provide a low-dimensional representation of high-dimensional data by applying a Nonlinear transformation. However, the complexity of the transformations and data structures can create wildly different…
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in…
In this work we propose a generalized additive functional regression model for partially observed functional data. Our approach accommodates functional predictors of varying dimensions without requiring imputation of missing observations.…
In a human-robot collaborative task where a robot helps its partner by finding described objects, the depth dimension plays a critical role in successful task completion. Existing studies have mostly focused on comprehending the object…
Providing machines with the ability to recognize objects like humans has always been one of the primary goals of machine vision. The introduction of RGB-D cameras has paved the way for a significant leap forward in this direction thanks to…
Refinement based formal methods allow the modelling of systems through incremental steps via abstraction. Discovering the right levels of abstraction, formulating correct and meaningful invariants, and analysing faulty models are some of…
In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…